**Preface to "Ion-exchange in Glasses and Crystals: from Theory to Applications"**

Ion-exchange (IEx) is a kind of diffusion process where the species in contact are charged particles, such as ions. In such a case, the local electric field generated by the ions'movement imposes some restrictions; thus, only coupled diffusion, namely, the interexchange of two or more ions, is permitted. The IEx process is a natural event, which occurs in soil, minerals, and biological systems. The origins of soil (and IEx) chemistry were in the observations of a few scientists in the early 1800s (among them, the Florentine Giuseppe Gazzeri [1]) and in the detailed studies of the Englishmen H.S. Thompson, in 1850 [2], and J.T. Way, in 1852 [3]. Way, in particular, performed multiple experiments and found that the uptake of K, Ca, and Mg by soils was due to the presence of complex silicates performing an ion-exchange function. The diffusion of Na<sup>+</sup> ions in glass was first studied in 1884 by E. Warburg [4]. The first practical industrial application of the IEx process occurred at the beginning of 1900, and was related to water treatment. It followed up on the studies of two groups of German chemists, namely, F. Harm and A. Rumpler [5] and R. Gans [6,7], who developed ¨ synthetic sodium-aluminosilicate exchanger materials. Since then, IEx has become a fundamental process in many applications involving the treatment and purification of water and, more generally, in catalysis, chromatography, and the food and pharmaceutical industries.

A different area where IEx has been utilised for many centuries, even well before the associated chemistry was understood, concerns glassy and ceramic materials. Luster ceramic pottery from Mesopotamia in the 9th century AD and stained glass windows in Gothic churches created in the 14th and 15th centuries in Europe are wonderful examples of ancient artworks produced through an IEx process [8]. Luster decorations, widely used in Medieval and Renaissance pottery in Mediterranean countries, substantially consist of a metal–glass nanocomposite (metal nanoparticles embodied in a silica glassy matrix). This is obtained from the reaction of the pottery glaze with a paste constituting a mixture of ingredients (e.g., copper and/or silver salts and oxides, vinegar, ochre, and clay) painted on its surface. Heating at a temperature of around 500–600 °C in a reducing atmosphere induces an ion exchange process between metals in the paste and alkali ions in the glaze; the Cu<sup>+</sup> and/or Ag<sup>+</sup> ions are then reduced to metal nanoparticles, aggregate, and remain trapped within the first layer of the glaze, producing brilliant reflections of different colors and iridescence.

A similar process has been used since the early 1300s to create a yellow color on clear window glass. The technique, known as silver stain or yellow stain, involves painting silver compounds (e.g., silver oxide or nitrate, sulphate, and chloride) dispersed in a clay medium onto the glass and then firing it in a kiln. During the heating, just above the glass transition temperature, the silver ions are exchanged with the alkali ions present in the glass (mostly Na<sup>+</sup> or K<sup>+</sup> ). Then, due to the presence of impurities in the glass, silver ions reduce to metallic silver nanoparticles, and the resulting color depends on the size, shape and concentration of the nanoparticles. One of the first documents describing this yellow stain dates back to around 1395–1396, when the glass painter Antonio da Pisa wrote a brief treatise on the various steps of the process of making a painted window [9].

IEx in glass, however, found large-scale industrial applications only at the beginning of 20th century, after the detailed studies of G. Schultze, who was the first, in 1913, to study the process using silver nitrate salt (AgNO3) as an ion source and to outline the induced modifications of the surface of the glass [10]. However, it took almost 50 years more to realise that such changes could be exploited to make the glass more robust: the substitution of small ions such as Li<sup>+</sup> or Na<sup>+</sup> in an alkali-containing glass with larger ions, such as K<sup>+</sup> from a molten KNO<sup>3</sup> bath, induces bi-axial residual compressive stress in the surface layers, which, in turn, strengthens the glassware [11]. K–Na exchange, similarly to Ag–Na exchange, also induces an increase in the refractive index in the diffused layer.

The 1960s and 1970s saw an extraordinary breakthrough in physics and technology, with the invention of laser and the development of low-loss optical fibers, making the design and implementation of ultra-wide-band communication systems feasible. Optical miniaturised components became necessary for the generation, modulation, coupling, switching and detection of optical signals: the article by S.E. Miller, in 1969 [12], was published at the time of pioneering research on planar optical waveguides and the starting point of a new R&D area, namely, integrated optics [13]. Glass has proven to be an excellent material for integrated optical circuits, thanks to its robustness, low propagation losses and low cost; IEx provided a relatively simple and low-cost technology for the fabrication of circuits. After early studies by T. Izawa in Japan [14] and T.G. Giallorenzi in the United States [15], it became clear that ion exchange in glass offered effective solutions to many fabrication problems.

At almost the same time, in 1965, A.A. Ballman at Bell Labs [16] and S.A. Fedulov and collaborators in Russia [17] independently reported the successful growth by the Czochralski technique of large and homogeneous single crystals of lithium niobate and lithium tantalate. These crystals, together with potassium titanyl phosphate (KTP), have acquired great importance in optoelectronics due to their excellent optical properties and their large piezoelectric, electro-optic and nonlinear-optical effects. IEx has proven to be very effective in these crystals as well, for the fabrication of integrated optical elements and devices (e.g., modulators, second-harmonic generators, ring resonators, interferometers, lasers, etc.). The exchangeable ion in these crystals is Li<sup>+</sup> , and the most efficient process is an exchange with H<sup>+</sup> (proton exchange), even if Ag/Li exchange in lithium niobate is possible [18].

Due to the relevance of ion-exchange technology for the development of advanced integrated optical components and devices in glasses and crystals, we considered it worthwhile to compile a Special Issue of *Applied Sciences* on this topic. The present volume collects articles published in 2021 [19]. Four papers are reviews and offer a broad overview of the field of IEx in glass, seen from different points of view. Even if ion-exchanged glass waveguides have been already studied for forty years, recently, some advances have been made in the theoretical modelling of the process. Prieto Blanco and Montero Orille [20] present equations that describe the evolution of the cation concentration rewritten in a more rigorous manner. Along with these equations, the boundary conditions for the usual IEx from molten salts, silver and copper films and metallic cathodes were established accordingly. Moreover, the modelling of some IEx processes that have attracted a great deal of attention in recent years, including glass poling, the electro-diffusion of multivalent metals and the formation/dissolution of silver nanoparticles, has been addressed.

The second review article, by Broquin and Honkanen [21], emphasises major breakthroughs in the field of passive and active devices for telecommunication applications. The section dedicated to sensors underlines the evolution of ion-exchange technology, which is developing from quite simple, although extremely performant functions, to more complex integrated optical microsystems.

Berneschi et al. [22] aimed to clearly show how glass and ion-exchange are paired; far from being an obsolete material/technology platform, this still plays a key role in various technological fields with interesting applications and industrial developments that also have repercussions at the level of everyday life. As an example, they underline the role that IEx, together with glass material engineering, can play in two areas: (a) the optimisation of substrates for the development of high-performance surface-enhanced Raman scattering (SERS) devices; and (b) the creation of increasingly high-performing flexible substrates towards the achievement of all-glass flexible photonics as a valid alternative to those developed so far with polymeric materials. The fourth review article, by Righini and Linares [23], presents an introduction to some fundamental aspects ˜ of integrated optical waveguides and devices, such as directional couplers, waveguide gratings, integrated optical amplifiers and lasers, all fabricated by IEx in glass. Then, some promising research activities on IEx glass-integrated photonic devices, and, in particular, quantum devices (quantum circuits), are analysed. According to the increasing interest for passive and/or reconfigurable devices for quantum cryptography or even for specific quantum processing tasks, the implementation of an active integrated quantum state generator device for quantum cryptography and passive devices with an IEx–glass platform is described, such as an integrated quantum projector.

Following these four review papers, the reader may find three original articles. The first, by Montero-Orille et al. [24], proposes a simple polygonal model to describe the phase profile of ion-exchanged gratings. This model enables the design of these gratings, and could also be useful to design more complex diffractive elements. Several ion-exchanged gratings were fabricated to validate the model and to characterise the processes involved in their fabrication; to show the practical utility of this model, the design and fabrication of a grating that removes the zero order and of a three-way splitter are reported, and their performance is analysed. In the study by Nikonorov et al. [25], the influence of small additives on the spectral and optical properties of Na<sup>+</sup>–Ag<sup>+</sup> ion-exchanged silicate glass is presented. Polyvalent ions, e.g., cerium and antimony, are shown to reduce silver ions to an atomic state and promote the growth of photoluminescent silver molecular clusters and plasmonic silver nanoparticles. Na<sup>+</sup>–Ag<sup>+</sup> ion-exchanged and heat-treated glasses doped with halogen ions, such as chlorine or bromine, exhibit the formation of photo- and thermochromic AgCl or AgBr nanocrystals. The presented results highlight the vital role of small additives to control the properties of silver nanostructures in Na<sup>+</sup>–Ag<sup>+</sup> ion-exchanged glasses. Possible applications of Na<sup>+</sup>–Ag<sup>+</sup> IEx glass ceramics include, but are not limited to, biochemical sensors based on SERS phenomena, temperature and overheating sensors, white light-emitting diodes, and spectral converters. Finally, Kip et al. [26] report an investigation of the ytterbium diffusion characteristics in lithium niobate. Ytterbium-doped substrates were prepared by the in-diffusion of thin metallic layers coated onto xand z-cut congruent substrates at different temperatures. The ytterbium profiles were investigated in detail by means of secondary neutral mass spectroscopy, optical microscopy, and optical spectroscopy. Diffusion from an infinite source was used to determine the solubility limit of ytterbium in lithium niobate as a function of temperature. The derived diffusion parameters are of importance for the development of active waveguide devices in ytterbium-doped lithium niobate.

Overall, this volume represents an updated overview of several areas in the field of ion-exchange in glasses and crystals for integrated optics applications. It certainly is not exhaustive, given the high number of papers published on this topic in the forty-year history of integrated optics, but the reader may find sufficient information, covering different topics, such as numerical modelling and the fabrication of ion-exchanged passive waveguides, the design and fabrication of passive and active components and devices, and prospects of applications in optical communications, optical sensing, and quantum photonics. For these reasons, this book may be useful for a broad audience, from MSc and PhD students to early-career researchers and teachers; we hope that it could trigger newcomers'interest and stimulate research to overcome present limitations. A large number of references integrate the physico-chemical descriptions.

All authors are highly acknowledged for contributing to the realisation of this Special Issue; the support from the *Applied Sciences* editorial staff has been greatly appreciated.

#### **References**

[1] Gazzeri, G. Compendio d'un trattato elementare di chimica. 3rd ed., Stamperia Piatti, Firenze, Italy, 1828.

[2] Thompson, H. S. On the absorbent power of soils. J. Royal Agricultural Society England 1850, 11, 68-74.

[3] Way, J.T. On the Power of Soils to Absorb Manure. J. Royal Agricultural Society England 1852,13, 123-143.

[4] Warburg, E. Ueber die Electrolyse des festen Glases. Ann. Physik 1884, 21, 622-646.

[5] Harm, F. and Rumpler, V. Internationaler Kongress fur Angewandte Chemie, Berlin. 2.-8. Juni ¨ 1903 (Deutscher Verlag, Berlin, 1904).

[6] Gans, R. Zeolites and similar compounds: Their construction and significance for technology and agriculture. Jahrb. Preuss. Geol. Landesanstalt 1905, 26, 179.

[7] Gans, R. Alumino-silicate or artificial zeolite, US. Patent No. 914,405; patented March 9, 1909.

[8] Mazzoldi, P.; Carturan, S.; Quaranta, A.; Sada, C.; Sglavo, V.M. Ion-exchange process: History, evolution and applications. Riv. Nuovo Cim. 2013, 36, 397–460.

[9] Lautie, C.; Sandron, D. Antoine de Pise. L'art du vitrail vers 1400. Editions du Comit ´ e des ´ Travaux Historiques et Scientifiques, Paris, 2008.

[10] Schulze, G. Versuche uber die diffusion von silber in glas. Ann. Physik 1913, 345, 335–367. ¨

[11] Kistler, S.S. Stresses in glass produced by nonuniform exchange of monovalent Ions. J. Am. Ceram. Soc. 1962, 45, 59–68.

[12] Miller, S.E. Integrated optics: an introduction. Bell Syst. Tech. J. 1969,

[13] Righini, G.C.; Ferrari, M., Eds., Integrated Optics, The IET, London 2020, 2 volumes.

[14] Izawa, T.; Nakagome, H. Optical waveguide formed by electrically induced migration of ions in glass plates. Appl. Phys. Lett. 1972, 21, 584-586.

[15] Giallorenzi, T.G.; West, E.J.; Kirk, R.; Ginther, R.; Andrews, R.A. Optical Waveguides Formed by Thermal Migration of Ions in Glass. Appl. Opt. 1973,12, 1240-1245.

[16] Ballman AA. Growth of piezoelectric and ferroelectric materials by the CzochraIski technique. J. Am. Cer. Soc. 1965, 48,112-113.

[17] Fedulov, S.A.; Shapiro, Z.I.; Ladyzhinskii, P.B. The growth of crystals of LiNbO3, LiTaO3 and NaNbO3 by the Czochralski method. Sov Phys Crystallography 1965,10, 218.

[18] Korkishko, Yu.N. and Fedorov, V.A. Ion exchange in single crystals for integrated optics and optoelectronics. Cambridge Intl. Science Pub., Cambridge, UK, 1999.

[19] https://www.mdpi.com/journal/applsci/special issues/Ion exchange Glasses

[20] Prieto-Blanco, X.; Montero-Orille, C. Theoretical Modelling of Ion Exchange Processes in Glass: Advances and Challenges. Appl. Sci. 2021, 11, 5070. https://doi.org/10.3390/app11115070

[21] Broquin, J.-E. and Honkanen, S. Integrated Photonics on Glass: A Review of the Ion-Exchange Technology Achievements. Appl. Sci. 2021, 11, 4472. https://doi.org/10.3390/app11104472

[22] Berneschi, S.; Righini, G.C.; Pelli, S. Towards a Glass NewWorld: The Role of Ion-Exchange in Modern Technology. Appl. Sci. 2021, 11, 4610. https://doi.org/10.3390/app11104610

[23] Righini, G.C.; Linares, J. Active and Quantum Integrated Photonic Elements by Ion ˜ Exchange in Glass. Appl. Sci. 2021, 11, 5222. https://doi.org/10.3390/app11115222

[24] Montero-Orille, C.; Prieto-Blanco, X.; Gonzalez-N ´ u´nez, H.; Li ˜ nares, J. A Polygonal ˜ Model to Design and Fabricate Ion-Exchanged Diffraction Gratings. Appl. Sci. 2021, 11, 1500. https://doi.org/10.3390/app11041500

[25] Sgibnev , Y.; Nikonorov, N.; Ignatiev, A. Governing Functionality of Silver Ion-Exchanged Photo-Thermo-Refractive Glass Matrix by Small Additives. Appl. Sci. 2021, 11, 3891. https://doi.org/10.3390/app11093891

[26] Ruter, C.E.; Bruske, D.; Suntsov, S.; Kip, D. Investigation of Ytterbium Incorporation in Lithium Niobate for Active Waveguide Devices. Appl. Sci. 2020, 10, 2189. https://doi.org/10.3390/app10062189

> **Jes ´us Li ˜nares Beiras, Giancarlo C. Righini** *Editors*

## *Review* **Theoretical Modelling of Ion Exchange Processes in Glass: Advances and Challenges**

**Xesús Prieto-Blanco \* and Carlos Montero-Orille**

Quantum Materials and Photonics Research Group, Optics Area, Department of Applied Physics, Faculty of Physics/Faculty of Optics and Optometry, Campus Vida s/n, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Galicia, Spain; carlos.montero@usc.es **\*** Correspondence: xesus.prieto.blanco@usc.es

**Abstract:** In the last few years, some advances have been made in the theoretical modelling of ion exchange processes in glass. On the one hand, the equations that describe the evolution of the cation concentration were rewritten in a more rigorous manner. This was made into two theoretical frameworks. In the first one, the self-diffusion coefficients were assumed to be constant, whereas, in the second one, a more realistic cation behaviour was considered by taking into account the so-called mixed ion effect. Along with these equations, the boundary conditions for the usual ion exchange processes from molten salts, silver and copper films and metallic cathodes were accordingly established. On the other hand, the modelling of some ion exchange processes that have attracted a great deal of attention in recent years, including glass poling, electro-diffusion of multivalent metals and the formation/dissolution of silver nanoparticles, has been addressed. In such processes, the usual approximations that are made in ion exchange modelling are not always valid. An overview of the progress made and the remaining challenges in the modelling of these unique processes is provided at the end of this review.

**Keywords:** ion exchange in glass; ion diffusion; glass waveguides; glass strengthening; glass poling; metal nanoparticles

#### **1. Introduction**

Ion exchange in glass has been used for centuries for the purposes of decoration and colouring. Glass lustre on ceramics with metallic nanoparticles from ion exchange has been known from the early Islamic culture during the 10th Century [1]. However, the scientific and industrial application of this technique dates back 60 years ago when potassium ion exchange (IE) was first applied in the chemical surface tempering of glasses [2,3]. Next, with the introduction of the concept of integrated optics in 1969 [4], ion exchange in glass was proposed as a waveguide fabrication process. Just a few years after this proposal, Izawa and Nakagome published the first work on ion exchange waveguides [5]. This kind of waveguide presents several advantages: fibre compatibility, low propagation losses and low cost. Moreover, ion exchange can be combined with other techniques, such as sol–gel, for the fabrication of passive and active (rare-earth-doped) integrated optical devices [6]. Currently, the main applications of ion exchange are in glass strengthening [7–11] and in the fabrication of photonic components for both guided-wave [12–18] and bulk optics [19–21].

In an IE process, cations (mostly Na+) close to the glass surface are replaced with other monovalent cations such as K+, Li+, Rb+, Cs+, Tl<sup>+</sup> or Ag<sup>+</sup> [22]. Molten salts of such cations are common sources of dopants, although a metallic film deposited on the glass surface can be also a source of cations. The exchange takes place by a purely thermal diffusion process or it can be assisted by an electric field. The new cations can change the electrical permittivity, the stress and even the absorption of the glass, these being changes proportional to the dopant cation concentration. By selective masking of the glass surface, ion exchange can be locally prevented or allowed, giving rise to custom-made elements

**Citation:** Prieto-Blanco, X.; Montero-Orille, C. Theoretical Modelling of Ion Exchange Processes in Glass: Advances and Challenges. *Appl. Sci.* **2021**, *11*, 5070. https:// doi.org/10.3390/app11115070

Academic Editor: Renato Torre

Received: 20 April 2021 Accepted: 24 May 2021 Published: 30 May 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

for specific purposes. The theoretical modelling of the IE processes ran parallel to the development of the technologies. This modelling was fundamental to the design and fabrication of most elements. For instance, in the field of integrated optics, some subjects as fibre compatibility or coupling losses depend strongly on the permittivity distribution and, hence, on the cation concentration. Therefore, the prediction of the cation concentration is of great importance to design devices based on IE technologies.

Here, we present a review of the theoretical modelling of IE processes in glass made up to now, as well as the last advances in this matter that have been reported in recent years. Ion exchange within a glass network is governed by diffusion and drift processes as a response to a concentration gradient and an electric field, respectively [23,24]. This gives rise to a concentration profile of the exchanging ions, which depends on the processing conditions of the substrate: temperature, exchange time, applied electric field, etc. The Nernst–Planck drift-diffusion equation describes this process. It establishes the proportionality among the flux density of each ion species and both the electric field and the concentration gradient. On the other hand, Poisson's equation and continuity equations for each ion must be fulfilled. This gives rise, in general, to three second-order coupled partial differential equations whose solution provides the evolution of both the cation concentrations and the electric potential. In the derivation of these equations, the charge neutrality approximation is usually assumed, which allows for some important simplifications without a relevant loss of accuracy in the most common cases [25,26]. All of these subjects are addressed in Section 2, where we present the basic model of ion exchange. This model assumes that the self-diffusion coefficients of the exchanged cations are constant for a given temperature. However, experimental measurements [27] showed that these coefficients depend on the cation concentrations. Therefore, this basic model was generalized to non-ideal cation behaviour and concentration-dependent self-diffusion coefficients by considering the so-called mixed ion effect [28,29]. Later, both models were rigorously generalised, and in the derivation of the equations, Faraday's law was considered instead of Ohm's law [30]. This leads to a non-standard Laplace equation for an effective electric potential. Accordingly, the boundary conditions for the most common IE processes were established. These conditions, together with the aforementioned partial differential equations, complete the theoretical modelling of the IE problem. On the other hand, some IE processes have attracted a great deal of attention in the last few years due to their remarkable applications. Among these, we must highlight: glass poling, electro-diffusion of multivalent metals and the formation/dissolution of silver nanoparticles. Their modelling has only been partially done so far [31–33], because the usual theoretical assumptions (mainly charge neutrality approximation and ideal cation behaviour) are not always valid in such processes. In Section 4, we give an overview of the progress made and the challenges still to be faced on this matter.

#### **2. Basic Model**

The simplest problem of ion exchange arise when two species of monovalent cations (A and B) exchange with each other in the same glass region at a given temperature *T*. Let us consider an infinite one-dimensional medium (*x* being the spatial coordinate) with a homogeneous concentration *C*<sup>0</sup> of fixed anions (typically -Si-O<sup>−</sup> radicals) and nonhomogeneous and variable cation concentrations *CA*(*x*, *t*) and *CB*(*x*, *t*), *t* being the time. Moreover, we considered that each cation is initially near its anion, that is they are paired, so *CA*(*x*, 0) + *CB*(*x*, 0)=*C*0. Consequently, space charge density is initially cancelled:

$$
\mathbb{C}\_0 = \mathbb{C}\_A + \mathbb{C}\_{B'} \tag{1}
$$

that is local charge neutrality is met. Our goal was to obtain the evolution of cation concentrations given these initial conditions.

#### *2.1. Nernst–Planck and Poisson Equations*

The initial non-homogeneity of cation concentrations, *CA*(*x*, *t*) and *CB*(*x*, *t*), and their random motion make them diffuse along the glass until their concentrations are homogeneous. This diffusion process is described by Fick's law:

$$\mathbf{J}\_{i}^{dif} = -D\_{i} \nabla \mathbf{C}\_{i} \qquad \mathbf{i} = A\_{i} \, \mathbf{B} \ \mathbf{j} \tag{2}$$

where *J<sup>i</sup>* is the flux density and *D<sup>i</sup>* the diffusion coefficient of each cation. However, the two interdiffusing cations have usually different diffusion coefficients and, therefore, different mobilities, which produce charge imbalances. These imbalances generate a strong internal electric field (*E*), which tends to balance the charges and restore charge neutrality (Equation (1)). Therefore, Fick's equation is no longer valid, and a drift term must be added on its right-hand side to take into account the effect of this electric field on the cation motion. This leads to the Nernst–Planck equation [34]:

$$J\_i = -D\_i \nabla \mathbb{C}\_i + D\_i \mathbb{C}\_i \frac{eE}{kT} \qquad i = A, B \ ; \tag{3}$$

where *e* is the proton charge, *T* the absolute temperature and *k* Boltzmann's constant. Note that some authors included, in the drift term of this equation, the Haven ratio. However, as we will see below, this parameter should not be incorporated into the model as a general rule. The occurrence of the above-mentioned electric field can be seen from a quantitative point of view by calculating the total flux density:

$$J\_0 = J\_A + J\_B = -D\_A \nabla \mathcal{C}\_A - D\_B \nabla \mathcal{C}\_B + (D\_A \mathcal{C}\_A + D\_B \mathcal{C}\_B) \frac{eE}{kT} \tag{4}$$

which depends on the electric field through mobility *u*:

$$
\mu = \frac{e}{k T \mathbb{C}\_0} (D\_A \mathbb{C}\_A + D\_B \mathbb{C}\_B). \tag{5}
$$

However, *J*<sup>0</sup> cancels in the current problem, that is,

$$J\_0 = \mathbf{0},\tag{6}$$

because there is no external field applied that generates a net current. This means that the imbalance of the diffusion of the two cations (*DA*∇*C<sup>A</sup>* + *DB*∇*CB*) is compensated by the internal field through the drift term *uC*0*E*. Note that Equation (4) is a generalization of Ohm's law. On the other hand, as long as there is no creation or destruction of cations from/to a metallic state, the continuity equation must be fulfilled:

$$\frac{\partial \mathcal{C}\_i}{\partial t} + \nabla f\_i = 0 \qquad i = A\_\prime B. \tag{7}$$

Now, by combining this equation and Equation (3) for, for instance, *i*=A and substituting, in the resulting equation, the electric field from Equations (4) and (6), we obtained the differential equation that gives the concentration evolution [23] of cation A:

$$\frac{\partial \mathcal{c}\_A}{\partial t} = \nabla (\mathcal{D}(\mathcal{c}\_A) \nabla \mathcal{c}\_A)\_\prime \tag{8}$$

where the charge neutrality (Equation (1)) was applied and a normalized concentration (*c<sup>A</sup>* =*CA*/*C*0) was used, and we defined the following interdiffusion coefficient:

$$
\tilde{D}(\mathbf{c}\_A) = \frac{D\_A}{1 - \mathfrak{ac}\_A},\tag{9}
$$

where *<sup>α</sup>*=<sup>1</sup> <sup>−</sup> *<sup>D</sup>A*/*DB*. The dependence of *<sup>u</sup>* and *<sup>D</sup>*¯ on *<sup>c</sup><sup>K</sup>* predicted by this basic model, for K+/Na<sup>+</sup> IE, can be seen in Figure 1a.

**Figure 1.** Self-diffusion and interdiffusion coefficients, as well as mobility, calculated from experimental data obtained by radiative tracers [27], as a function of the normalized concentration for K+/Na<sup>+</sup> IE. The Haven ratio was ignored. (**a**) Basic model—Equations (5) and (9)—which assumes that the self-diffusion coefficients remain constant with the cation mole fraction. (**b**) The same functions taking into account the MIE. Quadratic polynomials in *c*<sup>K</sup> were fitted to the logarithms of the experimental self-diffusion coefficients and then used to calculate the rest of the functions through the definitions (35) and (34). Note the difference between *D*¯ and *D*mob, which are the expected interdiffusion coefficients when the interaction among cations or the ideal mixture is assumed, respectively.

A more complex problem is the IE assisted by an external electric field. In such a case, Equation (6) is not met. Therefore, additional equations are necessary to calculate the total flux density (*J*<sup>0</sup> ) or, alternatively, *E*, which now includes the external field. As for *E*, it must fulfil Poisson's equation and Faraday's law of induction:

$$\nabla(\varepsilon \mathbf{E}) = \varepsilon(\mathbf{C}\_A + \mathbf{C}\_B - \mathbf{C}\_0) \tag{10}$$

$$
\nabla \times \mathbf{E} + \frac{\partial \mathbf{B}}{\partial t} = \mathbf{0} \,, \tag{11}
$$

where *e* is the glass electrical permittivity and *B* is the magnetic field, which will be assumed as time independent since the total current changes very slowly. On the other hand, we also assumed the charge neutrality approximation (Equation (1)). This cannot be done in general, due to the existence of the aforementioned external field; however, in most cases, this is a very good approximation (see the next subsection). Doing this, the addition of continuity Equation (7) leads to:

$$
\nabla f\_0 = 0.\tag{12}
$$

Now, by finding the electric field in Equation (4):

$$\frac{eE}{kT} = \frac{I\_0}{D\_A \mathcal{C}\_A + D\_B \mathcal{C}\_B} + \frac{D\_A \nabla \mathcal{C}\_A + D\_B \nabla \mathcal{C}\_B}{D\_A \mathcal{C}\_A + D\_B \mathcal{C}\_B} \, , \tag{13}$$

taking into account Equation (12) and doing the same steps as before, the following electrodiffusion equation is obtained:

$$\frac{\partial c\_A}{\partial t} + \frac{J\_0}{\mathbb{C}\_0} \frac{1 - a}{(1 - a c\_A)^2} \nabla c\_A = \nabla (\bar{D}(c\_A) \nabla c\_A)\_{\prime} \tag{14}$$

which is an extension of Equation (8). On the other hand, Equation (13) can be inserted into (11), leading to:

$$\nabla \times \left(\frac{J\_0}{D\_B \mathbb{C}\_0 (1 - \alpha \mathbf{c}\_A)}\right) = \mathbf{0},\tag{15}$$

where we used Equation (9). This equation, Equation (12), and the boundary conditions, which will be presented later, determinate the flux density *J*<sup>0</sup> . From this flux density, Equation (14) will provide the evolution of the concentration of cations. Finally, once *J*<sup>0</sup> and *c<sup>A</sup>* are known, the charge neutrality approximation can be checked. This will be analysed in the following subsection.

Alternatively, the last four equations can be expressed in terms of a scalar function. Indeed, an irrotational vector field is the gradient of a potential function *φ*, so:

$$\frac{J\_0}{D\_B \mathcal{C}\_0 (1 - \mathcal{a} \mathcal{c}\_A)} = -\frac{e}{kT} \nabla \phi\_\prime \tag{16}$$

where the factor −*e*/(*kT*) was included in order for *φ* to have the same units as the electric potential. From this equation and Equation (12), we obtained a non-standard Laplace equation:

$$
\nabla((1 - \mathfrak{ac}\_A)\nabla\phi) = 0,\tag{17}
$$

which is more convenient for resolution purposes than vector Equations (12) and (15). Note that this effective potential *φ* is not the electric potential *V*, whose minus gradient is the electric field *E* given by Equation (13). However, a relationship between them can be obtained [30] by inserting Equation (16) into Equation (13), that is:

$$
\phi = V + \frac{kT}{e} \ln(1 - \alpha c\_A). \tag{18}
$$

Under typical IE conditions, the difference between *V* and *φ* is no greater than a few tenths of a volt, which is negligible compared to the usual voltages (20–100 V) used in field-assisted IE. Despite this, this difference must not be ignored in the modelling, as significant errors in the calculation of the electric field could be made. Indeed, although both potentials are similar, their gradient is not always.

On the other hand, it is worth mentioning that Equations (12) and (15) are trivially solved in the one-dimensional case, that is *J*<sup>0</sup> is constant. This constant will be established from the experimental setup. If a constant current source is used, this value is set directly. Otherwise, when the external field is generated by a constant voltage source, the value of *J*<sup>0</sup> can be calculated from the voltage applied to the sample and Equations (14) and (16)–(18).

#### *2.2. Charge Neutrality Approximation in Field-Assisted Ion Exchange*

In the previous subsection, the charge neutrality was assumed in the field-assisted IE problem, as well as in the thermal-only case. However, this charge neutrality is not always fulfilled, especially when strong external electric fields are used and/or very high concentration gradients exist. In fact, some authors have modelled the silver concentration in channel waveguides by considering explicitly the space charge distribution [35], albeit at the cost of including other assumptions.

An estimation of the validity of the charge neutrality approximation can be made from Equation (13), which can be expressed as:

$$\frac{e\mathbf{E}}{kT} = \nabla \ln(\mathbf{C}\_A + \mathbf{C}\_B) + \frac{\frac{I\_0}{(\mathbf{C}\_A + \mathbf{C}\_B)D\_B} - \nabla c\_A}{1 - ac\_A} \simeq \frac{\frac{I\_0}{\mathbf{C}\_0 D\_B} - \nabla c\_A}{1 - ac\_A} \,\tag{19}$$

where we used the charge neutrality approximation and the definition of *α*. Now, we took divergences in this equation in order to compare it with Equation (10) and estimate the error made by this approximation. This is an iterative procedure. First, we used this approximated expression for the electric field. Next, we substituted it into Poisson's Equation (10) to obtain a more accurate value for *C<sup>A</sup>* + *CB*, which was introduced in the previous equation, and so on. However, a unique iteration will be enough to obtain an order of magnitude of the charge density [36]. Therefore, if we use Equation (12) and assume that *e* does not depend on *C<sup>A</sup>* and *CB*, we obtained:

$$\frac{\varepsilon^{2}}{\varepsilon kT}(\mathsf{C}\_{A} + \mathsf{C}\_{B}) - \frac{\varepsilon^{2}\mathsf{C}\_{0}}{\varepsilon kT} \simeq \frac{aI\_{0}\nabla c\_{A}}{(1 - ac\_{A})^{2}\mathsf{C}\_{0}D\_{B}} - \left(\frac{a\nabla c\_{A}}{1 - ac\_{A}}\right)^{2} - \frac{\nabla^{2}c\_{A}}{1 - ac\_{A}}.\tag{20}$$

Now, from this equation, we can obtain some conditions for the validity of the charge neutrality approximation by comparing each term on the right-hand side of this equation with the second term on the left-hand side. Therefore, for the second term on the right-hand side, this comparison provides:

$$\frac{\alpha \nabla c\_A}{1 - \alpha c\_A} \ll \sqrt{\frac{\epsilon^2 \mathbb{C}\_0}{\epsilon\_0 \epsilon\_r kT}} \simeq 1.1 \times 10^{10} \text{ m}^{-1} \text{ } \tag{21}$$

for a BK7 glass with a density of 2.4 g/cm<sup>3</sup> and 8.4% by weight of Na2O, which gives *<sup>C</sup>*<sup>0</sup> ' 3.9 <sup>×</sup> <sup>10</sup><sup>27</sup> <sup>m</sup>−<sup>3</sup> ; likewise, typical values for the temperature, T = 400 ◦C, and for the relative permittivity, *e<sup>r</sup>* = 10, were considered. As for the ion exchange, we chose for this assessment a Na+/K<sup>+</sup> IE in a soda-lime glass with a diffusion coefficient ratio *DK*/*DNa* ' 2.5 <sup>×</sup> <sup>10</sup>−<sup>2</sup> [37], which leads to *α* = 0.975. Therefore, ∇*c<sup>A</sup>* must fulfil the following condition:

$$
\nabla c\_A \ll 0.28 \,\text{nm}^{-1} \tag{22}
$$

In the worst case, *c<sup>A</sup>* = 1. This condition means a change, in the normalized concentration, from one to zero-point-nine at a distance much greater than 0.36 nm, which in practice is met in almost any IE process. Indeed, most IE processes use glasses with a higher Na2O content or their *α* values are less than the one of Na+/K<sup>+</sup> IE. Therefore, this condition is even less restrictive in those cases.

On the other hand, the third term on the right-hand side of Equation (20) is small under the same conditions as the second one. Finally, the first one is small if the second one is and, furthermore, if:

$$\frac{e l\_0}{1 - \alpha c\_A} \ll \frac{e^2 \mathcal{C}\_0^{3/2} D\_B}{\sqrt{\varepsilon\_0 \varepsilon\_r kT}} \sim 412 \text{ A/cm}^2 \text{.} \tag{23}$$

where we took into account [37] that *<sup>D</sup><sup>B</sup>* ' <sup>6</sup> <sup>×</sup> <sup>10</sup>−<sup>13</sup> <sup>m</sup>2/s, for T = 400 ◦C. That is, in the worst case (*c<sup>A</sup>* = 1), the current density must fulfil:

$$\text{eJ}\_0 \ll 10 \,\text{A/cm}^2.\tag{24}$$

This condition is ensured in practice because the highest current densities that have been used in field-assisted IE processes until now are much lower than this value. In fact, Joule heating should be taken into account for currents higher than a few mA/cm<sup>2</sup> , due to the strong dependence of diffusion coefficients on the temperature [38,39]. Therefore, the charge neutrality approximation is valid in most IE process, even for Na+/Rb<sup>+</sup> and Na+/Cs<sup>+</sup> ion exchanges, which give rise to very steep concentration profiles. In these kinds of profiles, although ∇*c<sup>A</sup>* may be very high, the denominator of Equations (21) and (23) is not close to zero, even for molar fractions close to one. Indeed, we assumed that *α* = 1 − *DA*/*D<sup>B</sup>* is constant, but actually, the diffusion coefficients depend on the molar fractions, so that if a cation has a low concentration, it also has a lower diffusion coefficient. In other words, if *c<sup>A</sup>* ' 1, then *α* < 0, and 1 − *αc<sup>A</sup>* is never close to zero. The basic model that we present in this section cannot explain these dependencies on the concentration of the diffusion coefficients, and therefore, this cannot be used to describe the whole range of molar fractions.

#### *2.3. Boundary Conditions*

When an external medium is in contact with the glass surface, each type of cation present in the glass and/or in the medium can either cross or not cross the glass/medium interface. This depends on the nature of such a medium. If a cation crosses the interface, a thermodynamic equilibrium is assumed between the crossing cations at both sides. Otherwise, the normal component of its flux density cancels. Therefore, the different boundary conditions for the Equations (14), (16) and (17) are obtained for a mask/air, a silver or copper film and a molten salt mixture, when none, one or both cations, respectively, cross the interface. Moreover, when the external medium is a conductor (metallic film or fused salt), its electric potential can also be chosen and directly affects the boundary condition of the potential *φ* through Equation (18).

In Tables 1 and 2, we summarize the boundary conditions for IE processes from molten salt mixtures and films, as well as under a mask or in air. The equations that govern these processes are also shown. Note that boundary conditions for other common IE processes as annealing or secondary ion exchanges are included in these cases. Indeed, boundary conditions for annealing processes are the same as for "mask/air", and the ones for secondary ion exchanges are included in the "salt" case, just using a different constant "C", which depends on the dopant concentration in the salt mixture and temperature through an equilibrium equation [40–43]. Moreover, the final concentration of the first process is the initial condition for the second one.

We show, in these tables, the two alternative forms presented in Section 2.1. In Table 1, the problem is formalized in terms of the normalized concentration of dopant cations *c<sup>A</sup>* and the total flux density *J***0**. This is a more straightforward form, which makes it easier to understand the physical problem of ion exchange. However, for resolution purposes, the form given in Table 2 is simpler because it is written in terms of *c<sup>A</sup>* and a scalar function *φ*, which can be seen as an effective electric potential [30].

The basic model of this section implicitly assumes an ideal cation behaviour in the glass. Therefore, for the sake of consistency, the same assumption was made in the electrochemical potentials to obtain the theoretical equations for the boundary conditions of Tables 1 and 2. However, the corresponding condition for *c<sup>A</sup>* in a glass–salt interface, as a function of the salt composition, must contain non-ideal terms on the glass side, as we will show in the next section. Owing to the molten salt being homogeneous, *cA*|*<sup>S</sup>* is constant along the surface. Hence, a mixed theory can be a pragmatic approach; similarly, experimental values for *cA*|*<sup>S</sup>* can be used to feed the numerical algorithms that model the ion exchange. On the other hand, the boundary conditions for *φ* are sometimes irrelevant

(thermal diffusion) or they can be approximated to those of *V* (diffusion assisted with strong fields). As a result, they were often ignored in models and experiments in the context of waveguide fabrication.

**Table 1.** Complete formulation of the IE problem (equations and boundary conditions), for the most common IE processes, in terms of the normalized concentration of dopant cations *c<sup>A</sup>* and the total flux density *J***0**; *e*ˆ*<sup>S</sup>* is a unit vector perpendicular to the sample surface, and C is a constant, which mainly depends on the dopant concentration in the salt.


**Table 2.** Complete formulation of the IE problem (equations and boundary conditions), for the most common IE processes, in terms of the normalized concentration of dopant cations *c<sup>A</sup>* and an effective electric potential *φ*; *e*ˆ*<sup>S</sup>* is a unit vector perpendicular to the sample surface, and C and F are constants.


#### *2.4. Some Particular Solutions*

Two noticeable one-dimensional solutions are obtained for both specific thermal and field-assisted IE processes. In the simplest thermal IE, a glass sheet is immersed in a molten salt, which contains foreign cations. The boundary conditions for *c<sup>A</sup>* and *φ* are constant over time and along the glass surface, then *J*<sup>0</sup> =0. The concentration profile of the dopants scales in depth proportionally to the square root of the diffusion time, but it retains its shape, that is *c*(*x*, *t*) = *cA*|*<sup>S</sup> f*(*x*/ √ 4*DAt*), being the origin of the coordinates at the glass surface [44]. The shape of *f* depends on *cA*|*<sup>S</sup>* and *α*. If either of them is small, the diffusion Equation (14) becomes linear and *f* tends to a complementary error function (erfc), which has an inflection point at the glass surface and decreases monotonically to zero inside the glass. Otherwise, the diffusion is faster near the surface, where the dopant concentration is high. This causes *f* to present a bump near the surface, being the inflection point displaced into the glass. *f* is often approximated by a Gaussian function, although other functions have been proposed [45–47].

When a voltage is applied between both surfaces of the glass sheet, a current normal to these surfaces appears. If *J*<sup>0</sup> is kept constant, a stationary solution of Equation (14) exists when the slow cations invade a region containing a higher concentration of fast cations [24]. In that case, the mole fraction profile of the slow cations is a step-like function that moves at a constant speed while maintaining its shape. Therefore, two regions with different concentrations are formed with an abrupt transition between them. The higher the step is, the sharper the front and the greater its velocity because the mobility of slow cations increases with its concentration. The stability results from a competition between diffusion and the non-linearity of the drift term. The former widens the profile, whereas the latter sharpens it because the rear region of the profile moves faster. On the other hand, if *V* is kept constant, *J*<sup>0</sup> decreases slowly over time, since the resistivity of the sample increases as the doped region becomes thicker. This effect may already be appreciable for doped regions a few microns deep, because the mobility ratio can reach several orders of magnitude [38,48]. In [38], the applied voltage *V* had to be corrected by 0.93 V to accurately describe the experimental depths because these models did not include the potential *φ*. Note that a combination of the boundary conditions of *φ* at both glass sides, as well as the difference between *φ* and *V* given by Equation (18) explain such a potential. Finally, it is worth noting that a stable profile is only formed if the slow cation chases the fast one. Otherwise, the profile extends indefinitely.

#### **3. The Mixed Ion Effect**

Constant diffusion coefficients were assumed in Section 2. However, they depend on both the temperature *T* and the molar fraction *cA*. In monoalkaline glasses, the temperature dependence follows the Arrhenius law:

$$D = D\_0 \exp\left(-\frac{Q}{kT}\right). \tag{25}$$

This is due to each cation needing to surmount a potential barrier of height equal to *Q* to move to another potential well. The diffusion coefficient is proportional to the number of cations that overcome this energy in a given instant. This number follows a Maxwell–Boltzmann statistic, which explains the above exponential law. According to the Stuart–Anderson model [49], the potential barrier has both an electrostatic component, corresponding to the energy necessary to separate the cation from its anion, and a mechanical component that describes the glass network distortion necessary for the cation to break through another potential well. Therefore, when two species of cations are present in the glass, it is natural that each one has its own diffusion coefficient. However, surprisingly, the *D*<sup>0</sup> and *Q* values of each species (*D*0*A*, *Q<sup>A</sup>* and *D*0*B*, *QB*) largely depend on the cation mole fraction, in such a way that each diffusion coefficient is reduced by up to several orders of magnitude as its respective mole fraction is approaching zero [27,50,51]. This reduction is mainly due to an increase of the activation energy of minority cations; furthermore, it is stronger than the difference between the diffusion coefficients of both species in their respective monoalkaline glasses (*DAA* ≡ *DA*|*cA*=<sup>1</sup> and *DBB* ≡ *DB*|*cA*=0). Consequently, *D<sup>A</sup>* and *D<sup>B</sup>* are equal for some intermediate mole fractions. We will show that this leads to a maximum value of the interdiffusion coefficient and a minimum value of the direct current (DC) conductivity for this intermediate mole fraction or its neighbourhood. Therefore, the DC conductivity shows an excess of activation energy with respect to the monoalkali glasses (this excess disappears with frequency in AC conductivity). This phenomenon, among others, is included in the so-called double-alkali effect, mixed alkali effect or, later, mixed mobile ion effect or mixed ion effect (MIE), since silver, thallium or copper cations behave similarly to alkali ones in glass [37,52–54].

#### *3.1. Brief Review of Theories*

The origin of the MIE has been debated for a long time, but no theory has been universally accepted yet. Some theories focus on an interaction among neighbouring cations

in such a way that mixed pairs are assumed to be more energetically stable than pairs of cations of the same species [15,55–59]. This assumption is supported by several experimental achievements. Namely, the interdiffusion coefficient presents a thermodynamic term for alkali IE [60,61] and for Ag+/Na<sup>+</sup> exchange [62]; we will show that this term is missing if cations behave as an ideal gas. Furthermore, the surface mole fraction of cations in ion exchanged glasses from molten salts (the salt boundary condition) must be explained on the assumption that a non-ideal cation behaviour both for double-alkali exchange [40,41] and for Ag+/Na<sup>+</sup> exchange [42,43]. On the other hand, mixing enthalpy experiments do not have a clear interpretation. A negative mixing enthalpy (net attraction among dissimilar cations) was found [63–65], which correlates linearly with the excess of activation energy for DC conduction. However, the former is about 20 times weaker than the latter. Besides, mixed pairs of cations would be expected to be much more likely than pairs of the same species in the presence of interaction, but nuclear magnetic resonance experiments [66–68], as well as neutron and X-ray diffraction [69] show that they are rather randomly distributed. Consequently, other authors attributed the MIE to relaxation processes in the glass structure [70–73]. In particular, each cation is assumed to modify its neighbourhood after a relaxation time to achieve an energetically favourable site. Therefore, in a monoalkaline glass, all the sites are of the same type. Once a foreign cation enters this glass and modifies a site, it is difficult for it to diffuse because all accessible sites are the wrong type. Even if the cation gains access to one of them, most likely, it will return before the new site relaxes. Moreover, diffusion is assumed to occur through conduction pathways, so a foreign cation can block several indigenous ones. This explanation is compatible with the ideal behaviour of cations, that is with a random distribution.

The theory that we assumed is relevant because, depending on it, the resulting diffusion equation is slightly different, as we will show below.

#### *3.2. The Cation Flux Density*

Let us consider the electrochemical potential (*µ*˜*<sup>i</sup>* ) of each cation species that has a chemical term depending on the thermodynamic activity (*a<sup>i</sup>* ) of that species and an electric term proportional to the cation charge (*e*) and the electric potential (*V*):

$$
\mu\_i = \mu\_i^0 + kT \ln a\_i + eV \qquad \text{i} = A\_\prime B\_\prime \tag{26}
$$

The flux density of each cation species is proportional to both the gradient of its electrochemical potential and its concentration. This leads to the Nernst–Planck equation:

$$J\_i = -D\_i \mathbf{C}\_i \nabla \sharp \tilde{\mu}\_i = -g\_i D\_i \nabla \mathbf{C}\_i + D\_i \mathbf{C}\_i \frac{e\mathbf{E}}{kT} \qquad \dot{\mathbf{t}} = A\_\prime \mathbf{B}\_\prime \tag{27}$$

where the *g<sup>i</sup>* 's are the thermodynamic factors:

$$\mathbf{g}\_i \equiv \frac{\partial \ln a\_i}{\partial \ln c\_i} \qquad i = A\_\prime B\_\prime$$

As mentioned above, some authors include the Haven ratio in the drift term of Equation (27). However, the Haven ratio should only be used to obtain *D<sup>i</sup>* from the experimental values of the diffusion coefficient of radioactive tracers: *D*∗ *i* [74]. The difference between them arises, for example, if the diffusion mechanism is the indirect interstitial one. In this case, a cation located in one interstice replaces a nearby regular site cation, which jumps to another interstitial site. Consequently, the total mass (or charge) displacement described by *D<sup>i</sup>* is different from that of a single cation, which is measured by the tracer. Moreover, the tracer is also affected by the thermodynamic factor, then a comparison between the mobility of a species and the corresponding tracer diffusion coefficient can result in an apparent Haven ratio [61].

If the MIE is fully due to the relaxations of the glass structure, the cation behaviour being ideal, the activity will be equal to the mole fraction, so *g<sup>i</sup>* = 1. On the contrary, if the cation interaction is the only thing responsible for the MIE, we will obtain *D<sup>i</sup>* = *Diiγ<sup>i</sup>* , *γ<sup>i</sup>* being the thermodynamic activity coefficient (*a<sup>i</sup>* =*γic<sup>i</sup>* ). Let us deduce that result. We divided all cations *A* into two sets, the ones that are hopping from one site to another in a given instant (*A* ↑ ) and the rest of them, which are fixed (*A* ↓ ). Although the former are much scarcer, both sets are in thermal equilibrium in any given small region in the glass; therefore:

$$
\mathfrak{f}\_A = \mathfrak{f}\_{A^\downarrow} = \mathfrak{f}\_{A^\uparrow} \tag{28}
$$

Now, we made two assumptions. First, we supposed that mobile cations behave ideally with respect to each other due their low concentration (*CA*<sup>↑</sup> *CA*<sup>↓</sup> ):

$$
\tilde{\mu}\_{A^\uparrow} = \mu\_{A^\uparrow}^0 + kT \ln \frac{\mathbb{C}\_{A^\uparrow}}{\mathbb{C}\_0} + eV \qquad i = A, B. \tag{29}
$$

Note that this could fail in the case of cooperative movement, that is, when two or more nearby cations change their site simultaneously. Second, we assumed that the reference potential of mobile cations (*µ* 0 *A*↑ ) is independent of *cA*; therefore, ∇*µ* 0 *<sup>A</sup>*<sup>↑</sup> =0. In addition to using Equation (27), the cation flux density can also be calculated from mobile cations, being proportional to both the gradient of their electrochemical potential and their concentration:

$$J\_A = J\_{A^\uparrow} = -\frac{D\_{A^\uparrow}}{kT} \mathcal{C}\_{A^\uparrow} \nabla \mathfrak{H}\_{A^\uparrow} = -D\_{A^\uparrow} \nabla \mathcal{C}\_{A^\uparrow} + \frac{eD\_{A^\uparrow}}{kT} \mathcal{C}\_{A^\uparrow} \mathbf{E}\_{\prime} \tag{30}$$

where *DA*<sup>↑</sup> is a temperature-dependent multiplicative coefficient and the factor 1/*kT* was introduced in order for *DA*<sup>↑</sup> to have units of a diffusion coefficient. By combining Equations (26), (28) and (29), we can find *CA*<sup>↑</sup> as:

$$\mathcal{C}\_{A^\uparrow} = \exp\left(-\frac{\mu\_{A^\uparrow}^0 - \mu\_A^0}{kT}\right)\gamma\_A \mathcal{C}\_{A\prime}$$

and replace it in Equation (30). The resulting flux density is:

$$J\_A = D\_{A\uparrow} \exp\left(-\frac{\mu\_{A\uparrow}^0 - \mu\_A^0}{kT}\right) \left\{-\left(\gamma\_A + \mathbb{C}\_A \frac{\partial \gamma\_A}{\partial \mathbb{C}\_A}\right) \nabla \mathbb{C}\_{A\uparrow} + \frac{e}{kT} \gamma\_A \mathbb{C}\_A \mathbb{E}\right\}$$

which agrees with Equation (27) by identifying:

$$D\_A = D\_{A^\uparrow} \exp\left(-\frac{\mu\_{A^\uparrow}^0 - \mu\_A^0}{kT}\right) \gamma\_A = D\_{AA} \gamma\_A.$$

Obviously, an identical derivation can be done for *B* cations to obtain *D<sup>B</sup>* = *DBBγB*.

Surprisingly, it was not necessary to make any assumptions about the particular dependence of *γ<sup>i</sup>* on the mole fraction. In short, under these cation interaction assumptions, the dependence of the diffusion coefficient of each species on the mole fraction was directly related to its thermodynamic activity coefficient. For the equations to remain valid, regardless of the MIE explanation, we will continue the derivation from Equation (27), without any assumptions on the thermodynamic term *g<sup>i</sup>* , which can be done in the last step.

#### *3.3. Generalized Equations and Boundary Conditions*

By following the same procedure as in the previous section, we replaced *E* with *J*<sup>0</sup> in the expression of *JA*, and then, we applied the continuity condition to obtain:

$$\frac{\partial c\_A}{\partial t} + \frac{\partial}{\partial c\_A} \left[ \frac{D\_A c\_A}{D\_A c\_A + D\_B c\_B} \right] \frac{I\_0}{\mathbb{C}\_0} \nabla c\_A = \nabla \left( \frac{(\mathcal{g}\_B c\_A + \mathcal{g}\_A c\_B) D\_A D\_B}{D\_A c\_A + D\_B c\_B} \nabla c\_A \right), \tag{31}$$

where the whole flux density *J*<sup>0</sup> can be obtained from the scalar potential *φ* as:

$$J\_0 = -(D\_A c\_A + D\_B c\_B) \frac{e \mathbb{C}\_0}{kT} \nabla \phi\_\prime \tag{32}$$

and *φ* in turn satisfies the following non-standard Laplace equation:

$$\nabla[\left(D\_A c\_A + D\_B c\_B\right)\nabla \phi] = 0.\tag{33}$$

In view of Equation (31), we can redefine the interdiffusion coefficient as:

$$D(c\_A) \equiv \frac{(g\_B c\_A + g\_A c\_B) D\_A D\_B}{D\_A c\_A + D\_B c\_B} \equiv (g\_B c\_A + g\_A c\_B) D\_{\text{mob}}.\tag{34}$$

It can be split into a mobility term *D*mob and a thermodynamic term (*gBc<sup>A</sup>* + *gAcB*), which is not in the definition (9) of the basic model. If cations behave ideally, the latter becomes equal to one, and the interdiffusion coefficient is reduced to the mobility term. If cation interactions are relevant, the thermodynamic term enhances the maximum of *D*¯ (*cA*) for intermediate values of *cA*, as can be seen in Figure 1b. Similarly, Equation (32) shows that the mobility is:

$$
\mu \equiv \frac{e}{kT} (D\_A c\_A + D\_B c\_B) \tag{35}
$$

which, in fact, is the same as Equation (5), but now, the *D<sup>i</sup>* 's are mole fraction dependent. This results in a minimum conductivity value for a mole fraction close to that at which the interdiffusion coefficient reaches its maximum. In contrast, the basic model leads to monotonic *u* and *D*¯ functions.

In order to impose the boundary conditions on *φ*, we need to relate it with the electric potential *v*. This can be done by the procedure followed in the above section, but the resulting expression is not so simple:

$$\phi = V + \frac{kT}{\varepsilon} \int\_{0}^{c\_{A}} \frac{D\_{A}c\_{A} \frac{\operatorname{d} \ln a\_{A}}{\operatorname{d} c\_{A}} + D\_{B}c\_{B} \frac{\operatorname{d} \ln a\_{B}}{\operatorname{d} c\_{A}}}{D\_{A}c\_{A} + D\_{B}c\_{B}} \,\mathrm{d}c\_{A}.\tag{36}$$

If the MIE is caused by cation interactions (*Dic<sup>i</sup>* = *Diia<sup>i</sup>* ), this expression can be integrated for any particular dependency of the activities on the mole fraction:

$$
\phi = V + \frac{kT}{e} \ln \frac{D\_A c\_A + D\_B c\_B}{D\_{BB}}.
$$

On the contrary, if cations behave ideally and relaxation processes are responsible for the MIE, then Equation (36) becomes:

$$\phi = V + \frac{kT}{e} \int\_0^{c\_A} \frac{D\_A - D\_B}{D\_A c\_A + D\_B c\_B} \,\mathrm{d}c\_{A\prime}$$

and the integration can only be performed once the dependencies of the diffusion coefficients on the mole fraction are known.

The starting point to impose the boundary conditions are the same as in Section 2, that is equal electrochemical potentials at both sides of the glass surface for cation species that can cross it and zero flux through it otherwise. However, the particular functions for the electrochemical potentials and flux densities must be chosen from the model of the glass behaviour.

#### *3.4. Changes in the Solutions with Respect to the Basic Model*

The main difference, with respect to the basic model, which is observed after the numerical solution of Equation (31), comes from the presence of a maximum in the interdiffusion coefficient for intermediate molar fractions (Figure 1b). Therefore, new qualitative

shapes of the profiles are seen when almost all indigenous cations are replaced by the foreign ones.

In Figure 2, we show a simulation of molar fraction profiles of potassium cations in a K+/Na<sup>+</sup> thermal exchange for several boundary conditions ( *<sup>c</sup>*K|*<sup>S</sup>* ). The profile for the lowest value of *c*K|*<sup>S</sup>* was similar to an erfc function. For intermediate values (0.4 and 0.6), the profiles showed a bump between the glass surface and the tail, near which there was an inflection point. Both characteristics were similar to those predicted by the basic model. Nevertheless, a second inflection point (or equivalently, a high slope at the surface) appeared for the highest values of the boundary condition. Because the interdiffusion was, in the present model, lower near the surface, the slope of the profile must increase to provide cations at a sufficient rate for the intermediate regions, where they diffuse faster. An approximate analytical profile was proposed to describe all of these cases [75]. In this work, the authors checked the quality of that profile through the measurement of the effective indices of ion exchange waveguides. They obtained an average deviation of 3 <sup>×</sup> <sup>10</sup>−<sup>4</sup> between measured and calculated effective indices, which corresponded to a deviation of ≈0.3% between concentration profiles. Similar results have been obtained by numerically solving the diffusion equation that governs the IE process [22]. Moreover, this author even monitored such a process as a function of the diffusion time.

**Figure 2.** Simulation of molar fraction profiles as a function of depth for a thermal IE by taking into account the MIE. Equation (31) was solved for *J*<sup>0</sup> =0 and the boundary conditions *c*K|*<sup>S</sup>* = 0.2, 0.4, 0.6, 0.8 and 1. The interdiffusion coefficient *D*¯ (*c*K) of Figure 1b was used.

A simulation for field-assisted IE can be seen in Figure 3. For the lowest boundary conditions ( *c*K|*<sup>S</sup>* = 0.1–0.3), the exchange was dominated by the diffusive term, and the stable profile was not formed yet. For intermediate values of *c*K|*<sup>S</sup>* (0.4–0.8), the stable profile was clearly formed, since the rear region of the profile was flat. Moreover, we can see that the velocity of the front and its slope increased with the boundary condition. Again, these characteristics agreed with the prediction of the basic model. Finally, for *c*K|*<sup>S</sup>* = 0.9–1,

a new effect appeared. The speed and the slope of the front saturated, while its rear part was no longer flat because the potassium cations were faster here than the sodium ones. Both regimes can be observed in experimental studies [76,77].

**Figure 3.** Simulation similar to that in Figure 2, but for a field-assisted IE with *J*0/*C*<sup>0</sup> = 80 nm/s.

#### **4. Future Challenges**

Some of the previous assumptions in the modelling of ion exchange in glass are not always valid. For example, the interdiffusion coefficient is reduced during the ion exchange of dopants, which generates compressive stress. This is probably due to a constriction of the interstitial sites [78–80]. Another issue is the generalization of the charge neutrality approximation to processes involving the simultaneous diffusion of three species (for example sodium, silver and potassium). Some of such processes were proposed in the past to improve the shape of narrow-channel waveguides [81,82] or, more recently, to obtain both antimicrobial and strengthening properties [10]. In [82], a simplified model was presented by considering that potassium cations are immobile. Unfortunately, little progress has been made in all of these issues in the last few years. Note that modelling of these processes in the MIE framework would require considerable experimental studies to obtain the interdiffusion coefficients. Nevertheless, there are some processes that also require more complete models, but that have recently attracted a great deal of attention due to their remarkable applications. Among them, we highlight: glass poling, electro-diffusion of multivalent metals and the formation/dissolution of silver nanoparticles.

#### *4.1. Glass Poling*

Glass poling is the distribution of the electric charges of the glass. This may result in a permanent electric field inside the glass, which can give rise to relevant non-linear effects on light propagation. Applications of glass poling include grating fabrication [83], second-harmonic generation [84] or the fabrication of optical waveguides with profiled electrodes [85]. Glass poling was initially applied to silica glass [86], which contains

residual amounts of cations (*C*<sup>0</sup> <sup>∼</sup> <sup>10</sup><sup>23</sup> <sup>m</sup>−<sup>3</sup> ). It is realized by subjecting the sample to a strong potential difference *U* (typically, a few kV) at a temperature of about 250–300 ◦C and, usually, not allowing charged species to enter the glass ("blocking anode") [87]. Therefore, the field rearranges the cations until a new equilibrium is achieved when the original field inside the glass is cancelled by charges located near the glass surface. That is, the applied field creates a layer, under the anode, a few micrometers thick and depleted of cations. Obviously, charge neutrality is not fulfilled here. Instead, the one-dimensional form of Equations (3) and (10) of the basic model shows that the layer thickness *d*, in equilibrium, is given by:

*d* = s 2*eU eC*<sup>0</sup> . (37)

This layer is charged and has a high electrical resistivity since its anions are fixed to the glass network. Furthermore, because the field is cancelled in the glass bulk, the applied voltage drops across the depleted layer. Therefore, a very strong field arises, which is independent of the thickness of the substrate. Besides, potentials above ∼1 kV generate structural changes in the layer [88]. Then, if the sample is sharply cooled to room temperature, the distribution of charges becomes frozen. Electric fields inside the silica glass can reach <sup>∼</sup>10<sup>7</sup> V/m, which induces a non-linear coefficient *<sup>χ</sup>*(2) <sup>∼</sup> 1 pm/V [89]. However, this process is idealized. In practice, other cations are often involved due to the high applied voltages. One of the possible cations is hydronium (H3O+) from air water vapour that forms a naturally hydrated layer in the glass. In this situation, called poling with a non-blocking anode, Equation (37) is no longer valid. Instead, a stable profile, such as described in Section 2.4, is formed because hydronium moves slower than sodium. In this case, a partially depleted region is still formed before the electric field increases enough to move the hydronium cations significantly [90]. The charge and the electric field are expected to be at their greatest values when the hydronium layer begins to form. Subsequently, a part of the applied voltage *U* drops across the hydronium layer [91]. In glasses with high alkali content, the situation is somewhat different, since air cannot provide hydronium at a sufficient rate. Moreover, as *C*<sup>0</sup> is large, *d* is small (see Equation (37)), and the electric field can become high enough to move other cations such as Ca+<sup>2</sup> or Mg+<sup>2</sup> [31,92]. Another situation of interest occurs when a BK7 glass, which contains sodium and potassium, is poled. Initially, only sodium cations are removed from the glass surface, as they move faster. Then, the field increases in the charged layer until potassium cations start to move and accumulates behind the sodium ones, filling the empty sites that the latter have just left. Simultaneously, a fully depleted surface layer is formed [92]. Poling of double-alkali glasses, with a non-blocking anode, was also simulated with similar conclusions [93]. One interesting result, which is obtained in high-alkali glasses, is the formation of a waveguide next to the depleted layer, this having non-linear properties. In all the previously cited works about the simulation of glass poling, the authors assumed diffusion coefficients constant, which is only an approximation. The diffusion coefficient in monoalkali glasses depends notably on the alkali content. Therefore, it is expected that the diffusion coefficient in the depleted layer is also different from bulk glass. Therefore, more experimental research on glass poling is still necessary to make clear, on the one hand, the conditions under which the charge neutrality approximation is valid and, on the other hand, whether the MIE or other effects are relevant enough to be considered in the modelling.

#### *4.2. Electro-Diffusion of Multivalent Metals*

Monovalent cations as Ag+/Na<sup>+</sup> and K+/Na<sup>+</sup> are by far the most used cations in IE processes in glass. However, some successful attempts at doping glass with multivalent cations have also been realized, mainly with transition metals, but also with rare-earths. For example, Gonella et al. obtained Co2+, Au3<sup>+</sup> and Cr3<sup>+</sup> diffusion profiles in silicate glasses [94,95]; and Cattaruzza et al. introduced Er3<sup>+</sup> cations inside soda-lime glasses [96]. These authors used field-assisted configurations with electric fields up to 400 V/mm,

as thermal-assisted IE is not very effective with multivalent ion species. This allowed for penetrations of cations of up to ∼1 µm from deposited films. The main utility of glass doping with multivalent transition metals arises from the possibility of converting the glass into an active media. Therefore, optical amplification or waveguide lasers have been demonstrated in erbium-doped glasses [97], and Cr4+-doped materials have been proposed as both laser gain materials and saturable absorbers for passive Q-switching in IR lasers [98].

The ion exchange with multivalent cations gives rise to concentration-dependent structural changes in the glass matrix. This is due to the local coordination rearrangements, which are produced at the ion sites [99]. In addition, the amount of metal that penetrates into the glass matrix, as well as the shape of the concentration profiles depend strongly on the process parameters. Therefore, the model presented in Section 3, which includes the MIE, should be used in the modelling of such processes. Likewise, when the multivalent cations are introduced into the glass, a region depleted of cations, similar to that observed in poled glasses, is formed. Therefore, the approaches used in the modelling of glass poling could be applied to the present processes. However, little work has been done in these directions, and a comprehensive model of electro-diffusion of multivalent metals is still lacking.

#### *4.3. Formation/Dissolution of Silver Nanoparticles*

Metal nanocluster formation following ion exchange can arise if both suitable dopant cations and post-exchange processing techniques are used. Among all dopants, silver stands out for its great diffusivity in glass and its high tendency to form metal clusters [33]. As for the post-exchange techniques, heat treatments (annealing) under different atmospheres [100,101] and (pulsed) laser irradiation [102] are commonly applied. The formation of metal structures can be regarded as a drawback and an advantage. For example, in light waveguiding, metal inhomogeneities must be avoided because they cause a high light absorption. On the contrary, some investigations have found these structures useful for sensing applications, through the surface enhancement of Raman scattering (SERS) [103], for fabricating photonic crystals [104] or, in general, for plasmonic optics [105,106].

Modelling of the formation and dissolution of silver nanoparticles is a very challenging task because the two complex processes compete dynamically. On the one hand, annealing or irradiation promotes silver aggregation and the formation of nanometre-sized clusters while, at the same time, the diffusion and dissolution of silver cations are produced. Therefore, at least three species must be included in the modelling: both exchanging cations and metallic silver. Moreover, this process is often done in gaseous atmospheres, which provide other cations that diffuse into the glass, increasing the number of species to be included in the model. On the other hand, this kind of process is strongly dependent on the cation concentration, so that the MIE should be considered. Finally, not enough experimental studies have been realized until now to characterize the great variety of mechanisms involved in these processes. Some theoretical descriptions of nanoparticle formation under specific post-exchange processing techniques (purely thermal annealing [107] and annealing in hydrogen atmosphere [108]) have been given. Both authors assumed the charge neutrality approximation that, under these processing techniques, is probably fulfilled. However, they did not assess the introduction of the MIE in their models and if that would lead to a better description of the cluster formation. Considerable work, both theoretical and experimental, must be done before having a complete theoretical model of this promising technique.

#### **5. Conclusions**

The improvements made in the last few years in the theoretical modelling of ion exchange in glass have contributed to a better understanding of the physical and chemical mechanisms involved in this process. The basic model that has been used for decades only allows for the accurate description of ion exchange problems where the dopant concentration is low. If higher concentrations are present, a model based on the mixed alkali effect must be considered. However, some aspects of this model are still open, because the physics and chemistry involved are not fully understood. On the other hand, a significant progress has been made in the modelling of some IE processes that have attracted much attention in recent years. These processes include glass poling, electrodiffusion of multivalent metals, and the formation/dissolution of silver nanoparticles. All of them have remarkable applications, both scientific, as well as technological.

**Funding:** This research was funded by Xunta de Galicia, Consellería de Educación, Universidades e FP, Grant GRC Number ED431C2018/11, and Ministerio de Economía, Industria y Competitividad, Gobierno de España, Grant Number AYA2016-78773-C2-2-P, European Regional Development Fund.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data used in this article data were extracted from Fleming, J.W., Jr.; Day, D.E. Relation of Alkali Mobility and Mechanical Relaxation in Mixed-Alkali Silicate Glasses. *J. Am. Ceram. Soc.* **1972**, *55*, 186–192.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

The following abbreviations are used in this manuscript:


#### **References**


**Jean-Emmanuel Broquin 1,\* and Seppo Honkanen <sup>2</sup>**


**Featured Application: ion-exchange on glass has been extensively studied for the realization of Planar Lightwave Circuits. Monolithically integrated on a single glass wafer, these devices have been successfully employed in optical communication systems as well as in sensing.**

**Abstract:** Ion-exchange on glass is one of the major technological platforms that are available to manufacture low-cost, high performance Planar Lightwave Circuits (PLC). In this paper, the principle of ion-exchanged waveguide realization is presented. Then a review of the main achievements observed over the last 30 years will be given. The focus is first made on devices for telecommunications (passive and active ones) before the application of ion-exchanged waveguides to sensors is addressed.

**Keywords:** integrated photonics; glass photonics; optical sensors; waveguides; lasers

**Citation:** Broquin, J.-E.; Honkanen, S. Integrated Photonics on Glass: A Review of the Ion-Exchange Technology Achievements. *Appl. Sci.* **2021**, *11*, 4472. https://doi.org/ 10.3390/app11104472

Academic Editor: Alessandro Belardini

Received: 25 April 2021 Accepted: 11 May 2021 Published: 14 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

#### **1. Introduction**

Unlike microelectronics where the CMOS technology emerged as the dominant platform, integrated optics or, as it is called nowadays, integrated photonics, does not rely on one single technological platform. Indeed, silicon photonics, III-V photonics, polymer photonics, LiNbO<sup>3</sup> photonics, and, last but not least, glass photonics co-exist in parallel, each of them presenting their own drawbacks and advantages.

As for ion-exchange on glass, also called glass integrated optics, it is based on a material that has been known and used for centuries. Glass is easily available and can be easily recycled. The ion-exchange technique, although it is based on using microfabrication tools, can be considered as a relatively low-cost approach, which allows realizing waveguides with low propagation losses and a high compatibility with optical fibers. Glass photonics is not a platform that has been developed for a specific application. Therefore, Planar Lightwave Circuits (PLCs) realized by ion-exchange on glass are found in many fields with a wide range of applications.

From its very beginning in 1972 [1], to products currently on the markets, thousands of papers have been published on this vivid topic. For this reason, making an extensive review of this technology is a cumbersome task. However, since excellent reviews have already been published in the past years [2–9], we can skip the pioneering years when the basis of the technology was set by testing several glasses and ions and making multimode waveguides. In this paper, we will hence focus on devices made by ion-exchange on glass, their performances, and their applications.

After a presentation of ion-exchanged waveguides, their realization process, their modelling, and their main characteristics, we will review devices made for telecommunication purpose. Then, we will review the use of ion-exchanged waveguides for the fabrication of optical sensors since these types of applications are taking a growing place in integrated photonics.

#### **2. Ion-Exchanged Waveguides**

#### *2.1. Principle and Technology*

Typically, an optical glass is an amorphous material composed by several types of oxides mixed together. According to Zachariasen [10], theses oxides can be sorted in three main categories: network formers like SiO2, GeO2, or P2O<sup>5</sup> that can create a glass on their own; intermediate network formers (Al2O3, TiO2, . . . ) that can hardly create a glass alone but can be combined with network formers; finally network modifier oxides like Na2O, K2O, CaO, or BaO that can be inserted in a matrix made by glass formers but are weakly linked to it because of a mismatch between their respective molecular binding structures.

The refractive index of a glass depends on its composition through an empirical relation [11]:

$$m = 1 + \sum\_{m} \frac{a\_m N\_m}{V\_0} = 1 + \frac{R\_0}{V\_0} \,\text{s}\tag{1}$$

where *a<sup>m</sup>* is the "refractivity constant" of the chemical element "*m*", *N<sup>m</sup>* the number of chemical element "*m*" by atom of oxygen, *V*<sup>0</sup> and *R*<sup>0</sup> are the glass volume and refractivity by atom of oxygen, respectively.

A replacement of a portion of one of the glass components by another one with the same coordination can therefore entail a change of refractive index. Providing that this exchange does not create strong mechanical stresses and does not strongly change the nature of the glass, (1) can be used to link the induced variation of the refractive index to the fraction *c* of substituting ions as follows:

$$
\Delta \mathfrak{m} = \frac{c}{V\_0} \left( \Delta R - \frac{\Delta V \ R\_0}{V\_0} \right),
\tag{2}
$$

∆*R* and ∆*V* are the variation of *R*<sup>0</sup> and *V*0, respectively, caused by the substitution. From (2), it can easily be deduced that a local change of the glass composition is creating a localized change of refractive index, which can be used to create a waveguide.

Since alkali ions are weakly linked to the glass matrix, they are natural candidates for such a process. Indeed, when alkali ions react with silica to form a multicomponent glass, the silica network is maintained because each silicon-oxygen tetrahedron remains linked to at least three other tetrahedra [12]. Therefore, one can exchange one alkali ion to another one without damaging the original glass. Throughout the years, several ion-exchanges have been demonstrated [13,14] but the topic of this article being integrated glass photonics, we will restrain ourselves on the few ones that have enabled realizing efficient devices. In this case, the ion that is present in the glass is usually Na<sup>+</sup> (sometimes K<sup>+</sup> ). It is nowadays mostly exchanged with silver (Ag<sup>+</sup> ), more rarely with potassium (K<sup>+</sup> ) or thallium (Tl<sup>+</sup> ).

The ion source that allows creating the higher refractive index waveguide's core can be either liquid or solid. The simplest way of performing an ion-exchange is described on Figure 1a. It consists in dipping the glass wafer in a molten salt containing a mixture of both the doping ions B<sup>+</sup> and the glass ones A<sup>+</sup> . The salt is usually a nitrate, but sulfates are sometimes used when a temperature higher than 450 ◦C is required for the exchange. Although the principle of the process is very simple, it must be kept in mind that ionic diffusion is a process that strongly depends on the temperature; this parameter should hence be homogeneous all other the wafer and consequently in the molten salt. In order to define the parts of the wafer that will be ion-exchanged, a thin-film has previously been deposited and patterned in a clean room environment to define the diffusion apertures. Once the ion-exchange is completed, the masking layer is removed and diffused surface waveguides are obtained. If a more step-like refractive index profile is required, an electric field can be applied to push the doping ions inside the glass, as described in Figure 1b [1]. Nonetheless, this complicates the set-up and might also induce the reduction of the doping ions into metallic clusters that dramatically increase the propagation losses (specifically when silver is involved). The use of a silver thin film has also been employed successfully for the creation of the waveguide's core [15]. The thin film can be either deposited on an

existing mask, as depicted on Figure 1c, or patterned directly on the glass substrate [16]. An applied electric field ensures an efficient electrolysis of Ag<sup>+</sup> ions into the glass by the consumption of the silver film anode. These three different processes allow realizing waveguides whose core is placed at the surface of the glass wafer and whose shape is, depending on the process parameters, semi-elliptical with a step refractive index change at their surface and diffused interfaces inside the glass. Intrinsically, such waveguides are supporting modes that are prone to interact with the elements present on the wafer surface. Interesting and even maximized for the realization of sensors, this interaction is often a drawback when dealing with telecom devices where the preservation of the quality of the optical signal is a key factor. For this reason, ion-exchanged waveguide cores are usually buried inside the glass. ited on an existing mask, as depicted on Figure 1c, or patterned directly on the glass substrate [16]. An applied electric field ensures an efficient electrolysis of Ag+ ions into the glass by the consumption of the silver film anode. These three different processes allow realizing waveguides whose core is placed at the surface of the glass wafer and whose shape is, depending on the process parameters, semi-elliptical with a step refractive index change at their surface and diffused interfaces inside the glass. Intrinsically, such waveguides are supporting modes that are prone to interact with the elements present on the wafer surface. Interesting and even maximized for the realization of sensors, this interaction is often a drawback when dealing with telecom devices where the preservation of the quality of the optical signal is a key factor. For this reason, ion-exchanged waveguide cores are usually buried inside the glass.

can be applied to push the doping ions inside the glass, as described in Figure 1b [1]. Nonetheless, this complicates the set-up and might also induce the reduction of the doping ions into metallic clusters that dramatically increase the propagation losses (specifically when silver is involved). The use of a silver thin film has also been employed successfully for the creation of the waveguide's core [15]. The thin film can be either depos-

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 3 of 18

**Figure 1.** Three main processes used to realize surface waveguides by an ion-exchange on glass. A+ and B+ represent the ions contained in the glass and the ones replacing them, respectively. (**a**) the glass wafer is dipped into a molten salt containing B+ ions entailing a thermal diffusion on the exchange ions through a diffusion aperture; (**b**) the diffusion process is assisted by an electric field; (**c**) an electrolysis of a silver thin film is used to generate Ag+ ions that are migrating by diffusion and conduction inside the glass. **Figure 1.** Three main processes used to realize surface waveguides by an ion-exchange on glass. A<sup>+</sup> and B<sup>+</sup> represent the ions contained in the glass and the ones replacing them, respectively. (**a**) the glass wafer is dipped into a molten salt containing B<sup>+</sup> ions entailing a thermal diffusion on the exchange ions through a diffusion aperture; (**b**) the diffusion process is assisted by an electric field; (**c**) an electrolysis of a silver thin film is used to generate Ag<sup>+</sup> ions that are migrating by diffusion and conduction inside the glass.

Figure 2 depicts the two main processes that can be used: the first one consists of plunging the wafer containing surface cores in a molten salt containing only the ions that were originally present in the glass. A reverse ion-exchange is then occurring, removing doping ions from the surface of the glass [17]. This process entails a quite important decrease of the refractive index change and an increase of the waveguide's dimension because of thermal diffusion, which practically limits the depth of the burying to one to two micrometers. In order to reach a deeper depth and ensure a good optical insulation of the guided mode, the reverse ion-exchange is quite often assisted by an electric field that forces the migration of the core inside the glass preventing hence a loss of refractive index variation. Moreover, by a proper tuning of the process parameters, circular waveguide cores can be obtained in order to maximize the coupling efficiency with optical fibers. Nonetheless, it must be noticed that the applied voltage can be close to 1 kV, which requires on one hand, a proper and well secured dedicated set-up, and on the other hand, an excellent quality of the glass wafer in order to prevent percolation path formation and short circuits. Figure 3 depicts an optical image of a buried optical waveguide realized on Figure 2 depicts the two main processes that can be used: the first one consists of plunging the wafer containing surface cores in a molten salt containing only the ions that were originally present in the glass. A reverse ion-exchange is then occurring, removing doping ions from the surface of the glass [17]. This process entails a quite important decrease of the refractive index change and an increase of the waveguide's dimension because of thermal diffusion, which practically limits the depth of the burying to one to two micrometers. In order to reach a deeper depth and ensure a good optical insulation of the guided mode, the reverse ion-exchange is quite often assisted by an electric field that forces the migration of the core inside the glass preventing hence a loss of refractive index variation. Moreover, by a proper tuning of the process parameters, circular waveguide cores can be obtained in order to maximize the coupling efficiency with optical fibers. Nonetheless, it must be noticed that the applied voltage can be close to 1 kV, which requires on one hand, a proper and well secured dedicated set-up, and on the other hand, an excellent quality of the glass wafer in order to prevent percolation path formation and short circuits. Figure 3 depicts an optical image of a buried optical waveguide realized on a Teem Photonics GO14 glass by a silver-sodium ion-exchange. Burying depth as high as 47 µm have been realized, as shown in Figure 4, but such extreme values are rarely required in practical devices where the burying depth is of the order of 10 µm.

lar profiles.

to the glass wafer substrate.

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 4 of 18

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 4 of 18

quired in practical devices where the burying depth is of the order of 10 µm.

**Figure 2.** (**a**) Thermal burying of a waveguide's core; (**b**) electrically assisted burying of the waveguide's core. The competition between ionic diffusion and transport allows obtaining quasi circu-**Figure 2.** (**a**) Thermal burying of a waveguide's core; (**b**) electrically assisted burying of the waveguide's core. The competition between ionic diffusion and transport allows obtaining quasi circular profiles. (**a**) (**b**) **Figure 2.** (**a**) Thermal burying of a waveguide's core; (**b**) electrically assisted burying of the waveguide's core. The competition between ionic diffusion and transport allows obtaining quasi circular profiles. (**a**) (**b**) **Figure 2.** (**a**) Thermal burying of a waveguide's core; (**b**) electrically assisted burying of the waveguide's core. The competition between ionic diffusion and transport allows obtaining quasi circu-

ANO3

ANO3 A+

ANO3

B+

ANO3 A+

B+

Vapp

Vapp

a Teem Photonics GO14 glass by a silver-sodium ion-exchange. Burying depth as high as 47 µm have been realized, as shown in Figure 4, but such extreme values are rarely re-

quired in practical devices where the burying depth is of the order of 10 µm.

a Teem Photonics GO14 glass by a silver-sodium ion-exchange. Burying depth as high as 47 µm have been realized, as shown in Figure 4, but such extreme values are rarely re-

quired in practical devices where the burying depth is of the order of 10 µm.

lar profiles.

light blue, the core is in pink, air is in dark blue. **Figure 3.** Image of a quasi-circular waveguide observed with an optical microscope, the glass is in light blue, the core is in pink, air is in dark blue. **Figure 3.** Image of a quasi-circular waveguide observed with an optical microscope, the glass is in light blue, the core is in pink, air is in dark blue. **Figure 3.** Image of a quasi-circular waveguide observed with an optical microscope, the glass is in light blue, the core is in pink, air is in dark blue.

applied electric field during the burying process was 650 kV/m; (**a**) image of the output of the waveguide observed with an InGaAs Camera at λ = 1.5 µm; (**b**) vertical cut of the measured intensity showing the position of the mode with respect **Figure 4.** Realization of deeply buried waveguides by an Ag+/Na+ ion-exchange on a GO14 TeemPhotonics glass. The applied electric field during the burying process was 650 kV/m; (**a**) image of the output of the waveguide observed with an InGaAs Camera at λ = 1.5 µm; (**b**) vertical cut of the measured intensity showing the position of the mode with respect to the glass wafer substrate. **Figure 4.** Realization of deeply buried waveguides by an Ag+/Na+ ion-exchange on a GO14 TeemPhotonics glass. The applied electric field during the burying process was 650 kV/m; (**a**) image of the output of the waveguide observed with an InGaAs Camera at λ = 1.5 µm; (**b**) vertical cut of the measured intensity showing the position of the mode with respect to the glass wafer substrate. **Figure 4.** Realization of deeply buried waveguides by an Ag+/Na<sup>+</sup> ion-exchange on a GO14 Teem-Photonics glass. The applied electric field during the burying process was 650 kV/m; (**a**) image of the output of the waveguide observed with an InGaAs Camera at λ = 1.5 µm; (**b**) vertical cut of the measured intensity showing the position of the mode with respect to the glass wafer substrate.

#### *2.2. Modelling Ion-Exchanged Waveguides*

Extensive work has been carried-out throughout the years to characterize and model ion-exchanges processes [18–22]. In this article, we will focus on a relatively simple description since it occurred to be reliable enough to allow us designing waveguides and predicting their optical behavior efficiently. Ion-exchange can be seen as a two-step process: first the exchange itself that occurs at the surface of the glass and creates a normalized

concentration *c<sup>s</sup>* of doping ions. For thin film sources, this concentration is linked to the applied current by the following relation: predicting their optical behavior efficiently. Ion-exchange can be seen as a two-step process: first the exchange itself that occurs at the surface of the glass and creates a normalized concentration ௦ of doping ions. For thin film sources, this concentration is linked to the

Extensive work has been carried-out throughout the years to characterize and model ion-exchanges processes [18–22]. In this article, we will focus on a relatively simple description since it occurred to be reliable enough to allow us designing waveguides and

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 5 of 18

*2.2. Modelling Ion-Exchanged Waveguides* 

$$\frac{\partial c\_s}{\partial \mathbf{x}} = \frac{f\_0(c\_s - 1)}{D\_{Ag}},\tag{3}$$
 
$$\text{where } \mathbf{x} \text{ is the distance of the horizontal and the horizontal axis, and the direction is the relative motion of the material.}$$

where *J*<sup>0</sup> is the ion flux created by the electrolysis, *x* is the direction normal to the surface, and *DAg* is the diffusion coefficient of silver in the glass. where is the ion flux created by the electrolysis, is the direction normal to the sur-

For liquid sources made of a mixture of molten salts containing B<sup>+</sup> and A<sup>+</sup> ions in order to replace A<sup>+</sup> ions of the glass, an equilibrium at the glass surface is usually rapidly reached, according to the chemical reaction: face, and is the diffusion coefficient of silver in the glass. For liquid sources made of a mixture of molten salts containing B+ and A+ ions in order to replace A+ ions of the glass, an equilibrium at the glass surface is usually rapidly

$$A\_{salt}^{+} + B\_{glass}^{+} \Leftrightarrow B\_{salt}^{+} + A\_{glass}^{+} \tag{4}$$

Considering that the amount of ions in the molten salt is much bigger than the one of the glass, the ion concentrations in the liquid source can be considered as constant, which allows deriving the relative concentration at the surface: Considering that the amount of ions in the molten salt is much bigger than the one of the glass, the ion concentrations in the liquid source can be considered as constant, which allows deriving the relative concentration at the surface:

$$\mathbf{x}\_s = \frac{\mathbf{K}\mathbf{x}\_B}{1 + \mathbf{x}\_B(\mathbf{K} - 1)},\tag{5}$$

*K* being the equilibrium constant of the chemical reaction (4) and *x<sup>B</sup>* = *C salt B* / *C salt <sup>B</sup>* + *C salt A* is the molar fraction of doping ions B<sup>+</sup> in the molten salt. being the equilibrium constant of the chemical reaction (4) and = ௦௧ ሺ ௦௧ + ௦௧ ⁄ ሻ is the molar fraction of doping ions B+ in the molten salt.

Since the refractive index is proportional to the relative concentration, according to (2), it is easy to fix the refractive index change at the glass surface by setting the ratio of B<sup>+</sup> ions in the liquid source. Figure 5 shows an experimental determination of this dependence for a silver/sodium ion-exchange on a Schott-BF33 glass. These data have been obtained by realizing highly multimode slab waveguides and retrieving their refractive index profile through m-lines measurements [23] and the Inv-WKB procedure [24,25]. Since the refractive index is proportional to the relative concentration, according to (2), it is easy to fix the refractive index change at the glass surface by setting the ratio of B+ ions in the liquid source. Figure 5 shows an experimental determination of this dependence for a silver/sodium ion-exchange on a Schott-BF33 glass. These data have been obtained by realizing highly multimode slab waveguides and retrieving their refractive index profile through m-lines measurements [23] and the Inv-WKB procedure [24,25].

**Figure 5.** Refractive index change measured at the surface of a Schott-BF33 glass for different AgNOଷ + ሺ1−ሻNaNOଷ molten salts at a temperature of 353 °C. **Figure 5.** Refractive index change measured at the surface of a Schott-BF33 glass for different *xB*AgNO<sup>3</sup> + (1 − *xB*)NaNO<sup>3</sup> molten salts at a temperature of 353 ◦C.

The ions exchanged at the glass surface entail a gradient of concentration inside the glass. Hence, B+ ions migrate inside the glass while A+ ions are moving towards the surface. Since the two species of ions have different mobilities, an internal electrical field ప௧ ሬሬሬሬሬሬሬ⃗ is created during the diffusion process. To this field an external applied field ሬሬሬሬሬሬሬሬሬ⃗ can be The ions exchanged at the glass surface entail a gradient of concentration inside the glass. Hence, B<sup>+</sup> ions migrate inside the glass while A<sup>+</sup> ions are moving towards the surface. Since the two species of ions have different mobilities, an internal electrical field −→ *Eint* is created during the diffusion process. To this field an external applied field −→ *Eapp* can be added, which results in ions fluxes −→ *J<sup>A</sup>* and −→ *J<sup>B</sup>* , for A<sup>+</sup> and B<sup>+</sup> , respectively, which are determined by the Nernst–Einstein equation:

$$\begin{aligned} \stackrel{\longrightarrow}{J\_A} &= -D\_A \left[ \stackrel{\rightarrow}{\nabla} \mathbb{C}\_A - \frac{\varepsilon}{\overline{H} \, k\_B T} \mathcal{C}\_A \left( \stackrel{\rightarrow}{E}\_{int} + \stackrel{\longrightarrow}{E}\_{app} \right) \right] \\ \stackrel{\longrightarrow}{J\_B} &= -D\_B \left[ \stackrel{\rightarrow}{\nabla} \mathbb{C}\_B - \frac{\varepsilon}{\overline{H} \, k\_B T} \mathcal{C}\_B \left( \stackrel{\rightarrow}{E}\_{int} + \stackrel{\longrightarrow}{E}\_{app} \right) \right] \end{aligned} \tag{6}$$

where *D<sup>i</sup>* is the diffusion coefficient of the ion i, *C<sup>i</sup>* its concentration, *e* is the electron charge, *k<sup>B</sup>* the Boltzmann constant, *T* the temperature and *H* the Haven coefficient. Assuming that all the sites left by ions A<sup>+</sup> are filled by ions B<sup>+</sup> , it can be written that at any position in the glass the relation *C<sup>A</sup>* + *C<sup>B</sup>* = *CA*0, where *CA*<sup>0</sup> is the concentration of A<sup>+</sup> ions before the exchange, is always valid. With this relation and Equation (6), the total ionic flux can be expressed as:

$$
\stackrel{\rightarrow}{J} = \stackrel{\rightarrow}{J\_A} + \stackrel{\rightarrow}{J\_B} = -D\_A \mathbb{C}\_{A0} \left[ a \stackrel{\rightarrow}{\nabla c} - \frac{e}{H k\_B T} (1 - ac) \left( \stackrel{\rightarrow}{E\_{int}} + \stackrel{\rightarrow}{E\_{app}} \right) \right] \tag{7}
$$

where the Steward coefficient *α* = 1 − *DB*/*D<sup>A</sup>* and the normalized concentration *c* = *CB*/*CA*<sup>0</sup> have been introduced.

If no electric field is applied, then the total current is null, which allows determining easily −→ *Eint*:

$$
\overrightarrow{E\_{\rm int}} = -\frac{Hk\_BT}{e}\frac{\overrightarrow{\alpha\nabla c}}{1-\alpha c} \tag{8}
$$

The second Fick's law implies that:

$$\frac{\partial \mathbb{C}\_B}{\partial t} = -\nabla \overline{J\_B} \,. \tag{9}$$

Combining (6), (8) and (9), the equation that governs the evolution of the relative concentration as a function of time is obtained:

$$\frac{\partial c}{\partial t} = \vec{\nabla} \left[ \frac{D\_B}{1 - ac} \vec{\nabla c} - \frac{eD\_B}{Hk\_B T} c \overrightarrow{E\_{app}} \right]. \tag{10}$$

Equation (10) can be solved numerically by Finite Difference or Finite Element schemes but for accurate modelling, the dependence of ionic mobility and diffusion on the concentration should not be neglected. The so-called mixed alkali effect plays indeed a significant role in ion-exchanges where a high doping concentration is required [26,27]. It must also be noticed that ion-exchange modifies the conductivity of the glass, which in turn, modifies the field distribution of −→ *Eapp*. Therefore, solving Equation (10) is actually much less obvious than it might appear and handling these problems has been the subject of a quite abundant literature [28–31]. Figure 6 displays typical refractive index profiles that have been obtained considering mixed alkali effect and the coupling between the ion-exchange and the applied electric field. Simulations have been done with an in-house software based on a finite difference scheme. It can be clearly seen how a proper choice of the experimental parameters can lead to circular waveguides. However, the maximum refractive index change is dropping from almost 0.1 to 10−<sup>2</sup> during the burial process because of the spreading of doping ions caused by thermal diffusion.

**Figure 6.** (**a**) Refractive index distribution of a thermally diffused waveguide, diffusion aperture width is 2 µm, exchange time is 2 min, *DB =* 0.8 µm2/min; (**b**) refractive index profile of the waveguide (**a**) after an electrically assisted burying in a pure NaNO3 molten salt, process duration is 1 h30 for an applied electric field of 180 kV/m. **Figure 6.** (**a**) Refractive index distribution of a thermally diffused waveguide, diffusion aperture width is 2 µm, exchange time is 2 min, *D<sup>B</sup>* = 0.8 µm2/min; (**b**) refractive index profile of the waveguide (**a**) after an electrically assisted burying in a pure NaNO<sup>3</sup> molten salt, process duration is 1 h30 for an applied electric field of 180 kV/m.

#### *2.3. Waveguide's Performances 2.3. Waveguide's Performances*

The main characteristics when dealing with integrated optics waveguides are their spectral operation range, their losses that can be split between coupling and propagation losses, and their behavior with respect to light polarization. The main characteristics when dealing with integrated optics waveguides are their spectral operation range, their losses that can be split between coupling and propagation losses, and their behavior with respect to light polarization.

#### 2.3.1. Passive Glasses 2.3.1. Passive Glasses

Since the first waveguides demonstrated by Izawa and Nakagome [1], huge efforts have been made to reduce the losses of the waveguides. Historically, scattering represented the main source of losses. Indeed, the quality of the photolithography used for the realization of the masking layer before the ion-exchange was an issue as well as scratches or dirt deposited on the glass surface or refractive index inhomogeneities, such as bubbles. These problems are typical optical glass issues that are encountered when a custom-made glass is realized for the first time in small volumes, but they are easily handled by glass manufacturers when a higher volume of glass is produced. Therefore, state-of-the-art ionexchanged waveguides are nowadays based on glass wafers specifically developed for this application or at least for microtechnologies. Among them, the more used are BF33 by Schott because of its compatibility with MEMS process, GO14 by TeemPhotonics SA and BGG31 by Schott [32], which have both been developed specifically for silver-sodium ion-exchanges. The interest of silver-sodium ion-exchange is that it allows the realization of buried waveguides solving, hence the problem of scattering due to surface defects or contaminations while dramatically improving the coupling efficiency with optical fibers. Nonetheless, silver-based technologies present also challenges since Ag+ has a strong tendency to reduce into metallic Ag creating metallic clusters that are absorbing the optical signals. The glass composition should therefore be adapted not only to remove reducing elements like Fe, As, or Sb, but also to create a glass matrix where Na+ ions are not linked to non-bridging oxygens [33]. The choice of the material for the masking layer should also be made with caution because the use of metallic mask can also induce the formation of Ag nanoparticles at the vicinity of the diffusion apertures [34]. Therefore, the use of Al or Since the first waveguides demonstrated by Izawa and Nakagome [1], huge efforts have been made to reduce the losses of the waveguides. Historically, scattering represented the main source of losses. Indeed, the quality of the photolithography used for the realization of the masking layer before the ion-exchange was an issue as well as scratches or dirt deposited on the glass surface or refractive index inhomogeneities, such as bubbles. These problems are typical optical glass issues that are encountered when a custom-made glass is realized for the first time in small volumes, but they are easily handled by glass manufacturers when a higher volume of glass is produced. Therefore, state-of-the-art ion-exchanged waveguides are nowadays based on glass wafers specifically developed for this application or at least for microtechnologies. Among them, the more used are BF33 by Schott because of its compatibility with MEMS process, GO14 by TeemPhotonics SA and BGG31 by Schott [32], which have both been developed specifically for silver-sodium ion-exchanges. The interest of silver-sodium ion-exchange is that it allows the realization of buried waveguides solving, hence the problem of scattering due to surface defects or contaminations while dramatically improving the coupling efficiency with optical fibers. Nonetheless, silver-based technologies present also challenges since Ag<sup>+</sup> has a strong tendency to reduce into metallic Ag creating metallic clusters that are absorbing the optical signals. The glass composition should therefore be adapted not only to remove reducing elements like Fe, As, or Sb, but also to create a glass matrix where Na<sup>+</sup> ions are not linked to non-bridging oxygens [33]. The choice of the material for the masking layer should also be made with caution because the use of metallic mask can also induce the formation of Ag nanoparticles at the vicinity of the diffusion apertures [34]. Therefore, the use of Al or Ti mask is now often replaced by Al2O<sup>3</sup> [35,36], SiO2, or SiN [37] ones.

Ti mask is now often replaced by Al2O3 [35,36], SiO2, or SiN [37]ones. Table 1 presents the main characteristics of single mode waveguides realized on GO14, BGG31, and BF33, respectively. GO14 and BGG31 that have been optimized for telecom applications and ion-exchange present very low propagation losses and birefringence that are key characteristics for data transmission. BF33 is not a glass that has been designed for ion-exchange but it is a relatively low-cost glass that presents a quite good Table 1 presents the main characteristics of single mode waveguides realized on GO14, BGG31, and BF33, respectively. GO14 and BGG31 that have been optimized for telecom applications and ion-exchange present very low propagation losses and birefringence that are key characteristics for data transmission. BF33 is not a glass that has been designed for ion-exchange but it is a relatively low-cost glass that presents a quite good refractive index

change and that is specifically indicated by its manufacturer for MEMS and microtechnology applications. Therefore, it is an excellent candidate for sensor realization and is mainly used for that. The relatively high propagation losses observed in BF33 is mainly due to the fact that this parameter is not very important in sensors and has, hence, neither been optimized nor measured accurately.


**Table 1.** Main characteristics of single mode waveguides realized on three different glasses.

We deliberately did not mention Tl+/K<sup>+</sup> ion-exchanged waveguides although the process is indeed the first one that has been used and the first one to be tentatively implemented in a production line. However, the advantages of a Tl+/K<sup>+</sup> ion-exchange, namely a high refractive index change and the absence of clustering and absorption, are strongly counterbalanced by its toxicity, which implies dedicated safety procedures and waste treatments. It is therefore very scarcely used.

#### 2.3.2. Active Glasses

The possibility of performing ion-exchange on rare-earth doped glasses was identified quite early. However, it was only in the 1990s with the development of WDM telecommunication that a lot of work was carried-out on the realization of efficient optical amplifiers and lasers. Because the solubility of rare earths into silicate glasses is quite low, which entails quenching due to clustering and reduces the amplifier efficiency, phosphate glasses rapidly emerged as the most efficient solution for obtaining high gain with compact devices. Among phosphate glasses, two specific references set the state of the art: they were the IOG 1 by Schott [41] and a proprietary glass referred as P1 by TeemPhotonics [42]. These two glasses succeeded in obtaining a high doping level without rare-earth clustering while being chemically resistant enough to withstand clean room processes and ion-exchange. The competition in the field of rare earth doped waveguides having been very hard, the characteristics of the different waveguides obtained in these glasses are difficult to find in the literature since the emphasis was mostly put on the active device performances, as will be detailed later.

#### 2.3.3. Exotic Substrates

Some exotic glasses like fluoride glasses [43] or germanate glasses [44,45] have also been used for the realization of ion-exchanged waveguides but the difficulty in making sufficiently good wafers available at a reasonable cost, strongly limited the research in these directions.

#### **3. Telecom Devices**

#### *3.1. Context and Historical Overview*

Optical Telecommunications was originally the reason why Miller introduced the concept of integrated optics in 1969 [46]. Therefore, the pioneering work of integrated photonics on glass has been mainly devoted to telecommunication devices pushing steadily towards the development of not only ion-exchange processes but also of a full technology starting from the wafer fabrication and ending with the packaging of the manufactured Planar Lightwave Circuits. Figure 7 shows this evolution by displaying on one side one of the first demonstrations of a 1 to 8 power splitter made by cascading multimode Yjunctions [47] and, on the other side, its 2006 commercially available counterpart, single mode and Telcordia 1209 and 1221 compliant [7,48].

**Figure 7.** 1 to 8 power splitter made by ion-exchange on glass (**a**) early demonstration in 1986; (**b**) qualified pigtailed and packaged commercially available product. **Figure 7.** 1 to 8 power splitter made by ion-exchange on glass (**a**) early demonstration in 1986; (**b**) qualified pigtailed and packaged commercially available product.

Once elementary functions, such as Y-junctions and directional couplers were demonstrated, studies were oriented towards all the functions that could be required for optical fiber communications like thermo-optic switches [49], Mach–Zehnder interferometers [50,51] and Multimode Mode Interference (MMI) couplers [52–55]. These buildings blocks have then been optimized and/or combined on a single chip to provide more functionality. In the next sections, we will review some of them and put the emphasis on the specificity brought by the use of ion-exchange on glass. Once elementary functions, such as Y-junctions and directional couplers were demonstrated, studies were oriented towards all the functions that could be required for optical fiber communications like thermo-optic switches [49], Mach–Zehnder interferometers [50,51] and Multimode Mode Interference (MMI) couplers [52–55]. These buildings blocks have then been optimized and/or combined on a single chip to provide more functionality. In the next sections, we will review some of them and put the emphasis on the specificity brought by the use of ion-exchange on glass.

#### *3.2. Wavelength Multiplexers 3.2. Wavelength Multiplexers*

small surface footprint [36].

mode and Telcordia 1209 and 1221 compliant [7,48].

A five-channel wavelength demultiplexer-multiplexer has been demonstrated as early as 1982 by Suhara et al. using silver multimode waveguides combined with a Bragg grating [56]. More advanced devices using single mode waveguides include Arrayed-Waveguide Grating (AWG) multiplexers, whose quite large footprint is compensated by their low sensitivity to the light polarization thanks to the use of silver based buried waveguides [38]. A good thermal stability provided by the thickness of the glass substrate is also reported but a fine thermal tuning of the AWG's response remained possible [57]. Add and drop multiplexing has been achieved by combining Bragg gratings with Mach– Zehnder interferometers or more originally with a bimodal waveguide sandwiched by two asymmetric Y-branches [58]. Bragg grating can be integrated on glass by etching [59], A five-channel wavelength demultiplexer-multiplexer has been demonstrated as early as 1982 by Suhara et al. using silver multimode waveguides combined with a Bragg grating [56]. More advanced devices using single mode waveguides include Arrayed-Waveguide Grating (AWG) multiplexers, whose quite large footprint is compensated by their low sensitivity to the light polarization thanks to the use of silver based buried waveguides [38]. A good thermal stability provided by the thickness of the glass substrate is also reported but a fine thermal tuning of the AWG's response remained possible [57]. Add and drop multiplexing has been achieved by combining Bragg gratings with Mach– Zehnder interferometers or more originally with a bimodal waveguide sandwiched by two asymmetric Y-branches [58]. Bragg grating can be integrated on glass by etching [59], wafer bonding [60], or photowriting [61–63].

wafer bonding [60], or photowriting [61–63]. Asymmetric Y-junctions are very interesting adiabatic devices that are well adapted to the smooth transitions between waveguides obtained by ion-exchange processes. Therefore, asymmetric Y-junctions have been used as stand-alone broadband wavelength multiplexers. For this type of applications, the asymmetry of the branches is obtained by a difference of the waveguide dimensions and a difference in their refractive index. Tailoring the refractive index of ion-exchanged waveguides can be achieved by segmenting the waveguide as demonstrated by Bucci et al. [64]. As can be seen on Figure 8, using vertical integration of deeply buried waveguides with selectively buried waveguides allowed obtaining a very broadband duplexing behavior while maintaining a relatively Asymmetric Y-junctions are very interesting adiabatic devices that are well adapted to the smooth transitions between waveguides obtained by ion-exchange processes. Therefore, asymmetric Y-junctions have been used as stand-alone broadband wavelength multiplexers. For this type of applications, the asymmetry of the branches is obtained by a difference of the waveguide dimensions and a difference in their refractive index. Tailoring the refractive index of ion-exchanged waveguides can be achieved by segmenting the waveguide as demonstrated by Bucci et al. [64]. As can be seen on Figure 8, using vertical integration of deeply buried waveguides with selectively buried waveguides allowed obtaining a very broadband duplexing behavior while maintaining a relatively small surface footprint [36].

**Figure 8.** Vertically integrated broadband duplexer (**a**) fabrication steps; (**b**) measured transmission (the insets display the observed device output's mode at specific wavelengths). Top and bottom branches are separated by 28 µm [36]. **Figure 8.** Vertically integrated broadband duplexer (**a**) fabrication steps; (**b**) measured transmission (the insets display the observed device output's mode at specific wavelengths). Top and bottom branches are separated by 28 µm [36].

#### *3.3. Waveguide Amplifiers and Lasers 3.3. Waveguide Amplifiers and Lasers*

Active devices have been linked to the development of ion-exchanged devices since the beginning of this technology. Indeed, Saruwatari et al. demonstrated in 1973 a laser made with an optical amplifier based on a buried multimode ion-exchanged waveguide realized in a neodymium-doped borosilicate glass [65]. However, research on active devices really became a major field of research with a strong competition at the beginning of the 1990s when a lot of studies were carried-out. Work was first concentrated on Nddoped amplifiers and lasers emitting at 1.06 µm since the four energy levels pumping scheme of this transition made it easier to achieve a net gain with the 800 nm pumping diodes available at the moment [66–70]. With the rise of Wavelength Division Multiplexing systems, optical amplifiers and sources operating in the C+L band (from 1525 nm to 1610 nm) became key devices and research on rare-earth doped integrated devices switched to the use of erbium ions whose transitions from the ଵଷ/ଶ <sup>ସ</sup> level to the ଵହ/ଶ <sup>ସ</sup> one is broad enough to cover this wavelength range. Dealing with Er3+ active ions, the main issue was to realize waveguides with low-losses and a good overlap of the pump and signal modes. Indeed, the pumping scheme of this rare earth being a three levels one, the ଵହ/ଶ <sup>ସ</sup> ground state absorbs the optical signal when it is not sufficiently pumped. Barbier et al. managed to solve this problem by developing a silver-sodium ion-exchange in their Er/Yb co-doped P1 glass [42]. 41 mm-long buried waveguides achieved 7 dB of net gain in a double pass configuration. This work has been followed by the demonstration of an amplifying four wavelength combiner [71] and the qualification of Erbium Doped Waveguide Amplifiers (EDWAs) in a 160 km-long WDM metro network [72]. This work has been completed by packaging and qualification developments in order to create Active devices have been linked to the development of ion-exchanged devices since the beginning of this technology. Indeed, Saruwatari et al. demonstrated in 1973 a laser made with an optical amplifier based on a buried multimode ion-exchanged waveguide realized in a neodymium-doped borosilicate glass [65]. However, research on active devices really became a major field of research with a strong competition at the beginning of the 1990s when a lot of studies were carried-out. Work was first concentrated on Nd-doped amplifiers and lasers emitting at 1.06 µm since the four energy levels pumping scheme of this transition made it easier to achieve a net gain with the 800 nm pumping diodes available at the moment [66–70]. With the rise of Wavelength Division Multiplexing systems, optical amplifiers and sources operating in the C+L band (from 1525 nm to 1610 nm) became key devices and research on rare-earth doped integrated devices switched to the use of erbium ions whose transitions from the <sup>4</sup> *I* 13/2 level to the <sup>4</sup> *I* 15/2 one is broad enough to cover this wavelength range. Dealing with Er3+ active ions, the main issue was to realize waveguides with low-losses and a good overlap of the pump and signal modes. Indeed, the pumping scheme of this rare earth being a three levels one, the <sup>4</sup> *I* 15/2 ground state absorbs the optical signal when it is not sufficiently pumped. Barbier et al. managed to solve this problem by developing a silver-sodium ion-exchange in their Er/Yb co-doped P1 glass [42]. 41 mm-long buried waveguides achieved 7 dB of net gain in a double pass configuration. This work has been followed by the demonstration of an amplifying four wavelength combiner [71] and the qualification of Erbium Doped Waveguide Amplifiers (EDWAs) in a 160 km-long WDM metro network [72]. This work has been completed by packaging and qualification developments in order to create a product line commercialized by TeemPhotonics.

a product line commercialized by TeemPhotonics. Meanwhile the phosphate glasses developed by Schott also gained a lot of attention. Patel et al. achieved a record high gain of 13.7 dB/cm in a 3 mm-long waveguide realized by a silver film ion-exchange [73]. Such a gain per length unit was made possible by a high Meanwhile the phosphate glasses developed by Schott also gained a lot of attention. Patel et al. achieved a record high gain of 13.7 dB/cm in a 3 mm-long waveguide realized by a silver film ion-exchange [73]. Such a gain per length unit was made possible by a high doping level of the glass in Er (8 wt. %) and Yb (12 wt. %).

doping level of the glass in Er (8 wt. %) and Yb (12 wt. %). Er-doped waveguide amplifiers being available, Er-doped lasers followed. Actually, the first proof of concept of an ion-exchanged waveguide laser was obtained on a modified BK7-silicate glass containing 0.5 wt. % of Er, with a potassium ion-exchange and two thin-film dielectric mirrors bonded to the waveguide's facets forming a Fabry-Perot cavity [74]. Nonetheless, from a strict point of view, this device was not a fully integrated laser because the mirrors were not integrated on the chip. Therefore, the next generation of Er-Er-doped waveguide amplifiers being available, Er-doped lasers followed. Actually, the first proof of concept of an ion-exchanged waveguide laser was obtained on a modified BK7-silicate glass containing 0.5 wt. % of Er, with a potassium ion-exchange and two thinfilm dielectric mirrors bonded to the waveguide's facets forming a Fabry-Perot cavity [74]. Nonetheless, from a strict point of view, this device was not a fully integrated laser because the mirrors were not integrated on the chip. Therefore, the next generation of Er-laser relied on the use of Bragg gratings as mirrors. In Distributed FeedBack (DFB) or Distribute Bragg

Reflectors configurations, these lasers presented a single frequency emission compatible with their use as transmitters in WDM systems. Similar for waveguide amplifiers, the use of phosphate glass entailed a major breakthrough in the performances. DBR lasers were demonstrated by Veasey et al. using a potassium ion-exchange [41], while Madasamy et al. manufactured similar devices with a silver thin film [75]. These approaches allowed integrating several lasers on a single chip to provide arrays of multiwavelength sources with one single grating, the wavelength selection being made by tuning the effective indices of the waveguides through their dimensions. Thanks to the use of highly concentrated molten salt of silver nitrate and a DFB configuration, Blaize et al. succeeded in creating a comb of 15 lasers with one single Bragg grating [76]. The emitters' wavelengths were spaced by 25 GHz and 100 GHz and set to be on the Dense WDM International Telecommunication Union (ITU) grid. The output power of these devices could be as high as 80 mW for a 350 mW coupled pump power [41], while a linewidth of only 3 kHz has been reported by Bastard et al. on their DFB lasers [77]. Figure 9 displays a picture of such a DFB laser pigtailed to HI1060 single mode fibers. The stability and purity of the emission of erbium doped waveguide lasers has been recently used to generate a Radio Frequency signal and successfully transmit data at a frequency of 60 GHz [78]. compatible with their use as transmitters in WDM systems. Similar for waveguide amplifiers, the use of phosphate glass entailed a major breakthrough in the performances. DBR lasers were demonstrated by Veasey et al. using a potassium ion-exchange [41], while Madasamy et al. manufactured similar devices with a silver thin film [75]. These approaches allowed integrating several lasers on a single chip to provide arrays of multiwavelength sources with one single grating, the wavelength selection being made by tuning the effective indices of the waveguides through their dimensions. Thanks to the use of highly concentrated molten salt of silver nitrate and a DFB configuration, Blaize et al. succeeded in creating a comb of 15 lasers with one single Bragg grating [76]. The emitters' wavelengths were spaced by 25 GHz and 100 GHz and set to be on the Dense WDM International Telecommunication Union (ITU) grid. The output power of these devices could be as high as 80 mW for a 350 mW coupled pump power [41], while a linewidth of only 3 kHz has been reported by Bastard et al. on their DFB lasers [77]. Figure 9 displays a picture of such a DFB laser pigtailed to HI1060 single mode fibers. The stability and purity of the emission of erbium doped waveguide lasers has been recently used to generate a Radio Frequency signal and successfully transmit data at a frequency of 60 GHz [78].

laser relied on the use of Bragg gratings as mirrors. In Distributed FeedBack (DFB) or Distribute Bragg Reflectors configurations, these lasers presented a single frequency emission

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 11 of 18

**Figure 9.** Picture of a DFB laser realized by silver-sodium ion-exchange on P1 phosphate glass at the IMEP-LaHC (device similar to [77]). **Figure 9.** Picture of a DFB laser realized by silver-sodium ion-exchange on P1 phosphate glass at the IMEP-LaHC (device similar to [77]).

Bragg gratings on phosphate glass can be made by photolithography steps and etching like in [41,76,77] or by direct UV inscription like in [79,80] and on IOG1. The use of a hybrid un-doped/doped IOG1 substrate allowed Yliniemi et al. [80] to realize UV-written Bragg gratings with high reflectance and selectivity, demonstrating hence a single frequency emission with an output power of 9 mW and a slope efficiency of 13.9%. Bragg gratings on phosphate glass can be made by photolithography steps and etching like in [41,76,77] or by direct UV inscription like in [79,80] and on IOG1. The use of a hybrid un-doped/doped IOG1 substrate allowed Yliniemi et al. [80] to realize UV-written Bragg gratings with high reflectance and selectivity, demonstrating hence a single frequency emission with an output power of 9 mW and a slope efficiency of 13.9%.

#### *3.4. Hybrid Devices 3.4. Hybrid Devices*

Ion-exchanged waveguides being made inside the glass wafer, they leave its surface plane and available for the integration of other materials or technologies. The realization of deeply buried waveguides [81] and selectively buried waveguides [82] acting as optical vias between two different layers increased furthermore the possibility of 3D integration. In order to overcome the quite weak chemical durability of an Yb-Er doped phosphate glass, Gardillou et al. [83] wafer bonded it on a silicate glass substrate containing surface Tl ion-exchanged strips. The higher refractive index active glass was then thinned by an appropriate polishing process to become a single mode planar waveguide. At the place where the planar waveguide was in contact with the ion-exchanged strips, the variation of refractive index provided the lateral confinement creating hence a hybrid waveguide. A gain of 4.25 dB/cm has been measured with this device. This approach has been pursued by Casale et al. [59] who realized a hybrid DFB laser combining a planar ion-exchanged waveguide made on IOG1 with a passive ion-exchanged channel waveguide realized on GO14. The Bragg grating was etched on the passive glass and encapsulated between the two wafers. Ion-exchanged waveguides being made inside the glass wafer, they leave its surface plane and available for the integration of other materials or technologies. The realization of deeply buried waveguides [81] and selectively buried waveguides [82] acting as optical vias between two different layers increased furthermore the possibility of 3D integration. In order to overcome the quite weak chemical durability of an Yb-Er doped phosphate glass, Gardillou et al. [83] wafer bonded it on a silicate glass substrate containing surface Tl ion-exchanged strips. The higher refractive index active glass was then thinned by an appropriate polishing process to become a single mode planar waveguide. At the place where the planar waveguide was in contact with the ion-exchanged strips, the variation of refractive index provided the lateral confinement creating hence a hybrid waveguide. A gain of 4.25 dB/cm has been measured with this device. This approach has been pursued by Casale et al. [59] who realized a hybrid DFB laser combining a planar ion-exchanged waveguide made on IOG1 with a passive ion-exchanged channel waveguide realized on GO14. The Bragg grating was etched on the passive glass and encapsulated between the two wafers.

Polymers have also been used to functionalize an ion-exchanged waveguide. As an example, a thin film of BDN-doped cellulose acetate deposited on the surface of ionexchanged waveguide lasers allowed the realization of passively Q-switched lasers on

Nd-doped [84] and Yb doped [85] IOG1 substrates. A peak power of 1 kW for pulses of 1.3 ns and a repetition rate of 28 kHz has been reported by Charlet et al. [86] and used successfully to pump a photonic crystal fiber and generate a supercontinuum [87].

Recently, a proof of concept of LiNbO<sup>3</sup> thin films hybridized on ion-exchanged waveguides have been reported [88]. The combination of these two well-known technological platforms for integrated photonics opens the route towards efficient low-loss non-linear integrated devices including electro-optic modulators.

Hybrid integration of semiconductor devices on glass wafers containing ion-exchanged waveguides have been reported for the first time in 1987, by MacDonald et al. [89] They bonded GaAs photodiodes on a metallic layer previously deposited and patterned on the glass wafer. Waveguides were done by a silver thin film dry process. Silicon [90] and germanium [91] photodetectors have been produced on potassium waveguides, while Yi-Yan et al. proposed a lift-off approach to bound thin III-V semiconductor membranes on the surface of a glass wafer containing ion-exchanged waveguide and realize Metal– Semiconductor–Metal (MSM) photodetectors [92].

#### **4. Sensors**

Integrated photonics is intrinsically interesting for the realization of optical sensors because it provides compact and reliable self-aligned devices that can be easily deported when pigtailed to optical fibers. Glass is a material that is chemically inert, bio-compatible, and mechanically stable. Therefore, making optical sensors on glass wafers or integrating optical glass chips into complex set-ups have encountered a huge interest. We will detail here a selection of ion-exchanged based glass sensors as examples of possible applications.

Although AWGs used in telecom are actually integrated spectrometers, they are not well adapted to the rapid measurement of full spectra. For this reason, a Stationary-Wave Integrated Fourier-Transform Spectrometer (SWIFTS) has been proposed and developed [93]. It is a static Fourier Spectrometer that measures directly the intensity of a standing wave with nanoprobe placed on a waveguide. In the instrument reported by Thomas et al. [94], the waveguide is made by a silver ion-exchange on a silicate glass and the nanoprobes are gold nanodots. The interaction of gold nano-antennas with an ion-exchanged waveguide has been studied by Arnaud et al. [95]. This spectrometer has a spectral measurement range that starts at 630 nm and ends at 1080 nm with a spectral resolution better than 14 pm. SWIFTS interferometers are currently integrated in the product line commercialized by Resolution Spectra Systems [96].

Displacement sensors allow measuring accurately the change of position of an object through interferometry. Helleso et al. [97] implemented a double Michelson interferometer on a glass substrate using potassium ion-exchange; the device provided two de-phased outputs in order to give access not only to the distance of the displacement but also its direction. However, having only two interferometric signals is not sufficient to prevent the measure from being affected by unexpected signal variations. For this reason, Lang et al. [98] proposed a new design for the interferometric head that provided four quadrature phase shifted outputs. The device made by potassium ion-exchange demonstrated a measurement accuracy of 79 nm over a measurement range of several meters when used with an HeNe laser as a source. After technological improvements and the use of a silversodium ion-exchange on GO14 glass, an evolution of this sensor is now commercialized by TeemPhotonics and presents a resolution of 10 pm for a 1530 nm–1560 nm operating wavelength range [48].

Measuring speed is also something that can be of major importance, specifically in the case of aircrafts where their True Air Speed (TAS), which is their speed with respect to the air surrounding them, conditions their lift. Airborne LIDARs have hence been developed as a backup to Pitot gauges in order to increase the safety of flight by providing a redundant accurate measurement of the aircraft TAS. The operation principle of an airborne LIDAR is based on the Doppler frequency shift measured on a laser signal reflected on the dust particles of the atmosphere. This shift being quite low and presenting a low amplitude

when compared to the emitted signal, a laser source that presents a narrow linewidth, a low Relative Intensity Noise and that is resilient to mechanical vibrations is required. Bastard et al. [99] realized such a laser source on an Er/Yb doped phosphate glass with silver ion-exchanged waveguides and a DFB structure. This laser presented a fiber coupled output power of 2.5 mW, a linewidth of 2.5 kHz, and a RIN that was 6 dB lower than the specification limit. The device has then been successfully implemented in the LIDAR set-up and validated in flight [100]. amplitude when compared to the emitted signal, a laser source that presents a narrow linewidth, a low Relative Intensity Noise and that is resilient to mechanical vibrations is required. Bastard et al. [99] realized such a laser source on an Er/Yb doped phosphate glass with silver ion-exchanged waveguides and a DFB structure. This laser presented a fiber coupled output power of 2.5 mW, a linewidth of 2.5 kHz, and a RIN that was 6 dB lower than the specification limit. The device has then been successfully implemented in the LIDAR set-up and validated in flight [100].

a redundant accurate measurement of the aircraft TAS. The operation principle of an airborne LIDAR is based on the Doppler frequency shift measured on a laser signal reflected on the dust particles of the atmosphere. This shift being quite low and presenting a low

*Appl. Sci.* **2021**, *11*, x FOR PEER REVIEW 13 of 18

Astrophysical research programs rely on telescopes with always higher resolution to detect exoplanets, young star accretion disks, etc. Optical long baseline instruments, which interferometrically combine the signal collected by different telescope have been developed for this purpose. Such complex interferometers are very sensitive to misalignment and vibrations, therefore the use of integrated optics as telescope recombiners have been studied. Haguenauer et al. [101] used a silver-sodium ion-exchange on a silicate glass to realize a two telescope beam combiner operating on the H atmospheric band (from λ = 1.43 µm to λ = 1.77 µm). Consisting of a proper arrangement of three Y-junctions, the device had two photometric and one interferometric outputs. The fringe contrast obtained in the laboratory was 92% and the device was included in the Integrated Optic Near infrared Interferometric Camera (IONIC) put into a cryostat and successfully qualified on the sky [102]. Figure 10 shows the MAFL chip [103] that was developed for the interferometric combination of three telescopes. The pigtailed instrument contained not only the science interferometers but also three other ones dedicated to metrology, which permitted measuring of the different optical paths. The functions multiplexing and demultiplexing the metrology signal and the science ones were also implemented on the chip. Astrophysical research programs rely on telescopes with always higher resolution to detect exoplanets, young star accretion disks, etc. Optical long baseline instruments, which interferometrically combine the signal collected by different telescope have been developed for this purpose. Such complex interferometers are very sensitive to misalignment and vibrations, therefore the use of integrated optics as telescope recombiners have been studied. Haguenauer et al. [101] used a silver-sodium ion-exchange on a silicate glass to realize a two telescope beam combiner operating on the H atmospheric band (from λ = 1.43 µm to λ = 1.77 µm). Consisting of a proper arrangement of three Y-junctions, the device had two photometric and one interferometric outputs. The fringe contrast obtained in the laboratory was 92% and the device was included in the Integrated Optic Near infrared Interferometric Camera (IONIC) put into a cryostat and successfully qualified on the sky [102]. Figure 10 shows the MAFL chip [103] that was developed for the interferometric combination of three telescopes. The pigtailed instrument contained not only the science interferometers but also three other ones dedicated to metrology, which permitted measuring of the different optical paths. The functions multiplexing and demultiplexing the metrology signal and the science ones were also implemented on the chip.

**Figure 10.** Picture of the MAFL combining module. The optical chip contains waveguides made by a silver sodium ion-exchange. **Figure 10.** Picture of the MAFL combining module. The optical chip contains waveguides made by a silver sodium ion-exchange.

The chemical durability of silicate glasses is a major advantage when a use in harsh environment is required. The opto-fluidic sensor developed by Allenet et al. [104] represents a quite extreme example of this. Indeed, the ion-exchange technology developed by Schimpf et al. [35] on BF33 glass has been employed to realize a sensor for the detection of plutonium in a nuclear plant environment. The fully pigtailed and packaged device that is depicted on Figure 11, has been successfully tested in a nuclearized glove box, detecting plutonium dissolved in 2 Mol nitric acid without a failure over a period of one month. Such a reliability was achieved by co-integrating microfluidic channels fabricated by HF wet etching on one BF33 wafer with silver ion-exchanged waveguides realized on The chemical durability of silicate glasses is a major advantage when a use in harsh environment is required. The opto-fluidic sensor developed by Allenet et al. [104] represents a quite extreme example of this. Indeed, the ion-exchange technology developed by Schimpf et al. [35] on BF33 glass has been employed to realize a sensor for the detection of plutonium in a nuclear plant environment. The fully pigtailed and packaged device that is depicted on Figure 11, has been successfully tested in a nuclearized glove box, detecting plutonium dissolved in 2 Mol nitric acid without a failure over a period of one month. Such a reliability was achieved by co-integrating microfluidic channels fabricated by HF wet etching on one BF33 wafer with silver ion-exchanged waveguides realized on another wafer. The two wafers have been assembled by molecular adherence avoiding hence the use of radiation sensitive epoxy glues.

hence the use of radiation sensitive epoxy glues.

**Figure 11.** Picture of an optofluidic sensor realized on BF33 glass wafer for the measurement of radioactive elements diluted in highly concentrated nitric acid. **Figure 11.** Picture of an optofluidic sensor realized on BF33 glass wafer for the measurement of radioactive elements diluted in highly concentrated nitric acid.

another wafer. The two wafers have been assembled by molecular adherence avoiding

#### **5. Conclusions 5. Conclusions**

In this paper, we reviewed over thirty years of activities in glass photonics. The ionexchange realization process as well as its modelling has been exposed. Passive and active devices for telecommunication applications have then been presented with the emphasis on the major breakthroughs of this field. The section dedicated to sensors underlines the evolution of the ion-exchange technology, which is moving from quite simple, though extremely performant functions, to more complex integrated optical microsystems. The authors hope that the picture of glass photonics that they presented will soon be outdated by the new results that are currently being elaborated in the many laboratories of universities and companies involved in this field throughout the world. In this paper, we reviewed over thirty years of activities in glass photonics. The ionexchange realization process as well as its modelling has been exposed. Passive and active devices for telecommunication applications have then been presented with the emphasis on the major breakthroughs of this field. The section dedicated to sensors underlines the evolution of the ion-exchange technology, which is moving from quite simple, though extremely performant functions, to more complex integrated optical microsystems. The authors hope that the picture of glass photonics that they presented will soon be outdated by the new results that are currently being elaborated in the many laboratories of universities and companies involved in this field throughout the world.

**Funding:** The visit of Pr Broquin at the University of Eastern Finland is funded by the Nokia Foundation within the frame of the Institut Français de Finlande—Nokia Foundation Distinguished Chair. This work is also part of the Academy of Finland Flagship Programme, Photonics Research and Innovation (PREIN), decision 320166. **Funding:** The visit of Pr Broquin at the University of Eastern Finland is funded by the Nokia Foundation within the frame of the Institut Français de Finlande—Nokia Foundation Distinguished Chair. This work is also part of the Academy of Finland Flagship Programme, Photonics Research and Innovation (PREIN), decision 320166.

**Institutional Review Board Statement:** Not applicable. **Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable. **Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest. **Conflicts of Interest:** The authors declare no conflict of interest.

#### **References References**

