*2.2. Waveguides*

Waveguides for sensing, including those for WERS and WIRS, have been evolving to guarantee minimum losses and high light–analyte interaction. Losses can be divided into the absorption of the material, leakage to the substrate, bending losses, and scattering losses due to fabrication or material imperfections (inhomogeneity or crystal grains). To minimize them, a proper choice of both the material and the waveguide design is crucial.

Aside from the transparency of the waveguide material in the targeted wavelength range, refractive index, photo-stability up to high intensities, low level of fluorescence or Raman background, toxicity, availability/cost, and ease of production are the main selection criteria. From the great variety of materials proposed, materials compatible with CMOS/mass production, such as silicon, germanium, silicon oxide and silicon nitride, are the most common [56]. Nevertheless, a wide range of other materials has been reported, including polymers (i.e., photoresists and Teflon) [57], halides, chalcogenides (i.e., CaF2, NaBr and ZnSe) [28,58], oxides (i.e., alumina, titania and tantala) [59,60], diamond (due to its advantages for quantum photonics) [61,62], or InGaAs [63]. Recently, a review on waveguide materials has been published by Yadav and Agarwal [64].

Doped silica (UV-written) and silicon nitride over a silica bottom cladding have been the main materials used for on-chip waveguiding in the visible- to the NIR range; however, alternatives such as tantalum pentoxide have recently emerged. These materials have also been used, to a lesser extent, in the MIR, despite the presence of residual O-H and N-H groups that limit their transparency in certain frequency bands. For MIR applications, silicon on silica (i.e., silicon-on-insulator, SOI) and, less frequently due to increased costs, germanium on silica (germanium-on-insulator, GOI), have been the materials of choice due to their transparency at longer wavelengths. SiGe alloys possess the highest refractive indices of all the CMOS-compatible materials mentioned above and can, in addition, be doped in order to tailor their refractive index. The high refractive index has also been shown to be highly useful in avoiding mode leakage into the substrate, enhancing the electric field at the waveguide interface and, thus, the light–analyte interaction. Besides SOI and GOI, silicon on nitride, silicon on alumina, and germanium on silicon (or silicongermanium alloy on silicon) have been proposed as novel waveguide alternatives in MIR, due to their capability of avoiding absorption by silica bottom cladding, especially above 3.5 μm [65,66]. Diamond also appeared recently on the scene as an ideal material with a

transparency range from 0.22–20 μm; nevertheless, its applications are limited due to the difficulty of processing and high cost [67].

The processing of these materials into photonic waveguides has also developed greatly during the last decades, not only to account for more complex designs and profiles but additionally to decrease losses. While the homogeneity of the materials is highly dependent on the deposition technique and post-treatment, the surface and mainly the sidewall roughness are subject to the etching protocol that is followed. The former will decrease bulk scattering, the latter, the surface scattering. A great number of deposition and etching protocols are already available in the literature and depend greatly on the materials, the etch rate, selectivity and profiles, or the design. We will not go further into the topic, but we do encourage our readers to find further information in the work of William et al. [68].

Finally, the waveguides' design is crucially important when high sensitivity to the surrounding environment is targeted. Unlike waveguides developed for communication purposes, waveguides for gas sensing need to ensure high light–analyte interaction, assuming the strong presence of the optical field outside the solid waveguide core. The amount of this interaction can be described using the evanescent field confinement factor, Γ, which is defined as in [69]:

$$
\Gamma = \left(\frac{\mathbf{n\_g}}{\mathrm{Re}\{n\_{cl}\}}\right) \iint\_{cl} \frac{\varepsilon |E|^2 dx dy}{\iint\_{-\infty}^{\infty} \varepsilon |E|^2 dx dy} \tag{1}
$$

The absorption along the waveguide length is then given by a modified Lambert-Beer law:

$$I = I\_0 \exp\left[-\alpha \Gamma \ L\right] \tag{2}$$

Here, ng is the group index, *ncl* is the cladding's refractive index (equal to approx. 1 in the air), ε(*x*, *y*) is the permittivity, *E*(*x*, *y*) is the electric field, *α* is the bulk absorption, and *L* is the length of the waveguide. It is important to stress that the absorption not only depends on the evanescent field fraction but also on the waveguide dispersion through the group index ng. Reporting only the evanescent field fraction and omitting the effect of dispersion is a common misconception in the literature, making it difficult to quantify and compare the light–analyte interaction across the different waveguide platforms reported in the literature.

Besides the confinement factor Γ, the sensitivity of the waveguide is also determined by the physical path-length of the waveguide *L* that is typically limited by the waveguide loss. Therefore, the ratio between the evanescent field confinement factor and the propagation loss was introduced by Kita et al. [70] as an additional figure of merit that fully determines the sensing performance of the waveguide. Both the confinement factor and the losses will be dependent on the material and the processing, as well as on the waveguide design [71].

The most common waveguides reported for sensing can be classified into five different designs: rib, strip, slot waveguides, sub-wavelength gratings and photonic waveguides [72]. Rib and strip waveguides can be realized swiftly in one step with UV lithography and easyetching protocols. The former is characterized by a shallow step defining the waveguide, with a small side-wall area and, therefore, little surface scattering compared to other designs. The strip waveguide (Figure 1a) is etched all the way down to the bottom cladding and exhibits more scattering loss but, unlike rib waveguides, it allows scientists to confine light tightly in the horizontal axis, resulting in minimal bending loss. According to Kita et al., who compared the performance of strip, rib, and slot waveguides for sensing, the strip waveguide is the preferred geometry for bulk absorption sensing and refractometry and is comparable in performance to other, more complicated, geometries for surface-sensitive refractometry and absorption sensing [70].

**Figure 1.** Different waveguide designs reported for WIRAS: (**a**) Strip, slot and subwavelength grating waveguides (SWG) (reproduced with permission from reference [70] © 2021 Optical Society of America). (**b**) Suspended subwavelength grating waveguide and (**c**) suspended photonic crystal waveguide. The insets show SEM images of the fabricated structures (reprinted with permission from reference [63], copyright 2020 American Chemical Society). (**d**–**f**) Suspended waveguides on pedestals; the inset in image (**e**) shows the cross-section and the electrical field distribution (reproduced with permission from reference [73], (© 2021 Optical Society of America). (**g**) Schematic and SEM image of a self-standing rib waveguide. (**h**) Simulated confinement factor of the waveguide in (**g**) at TM and TE polarizations, as a function of layer thickness, while the inset shows the electric field distribution at a thickness of 350 nm. Reproduced from reference [69], licensed under a Creative Commons Attribution 4.0 International License http://creativecommons.org/licenses/by/ 4.0/ assessed on 9 September 2021.

Slot, subwavelength grating (SWG), and photonic crystal waveguides have been reported as alternative designs that are capable of increasing the interaction with the surroundings by several times. Slot waveguides consist of two strips of high-refractive-index materials, separated by a subwavelength-scale low-refractive-index slot region that strongly confines light (Figure 1a). This design presents a light–analyte interaction more than 5 times larger than strip waveguides, which is highly desirable for gas sensing, while material losses are reduced due to the low intensity of the electric field in the material [70,74,75]. This design presents a good compromise between simplicity, air confinement factor, losses, and costs, and has been tested experimentally many times for both IR and Raman spectroscopy [76,77]. Despite the advantages, this design requires electron beam lithography in most cases to pattern the slot, which is typically of the order of 100 nanometers, and additional care needs to be taken during etching to guarantee a well-defined slot and little roughness [78].

A SWG waveguide (Figure 1a,b) is based on a periodic arrangement of two different materials having a period that is much smaller than the wavelength of light. It is characterized by field distribution with an air confinement factor 4–5 times higher compared to the strip waveguide [70]. Although, theoretically, no losses are expected from the design, the experimental propagation loss is normally above 2 dB/cm, due to imperfections arising during fabrication, particularly surface roughness and variability in the size of the waveguide segments [79].

Photonic crystal waveguides are distinguished by their ability to slow down light, i.e., to reduce the group velocity of the propagating waveguide mode as a result of coherent scattering on the photonic crystal lattice. Group velocity reduction by factors of between 1.5 and approx. 100 have been reported, and a corresponding increase in the interaction with the analyte has been observed in sensing experiments, both at NIR [80] and MIR wavelengths [81]. These waveguides are commonly formed by a linear defect in a photonic crystal lattice, patterned into a high-index dielectric membrane (see Figure 1c). The main drawback can be attributed to the difficulty of fabrication, a sensitivity to disorder that may lead to spectrally uneven enhancement, and an increased surface area that brings greater surface scattering and reflections [82]. Using slow light increases analyte-field interaction but, at the same time, it increases the interaction with the material, including absorption and scattering. In most demonstrations, the waveguide lengths are thus limited to hundreds of micrometers or, at most, millimeters.

To improve the light–analyte interaction even further, the bottom cladding can be removed either partially or completely. Partial bottom cladding removal was used to realize air-suspended waveguides supported by pedestals [49,83] or pillars [73,84] (Figure 1d–f). Complete cladding removal results in self-standing rib waveguides (Figure 1g), subwavelength grating waveguides (Figure 1b) [85], and photonic crystal waveguides (Figure 1c) [63]. Air-suspended structures appeared recently in the literature, exhibiting the largest reported confinement factors surpassing 100% (Figure 1h) [69] and reduced propagation losses [69,73]. By etching away the material beneath the waveguide, absorption due to the bottom cladding can be completely removed, leakage to the substrate avoided, and the volumetric interactions with the surrounding analyte increased [86]. Additionally, the lack of bottom cladding is well-suited for TM polarization which, in thin suspended waveguide designs, has minimal electric field overlap with the core material. This further increases the evanescent field confinement and decreases losses attributed to absorption in the constituent materials. Despite these advantages, the waveguide processing is complex and requires several lithography and etching steps; the structures are rather fragile, necessitating careful handling; and monolithic integration with laser sources and detectors appears more challenging than for waveguides supported by solid bottom cladding.

In order to achieve the lowest possible detection limits, the increase in sensitivity has to go hand-in-hand with the reduction of noise. An important noise source in integrated photonic circuits is a so-called interferometric noise, arising due to reflections from facets or defects, manifesting itself as spectral fringing in transmission. Such noise may interfere significantly with the recorded spectrum. For this purpose, antireflection

coatings on the waveguide facet [87], the use of subwavelength gratings on the waveguide facet [88], or the use of appropriate signal processing algorithms [89] have been proposed to reduce the effect of the fringes. Substantial fringe reduction has also been achieved in air-suspended waveguides, characterized by strongly delocalized guided modes with an effective mode index close to unity. This automatically minimizes reflections at the facets or structural defects of the waveguide, leading to clear spectral transmission that is free from interferometric noise [69].

Another important point to consider in the context of high-index contrast waveguides for IR absorption spectroscopy is the possibility of saturation of the absorption signal, due to the intrinsically high intensity of the strongly confined guided modes. This typically occurs at high laser powers, in combination with intense absorption lines, where the excitation rate of the molecules can become faster than their relaxation rate [90]. To date, the literature mentions only sporadically the effects of saturation in waveguides, and detailed theoretical description is entirely absent. However, a waveguide design with a strongly delocalized field would mitigate this effect.
