**1. Introduction**

Wearable interferometric sensors require a small size, high selectivity, and sensitivity if biomedical applications are envisaged. These three requirements often involve counterrunning demands and have previously been found to be difficult to satisfy in a single system. Such a limitation is also relevant in many other application fields of photonic methodologies: highly accurate metrology; health and environmental monitoring; food sensing; quality control in industrial fabrication; smart personal environments; and high data rate communication technologies. Wearable interferometric sensors are characteristically lightweight with a small footprint as a result of miniaturization, which at the same time enables low-cost, precision, and high efficiency. Photonic sensorics [1–10] enable extraordinary sensitivity, outstanding selectivity, and broad application fields [1] such as industrial production control, environmental trace gas detection, agriculture growth monitoring, medical prevention and medical diagnosis, and fiber optic communication technologies. Many of the optical sensors use fiber or optical waveguide technology and are already integrated in communication systems, with high

Hillmer, H.; Woidt, C.;Kobylinskiy, A.; Kraus, M.; Istock, A.; Iskhandar, M.S.Q.; Brunner, R.; Kusserow, T. Miniaturized Interferometric Sensors with Spectral Tunability for Optical Fiber Technology—A Comparison of Size Requirements, Performance, and New Concepts. *Photonics* **2021**, *8*, 332. https://doi.org/10.3390/ photonics8080332

**Citation:**

Received: 28 June 2021 Accepted: 26 July 2021 Published: 13 August 2021

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potential for future integration in wearable interferometric sensors or in devices used for smart personal environments. However, a key challenge remains that of combining their outstanding performance in terms of resolution and efficiency while being miniaturized as much as possible at the same time.

In this review, methodologies of optical sensing in the near-infrared (NIR), visible (VIS), and ultraviolet (UV) spectral wavelengths ranges are introduced. This review also refines one of our recent papers [11], extending it toward integration into optical fiber technology and the improvement of the estimation of minimum size requirements, as well as formulates new insight into tunability efficiency.

A systematic overview of the different spectroscopic sensing principles is shown as a block diagram in Figure 1. In principle, the wide variety of sensor types can be categorized into different schemes. From a physical point of view, classification in accordance with the optical working principles is appropriate. For potential economic exploitation, classification with respect to robustness, complexity, recording and analyzing speed, potential applicability for high volume manufacturing, and the consideration of price aspects would be rather helpful. The block diagram shown here distinguishes in the first level between different optical working principles and focuses in the second level on sensor concepts that are particularly suitable for miniaturization and compatible with waveguide technology. The sensor concepts listed in the bottom row are considered in detail in this contribution.

**Figure 1.** Block diagram of the sensor and spectrometer types considered in this review. This diagram should provide a general overview and an orientation throughout this extensive paper.

Traditional optical spectrometers [4,8–10] use prisms or gratings as dispersive or diffractive elements to dissolve the studied optical information into a spectrum (intensity versus wavelength plot). A transmission grating is depicted in Figure 2. As a general rule, a higher grating order means higher resolution; however, unfortunately, this also means a smaller intensity. To overcome this major disadvantage, the gratings are often blazed (exhibiting e.g., a saw-tooth structure) to transform the desired highest intensity from the zero order into higher diffraction orders [4]. This enables a rather high resolution and a relatively high intensity to be achieved at the same time.

**Figure 2.** Schematic design of a transmission grating spectrometer with a symbolic grating shape.

There are different options to miniaturize the sensors, and Micro-Electro-Mechanical Systems (MEMS) represent one miniaturization option that enables wavelength tuning. In particular, FP and photonic crystal sensor systems or grating spectrometers can be miniaturized using MEMS. Actuation in MEMS-based devices was demonstrated for different material systems and wavelength ranges using different methodologies such as thermal, electromagnetic, piezoelectric or electrostatic actuation methodologies. Even in traditional grating spectrometers, MEMS can be applied to rotate the grating [12–15] and enable good performance.

More advanced methodologies use interferometry [3,4,16–20] for optical sensing based on the Mach–Zehnder, Fabry–Pérot, Michelson, and Sagnac principle. Additionally, there are many others which are closely related to these concepts. In the Michelson interferometer [3,4] the incident light beam (input) is split into two parts that are reunified again at a later stage before reaching the photodiode sensor as the output beam. Precisely delaying one of the two beams generates a distinct phase shift, though a proper calibration has to be completed before using the interferometric sensor. Next, the interferogram (intensity as a function of the varying phase delay) is converted into the wavelength range, thus, delivering the spectrum of the input. The smaller the considered light wavelength, the higher mechanical precision required to obtain the phase shifts. Therefore, the involved mechanics is less complex in the NIR compared to the VIS range. Fourier spectroscopy [3] uses the Michelson interferometer in the NIR, in which the interferogram is the Fourier transform of the input signal [3].

The input beam is also separated into two branches in the Mach-Zehnder interferometer [19,20]. Likewise, the two waves propagating through the branches experience different optical path lengths (defined as the product of refractive index and physical length). The two beams are then reunified, and the varying phase shifts between the two beams result in different corresponding intensities of the output beam. Integrated Mach-Zehnder interferometers can be implemented using ridge or embedded waveguides. Today, integrated Mach-Zehnder interferometers are often applied as modulators or sensors and were demonstrated in many various materials such as Si, InP, LiNbO3, dielectric materials, inorganic glass, organic glass and polymers. By integrating a plate capacitor to one of the waveguide branches, the effective refractive index of that waveguide branch can be tuned via the capacitor voltage (i.e., the variable electrical field), making use of the electrooptic effect. Tuning the voltage produces an interferogram, and Fourier transforming the interferogram gives the spectra. A very important variant of the Mach-Zehnder interferometer is the derived arrayed waveguide grating (AWG) [21–27]. The AWG and Mach-Zehnder interferometers are perfectly adapted for use in fiber optical systems. Therefore, the AWG represents a significant waveguide-based sensor type and a basic device in dense wavelength division multiplex (DWDM) systems for present high-speed and high bitrate optical data and telecommunication systems. More than 100 waveguide branches of tailored lengths can be combined in an AWG. These interferometric devices are also named phased arrays. Yoshikuni et al. have contributed pioneering work in the field of AWGs for fiberoptic telecommunication in the 1.5 μm communication bands, in which channel spacings of 50 GHz were achieved [22–24]. AWG consist of *M* waveguides (related to *M* fiberoptic DWDM channels) of different optical path lengths which are introduced not by the effective refractive index, but by the varying physical lengths. The individually tailored lengths lead to distinct phase shifts at the output of the different waveguides. The waveguide couples the waves out into a free beam section in which (mode) confinement is only given by a vertical waveguide structure. At the opposite end of the free beam section, light constructively interferes only at specific positions. Another *M* waveguides are beginning exactly at these positions, representing the output ports. The waveguides are spectrally ordered. Therefore, each individual output waveguide only guides light in an interval of Δ *λi* with a central wavelength *λi* (vacuum wavelength), where *i* = 1 ... *M*. These Mach-Zehnder and AWG sensors constitute a second interferometric sensor design.

The third sensor design, based on the Fabry-Pérot (FP) principle [4,28–58], uses also interferometric methodologies and is well suitable for fiberoptic sensors. Although no beam splitters are involved and only two transparent dielectric parallel mirrors are present, the FP interferometer involves multipath interference and is highly complex. The important optical element embedded between the two mirrors is the FP cavity. Inside the FP interferometer cavity, some wavelengths are dimensioned in a way that they can constitute standing light waves, and thus fulfilling the FP condition. For a vacuum (air) cavity and two perfectly flat metal mirrors embedding the cavity, the condition can be described by a simple formula: a multiple of half of the vacuum wavelength equals the cavity length. These explicit standing wavelengths are the cavity modes. However, in real conditions which have to be considered in interferometric sensorics, the modes (standing waves) penetrate into the dielectric mirrors. Even by replacing the vacuum wavelength in the FP condition with the wavelength in the medium (vacuum wavelength divided by the cavity refractive index), it is still a very rough approximation. This phenomenon is detailed later in Section 10. The wavelength of each specific mode (standing wavelength) passes the interferometer nearly unattenuated (almost 100% of the input intensity). It is quite common to refer to FP interferometers as FP filters, where the modes are also defined as FP filter lines. The reason for a specific wavelength passes the filter unattenuated and unreflected is due to constructive interference of all multipath waves at the FP output. All the remaining wavelengths which do not constitute modes experience destructive interference at the output. They are reflected by the FP filter and show constructive interference in the reflected beam. By shifting one of the mirrors precisely parallel along the optical axis, the corresponding spectrum, i.e., a spectral tuning of the wavelength, is obtained. Therefore, this interferometer also constitutes a spectrometer. By applying MEMS technology, wavelength tuning can be obtained by displacing one or both mirrors using MEMS actuation [37–57].

Adding optical substructures in the nanometer range onto membranes or cantilevers of MEMS offers further options to optimize the optical sensor assets. As the substructure size is roughly a factor of 100 below the typical dimensions of MEMS membranes or cantilevers, an integration of substructures is not affecting the general contour or functionality of these MEMS sensors. Often, 1D or 2D photonic crystal (PC) structures are integrated into membranes to enable specific guided mode resonances (GMR) [59,60]. In this case, the released MEMS layer is a slab waveguide with light waves incident in normal direction to the interfaces of the slab. Without integrating a PC structure, the free space mode is not able to couple to a guided mode in the slab. In contrast, it will be reflected and transmitted at each interface, constituting a typical thin-film spectrum. If a grating pattern with a period in the range of the desired wavelength range is added, this will lead to resonant coupling

of a part of the incident wave into a leaky mode inside the slab. Because of its leaky nature, the mode will couple back—out of the slab—into both vertical directions and superimpose with the residual incident and transmitted free space mode (known as continuous mode). This results in a filter resonance line with Fano characteristics, both in transmission and reflection [61]. If the resonant coupling conditions are tailored appropriately, line shape and spectral width are influenced. Narrow linewidths are accomplished by applying low coupling strengths, while broadband reflections can be obtained using strong coupling and applying an overlap of several individual resonances. Sensors using the GMR can be strongly miniaturized [62] since they replace vertical periodic patterns of distributed Bragg reflectors (DBR) by horizontal pattern inside a single membrane. This means that they translate full FP filters into a narrowband Fano resonance of a PC slab. However, their fabrication and application are a real challenge due to their strong angle dependency. Therefore, use of very flat membranes or cantilevers is crucial, but this effect also restricts the acceptable angular spectrum of the incident light beam. As a consequence, the spot diameter and related divergence which can be used are restricted.

If the axial symmetry of 90◦ is disturbed in the PC-based sensors or in the sensor lattice itself, altered conditions are obtained for in- and out-coupling along the x- and y-direction, thus enabling further polarization selectivity of the sensor element. In the simplest case, this is obtained by a line grating (1D PC). A higher degree of control on coupling properties is achieved by 2D PC patterns with elements owning elliptical [63–65] or keyhole [66] shapes. Please note that the x- and y-coordinates are spanning the in-plane directions. An alternative to enable polarization selectivity is using sub-wavelength structures. In this case, the interaction with the incident waves is defined by the effective refractive index method. Appropriate designs of the pattern disrupt the 90◦ symmetry, leading to different effective indices for transverse magnetic (TM) and transverse electric (TE) polarization, and subsequently resulting in structural birefringence [67].

Nano-optic effects may be also used to substitute the dispersive elements of sensors. Surface-plasmon-polaritons (SPP) reveal resonances and interact efficiently in the optical nearfield. However, they experience the same critical trade-off between resolution of grating spectrometers and their ability for downscaling because they are based on the angular dispersion of the spectrum as well. In addition, the standard Kretschmann method of excitation makes downscaling quite difficult due to the required bulky prisms. The problem was addressed using a metallic grating coupler for surface plasmons positioned on a scanning MEMS cantilever, and then to read out the influence on the photodiode current of an integrated photosensor [68]. An alternative to improve the resolution of miniaturized spectrometers is achieved via the super prism effect in PC structures. The dispersion properties of a periodic 2D pattern can be designed to be much more pronounced than those of a 1D grating if the shape of the photonic bands is appropriately tailored close to the bandgap [69]. Nonetheless, it was shown that with 1D structures in form of chirped, resonant, or general layer stacks, a strong super prism effect is possible as well [70].

Continuing with this general overview of optical sensing, methodologies and instrumentation, the focus is now placed on the miniaturization potential of grating spectrometers. Concerning size, optical grating spectrometers used in the NIR, VIS, and UV span a length between several mm and a few meters. The optical resolution Δ *λ/λ* of the grating spectrometer is obtained by multiplying the diffraction order *n* with the number of illuminated grating periods *N*, approximately. If we have to miniaturize the grating spectrometer, we are forced to reduce *N* since it is impossible to reduce the grating period (the application defines the wavelength range we have to consider). In addition to the resolving power of the grating, the pixel sizes and the path lengths determine the resolution of the spectrometers, as can be seen in Figure 2. Thus, we can only reduce the size of the grating, and this means to reduce the total number of grating lines *N* and to shorten the optical path length inside the spectrometer. Decreasing *N* reveals a strong and negative impact on the spectral resolution. The first two photos (from left) in Figure 3 display the mini transmission grating spectrometer PEBBLE from the company Ibsen Photonics, Denmark [71] and the mini

reflection grating spectrometer C10988MA-01 from the japanese company Hamamatsu Photonics, in which that of Hamamatsu reveals stronger miniaturization. In the second column (from left) in Figure 3, data from the two smallest grating spectrometers, C12880MA and C14384MA [72], are included. Currently, the C14384MA-01 and the PEBBLE are most probably the smallest grating-based optical mini spectrometers available in the market. The corresponding package dimensions of the C14384MA-01 are located in the sub-centimeter range. Scaling down this spectrometer could only be accomplished at the expense of the grating size, i.e., to work with a rather limited number of grating lines *N*. For the spectral range of 540–1050 nm, the datasheets of the spectrometer reveal full width at half maximum (FWHM) of 17–25 nm (equivalent to linewidths) and corresponding resolutions Δ *λ/λ* of 42–56. This sensor type makes the most efficient use of available light compared to all other sensor methodologies, and it is compatible with fiberoptic systems since it is also available with fiber pigtails. However, if strong miniaturization is required, the achievable resolution is often not sufficient: As already mentioned, grating spectrometer resolution and is strongly decreasing with shrinking size. Luckily, there are many alternative methodologies providing high resolution independent of size, and some of them will be discussed and compared in this review.

Concerning wavelength dispersing options for fiberoptic, sensor principles which (i) are compatible to fiber technology, (ii) have high resolution, and (iii) reveal strong miniaturization potential are considered. The following alternatives are included (and summarized in Figure 3): Static FP filter arrays on complementary metal oxide semiconductor (CMOS) sensor arrays or charge coupled devices (CCD) [28–37], MEMS tunable FP filter arrays [38–57] on photodetector (PD) arrays, AWG structures [21–27], MEMS tunable photonic crystal (PC) filters [62,73–77], plasmonic MEMS cantilevers [68] and thermally tuned chirped fiber Bragg gratings (FBG). Compared to the mini grating spectrometers mentioned above, all these alternatives reveal higher resolution, lower FWHM, and are much smaller in size. The content of Figures 1 and 3 will be considered throughout the whole review. Please note that there are other alternatives than those mentioned in Figure 3, such as MEMS grating spectrometers or Fourier spectrometers which were also strongly miniaturized in the past. However, these are beyond the scope of our paper. The focal points of our review are (i) to describe their method of integration into optical fiber systems, (ii) to show alternative fabrication technologies such as nanoimprint, (iii) to enlarge wavelength tuning behavior, (iv) to identify limits for optical sensor miniaturization, and (v) to envisage performance improvement and cost reduction.

This review emphasizes FWHM, resolution, and potential miniaturization limits with the focus on FP-type interferometers, and delivers various quantitative comparisons. The efficiency in using available light is discussed in detail and the different sensor methodologies are compared with respect to efficiency in this review. There is another recent and well elaborated review paper about miniaturized spectrometers [78] emphasizing the classification of spectrometer methodology and focusing on computational (reconstructive) and Fourier transform methodologies. It is more qualitative rather than quantitative with regard to miniaturization limits, since it only gives the extension in 1D. In contrast, our review gives the required area in 2D. Efficiency is not included in the scope of [78], but it is crucial for signal-to-noise ratio. Thus, our review and the review [78] ideally complement each other.


**Figure 3.** This review benchmarks different miniaturized optical sensors. The comparison concerns mainly optical properties, economic questions and manufacturing challenges. *λ* always denotes the vacuum wavelength. The abbreviations have the following meaning: arrayed waveguide grating (AWG), Fabry-Pérot (FP), microelectro-mechanical system (MEMS), full width of half maximum (FWHM) and quantum dot (QD). References inside the table: transmission grating spectrometer [71,80], reflection grating spectrometer [72], AWG [22–24,26], static FP filter [36], tunable MEMS FP filters [48,56], MEMS tunable PC filter [76], plasmonic MEMS sensor [68], tunable chirped FBG [79].

The review is organized as follows: Section 2 deals with FP filter methodologies, microspectrometers based on FP filter arrays, and our nanospectrometer based on static FP filter arrays which is fabricated by nanoimprint. The digital fabrication methodology for cavity arrays of different heights is demonstrated for the technological fabrication of 3D nanoimprint templates by digital etching in Section 3. This methodology is applied for the fabrication of static FP filter arrays in the VIS spectral range and is also demonstrated in Section 3. Here, a single nanoimprint is demonstrated over three DBR stacks of different design wavelengths and thus different total heights. Section 4 includes experimental results of static FP filter arrays in the VIS range. In Section 5, the design an FP filter array on a detector array with mounted fiber is shown. Section 6 deals with the question to make the most of available light. A methodology is demonstrated which partially compensates for the low efficiency in using available light. This weakness is characteristic for many high resolution optical sensors which have the ability of being strongly miniaturized without loss in resolution. Efficiency boosting is demonstrated by spectral preselection and shown in a laboratory demonstrator. Section 7 briefly describes differences in fabrication of static FP filter arrays if we switch from the VIS to the NIR spectral range. Section 8 describes single air-gap MEMS tunable FP filters for the VIS and NIR spectral range. Section 9 presents methodology, fabrication and characterization of InP multiple airgap MEMS tunable sensors for the NIR. Section 10 provides a broader view on the limits of MEMS tunable FP filters regarding materials and geometric design. Section 11 contains an overview of further concepts for miniaturized optical sensors based on plasmonics, ring resonators, quantum dots, spatial heterodyning, and photonic crystals on fiber tips and in MEMS membranes. Section 12 estimates and illustrates potential space requirements for different sensor methodologies with maximum miniaturization. For the optical sensors shown in Figure 3, the potential space in the area is calculated according to the requirement to cover 400 nm in the VIS spectral range and 500 nm in the NIR for the case of maximum miniaturization. Section 13 deals with the limits of 2D and 3D nanoimprint lithography and discusses the strength of nanoimprint to reduce fabrication time and cost with regard to the six sensor types compared in Figure 3. Subsequently, the limits of wide wavelength tuning are summarized.

#### **2. Methodology of Static FP Sensor Arrays**

The static FP sensor array consists of an FP filter array on a photodiode CMOS array or a CCD array. In the literature, these static FP sensor arrays are also called microspectrometers or nanospectrometers, depending on whether or not nanoimprint technology is applied in the fabrication.
