【Filter】Thermally Tunable FP Filter

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Translation of the 2025 article by Bruno Esteves – **Thermally Tunable Fabry‑Pérot Filter for Miniaturization of High‑Resolution Spectrometers**

### Abstract
This study presents a novel implementation of a large‑gap tunable Fabry‑Pérot interferometer for high‑resolution spectroscopy. The device employs a solid resonant cavity made of common, unmodified glass substrates and leverages the **thermo‑optic effect** and **thermal expansion** to control the transmission wavelength, instead of complex mechanical systems. This simplifies miniaturization and enhances device integration. Experimental results show that with a **700 μm solid glass cavity**, a wavelength tuning shift of **5.7 pm/°C** is achieved over a **free spectral range (FSR) of 137.1 pm**, exhibiting excellent linearity for precise, predictable wavelength control. Designed to meet the miniaturization needs of Brillouin spectral signal acquisition—applications requiring ultra‑high spectral resolution filters—the proposed design addresses the limitations of conventional tunable Fabry‑Pérot filters, which rely on complex piezoelectric actuators to adjust mirror spacing and alignment, compromising practicality. This work promises high‑precision, high‑resolution, low‑maintenance filters ideal for miniaturized spectral measurements.

**Keywords**: Fabry‑Pérot; Tunable Optical Filter; Brillouin Spectroscopy; Glass Resonant Cavity; Thermal Modulation

### 1 Introduction
Brillouin scattering is an inelastic scattering phenomenon that occurs when photons interact with acoustic phonons and magnons in materials, inducing wavelength shifts. The resulting frequency shift ranges from **0.1 to 100 GHz**, providing information on the viscoelastic properties of target materials. Brillouin scattering signals lie adjacent to the Rayleigh peak and are orders of magnitude weaker, making their detection and quantification extremely challenging.

State‑of‑the‑art Brillouin spectrometers offer sufficient resolution to probe viscoelastic properties of materials and tissues with high quality, finding applications in materials science, food, healthcare, and other industries. However, traditional spectral measurement systems, while versatile and practical, often require bulky, complex filtering setups to achieve the spectral resolution needed for precise measurements. In these systems, cascaded air‑gap Fabry‑Pérot filters deliver the highest resolution and contrast via precision piezoelectric actuators that adjust mirror spacing and alignment, but this renders them highly vibration‑sensitive. Combined with the operational challenges of complex actuators, miniaturization and integration remain difficult.

These limitations are particularly pronounced in medical diagnostics and other size‑constrained applications where device integration and usability are critical. In recent years, significant progress has been made in the development of miniaturized devices based on Fabry‑Pérot interferometers, showing great potential for spectrometer miniaturization. Air‑gap and liquid‑gap filters based on low‑order, small‑gap designs have been successfully fabricated, typically adopting piezoelectric‑based cavity length modulation systems. While effective, piezoelectric solutions still suffer from numerous drawbacks, including structural complexity, vibration sensitivity, and high maintenance requirements.

As an alternative, tunable solid‑cavity Fabry‑Pérot filters based on the thermo‑optic effect (refractive index changes with temperature) and thermal expansion have been investigated. Thermal tuning offers advantages such as structural simplicity, compactness, and low maintenance, which are crucial for applications like miniaturized spectroscopy. However, challenges remain, especially in heat‑constrained environments such as high vacuum, requiring additional design considerations, e.g., integrated heat sinks.

Despite remarkable progress, miniaturization of high‑resolution filters required for Brillouin spectroscopy remains challenging. One major obstacle is maintaining parallel mirror alignment across the required cavity length range, particularly in tunable designs that typically demand mirror position adjustment.

This study proposes a new method to achieve tunability in large‑gap Fabry‑Pérot interferometers. The core is a **solid glass resonant cavity** fabricated from common glass substrates, with transmission wavelength controlled via thermal modulation (material expansion and refractive index changes). The result is a **monolithic, moving‑part‑free** device with mirror alignment guaranteed during fabrication, making it suitable for use outside laboratory environments. Using such substrates as resonant cavities enables much longer cavity lengths than traditional thin‑film‑deposited solid resonators, achieving higher resolution.

The proposed device structure is illustrated in Figure 1. It consists of a solid glass plate serving as the resonant cavity, a pair of Bragg mirrors deposited on both sides, and a metal layer on top of one mirror. The metal layer functions as a heating resistor to control device temperature and as an optical mask to block stray light transmission.

Figure 1 Schematic diagram of the proposed filter
(a) Cross-section of the filter, with each layer marked in the fabrication order(b) Schematic diagram of the complete device
2 Methods
2.1 Fabry-Pérot Theory
For a Fabry-Pérot filter, when the incident light beam is normal to the filter surface, the transmittance T of light at a specific wavelength (lambda) is given by the following equation:

where: (t_0) is the maximum transmittance (determined by system loss); F denotes the mirror finesse (dependent on surface flatness and reflectivity); L represents the cavity length; n is the refractive index of the cavity.
As shown in Figure 2, the transmission peak (lambda_p) occurs at wavelengths complying with the formula below. Since both L and n are temperature-dependent, tuning the cavity temperature enables scanning of (lambda_p) across the spectral range and realizes the tunability of the filter.

Figure 2 Schematic of the frequency/transmission characteristics of a high-order Fabry-Pérot interferometer
2.2 Cavity Size Limitations
To ensure proper discretization of the target spectral features, several considerations and constraints must be evaluated, most of which relate to the properties of the optical cavity. The larger the cavity length L, the higher the resolution, since (deltalambda) is inversely proportional to L (when (L gg lambda_p)). Although resolution improves (i.e., (deltalambda) decreases) with increasing L, there is an upper limit on L due to its direct correlation with the free spectral range (FSR), which is related to the width (Delta B) of the target Brillouin spectrum.
Since the measured intensity is the sum of (T_lambda) for all (lambda_p) satisfying Equation (2), the full wavelength width of the sample must be smaller than (Deltalambda) (i.e., the FSR). The finesse F is given by (F = Deltalambda/deltalambda).
The free spectral range (FSR) is defined as:

Therefore, the upper limit of L is determined by the criterion (text{FSR} > Delta B). Theoretically, the optimal filter is achieved with the maximum value of L that satisfies this condition. For typical Brillouin signals, the maximum expected frequency shift reaches 100 GHz, which corresponds to a spectral broadening of approximately 189 pm at the wavelength of 532 nm (including the width of the Brillouin peak). Accordingly, filters with an FSR greater than 189 pm can resolve such signals accurately. A smaller difference between the FSR and this value leads to higher achievable resolution. For specific applications, the system is generally designed for a narrower spectral broadening based on the maximum anticipated Brillouin frequency shift, so the optimal FSR varies accordingly.
2.3 Cavity Selection
The transmission wavelength of a filter depends on the mirror spacing. For materials with a constant refractive index n, even a minor thickness variation of several nanometers will increase (deltalambda) and degrade the resolution. Polishing glass substrates to obtain smooth surfaces with nanometer-level flatness over an effective area of several square millimeters is feasible. However, precisely grinding both surfaces of a solid glass plate while maintaining parallelism poses a greater challenge, which has rarely been addressed in existing research. Despite this difficulty, it is theoretically believed that small regions with satisfactory parallelism on the scale of several square millimeters randomly exist within large areas of inferior parallelism for glass produced via various manufacturing processes. A Fizeau interferometer was set up to verify this assumption.
A 200 mW continuous-wave laser (Oxxius L1C532S) operating at 532 nm was used in the experiment. It features an extremely narrow spectral linewidth (≤ 1 MHz) and excellent wavelength stability, with a wavelength drift of less than 1 pm over 8 hours under a temperature variation of 3 K.

This laser is well suited for the present experiment and subsequent characterization tests.

Figure 3 Schematic of the Fizeau interferometer for evaluating surface parallelism of glass samples
(a) Interferogram of the glass slide sample
(b) Variation in spacing between the two surfaces of the glass obtained via DFTFringe software
In the interferogram, connected regions with identical light intensity share the same thickness. The thickness variation correlates with intensity change, and the thickness difference between adjacent fringes is constant, which is expressed by the formula below:

This setup is well suited for substrate evaluation. It enables direct observation of interferograms across the entire area, allowing rapid screening and rejection of substrates with dense interference fringes. Substrates with the fewest fringes (fringe spacing < 10 mm) were selected for further analysis using the open-source interferogram software DFTFringe, to identify regions with minimal thickness variation.
Borosilicate glass possesses positive thermo-optic and thermal expansion coefficients within the operating temperature range, facilitating the establishment of the correlation between temperature and transmission spectral shift. In this work, borosilicate glasses fabricated via different processes and with various thicknesses were tested, including conventional microscope slides and coverslips produced by float, rolling and drawing techniques, as well as double-side polished glass wafers. Glass plates with satisfactory parallelism were found among all samples. Notably, double-side polished glass wafers delivered the largest qualified areas and the highest yield.
Glass substrates were further selected according to thickness and refractive index to fully cover the spectral broadening range of target Brillouin signals. Another criterion was to keep the minimum temperature required to achieve two consecutive transmission orders below 200 °C, for ease of assembly and compatibility with characterization instruments. Two types of glass substrates were finally chosen for the early-stage prototypes.
A 110 μm coverslip made of D 263 M borosilicate glass with a refractive index of 1.5265 at 532 nm was adopted to fabricate a filter with an FSR of 841.4 pm. Meanwhile, a 700 μm double-side polished Borofloat33 borosilicate glass wafer (n = 1.4739 at 532 nm) was used to produce another filter with an FSR of 137.1 pm.
Both surface roughness and parallelism affect filter performance, making substrate quality evaluation essential. The root-mean-square roughness ((R_q)) of selected substrates was measured using a mechanical profilometer. Over a linear scanning length of 100 μm, the (R_q) value was 1 nm for the coverslip and 0.62 nm for the glass wafer.
2.4 Bragg Mirrors
Apart from the quality of the Fabry-Pérot resonant cavity, device performance is strongly determined by the mirror properties, mainly reflectivity and absorptivity. Bragg mirrors were developed and employed in this study, which exhibit higher reflectivity than conventional metallic mirrors. Such mirrors consist of N pairs of alternating high-refractive-index ((text{TiO}_2)) and low-refractive-index ((text{SiO}_2)) layers, each with a thickness equal to a quarter wavelength d. An additional high-refractive-index layer is deposited on the top, resulting in a total layer number of (2N+1).

The TiO₂ thin films ((d=52.99), (n=2.51)) were deposited by reactive sputtering, and the SiO₂ thin films ((d=90.66), (n=1.47)) were prepared via electron beam evaporation. The deposition process was iterated until the thin films acquired stable and optimal properties. An ellipsometer was used to measure and optimize the film thickness and refractive index, while a mechanical profilometer was adopted to verify thickness accuracy. The ellipsometer was also operated in transmission mode to characterize the transmittance of the fabricated Bragg mirrors.
2.5 Fabrication Process
Two types of filter prototypes were fabricated, using 110 μm coverslips and 700 μm double-side polished glass wafers as resonant cavities respectively. Both substrates were verified by a Fizeau interferometer and featured large areas with uniform thickness. Different cavity thicknesses were selected to investigate their effects on the optical performance and tuning characteristics of the filters.
The Bragg mirrors were designed with (N=1). Since characterization was the primary objective for the initial prototypes, a low N value produced broader transmission peaks and higher minimum transmittance. This reduced the requirements for the resolution and sensitivity of the characterization system, without interfering with the research on thermal tuning performance. Although the reflectance improvement of (N=1) Bragg mirrors over metallic mirrors was limited, they were still adopted for the prototypes. Bragg mirrors can minimize optical absorption, and their reflectance as well as filter resolution can be easily enhanced by increasing the number of film layers.
After depositing mirrors on both sides of the substrate, the Fizeau interferometer was used to locate the region with maximum transmittance. A circular area with a diameter of 1 mm was selected as the light transmission zone for each sample, which was then masked with polyimide tape of the same size to prepare for the deposition of metal thin films serving as heating resistors and light-blocking masks.
For the filter with a 700 μm-thick optical cavity, a 200 nm-thick titanium film was deposited by DC sputtering to form the heating resistor. For the thinner filter with a 110 μm optical cavity, a 50 nm-thick aluminum film was deposited by electron beam evaporation instead.
Upon completion of film deposition, the device was mounted on a 3D-printed flat holder. One corner was fixed directly with polyimide tape, while the opposite corner was supported by glass spacers and allowed to slide horizontally. This structure enabled the filter to expand freely in all directions without deformation. Copper wires were bonded to both sides using silver conductive adhesive to finish device assembly.

Figure 4 Schematic of the filter mounted on the optical holder
One corner is fixed rigidly, and the opposite corner is supported by glass spacers to enable sliding. This design allows the filter to expand in all directions without mechanical deformation.
2.6 Device Characterization
The fabricated filters operate at a high transmission order near 532 nm, so the spacing between adjacent transmission peaks is approximately constant. Accordingly, the variation of the product (ncdot L) can be regarded as the shift of the transmission spectrum.
The device was heated by applying a constant current to the resistive layer. A calibrated photodiode was used to quantify transmittance, and an infrared thermal imager was adopted for temperature measurement. The device temperature was defined as the average temperature of the glass surface within the aperture of the resistor. The characterization system is illustrated in Figure 5.

Figure 5 Characterization system for correlating filter temperature and transmittance
3 Results and Discussion
3.1 Bragg Mirrors
The first batch of filter prototypes was fabricated with Bragg mirrors of (N=1). Meanwhile, mirrors with N ranging from 1 to 5 were simulated, fabricated and characterized. Simulations were carried out based on the optical models of deposited SiO₂ and TiO₂ thin films acquired via ellipsometer measurements, to explore the potential resolution achievable with the proposed fabrication process.

Figure 6 Simulated and measured reflectance of Bragg mirrors(a) Simulated reflectance for different numbers N of high/low refractive index layer pairs(b) Measured reflectance of fabricated Bragg mirrors with (N = 1) to 5
As illustrated in the figure, an obvious wavelength shift exists between the peak reflectance of simulated and fabricated mirrors. This discrepancy is consistent with deviations in layer thickness and refractive index across different deposition batches. Despite such variations, the performance of the fabricated mirrors agrees well with theoretical predictions. When N is sufficiently large, the Bragg mirrors exhibit a substantial performance improvement over metallic mirrors.
3.2 Fabry-Pérot Filters
Full Fabry-Pérot filter models with mirror pairs up to (N=5) were simulated for prototypes with 700 μm and 110 μm cavities. The influence of mirror quality on finesse and spectral resolution was evaluated accordingly.

Figure 7 Simulated transmission spectra of Fabry-Pérot filters(a) Cavity length: 700 μm(b) Cavity length: 110 μm
The finesse was calculated for simulated filters with (N=1) using the aforementioned SiO₂ and TiO₂ layers. The values are 9.24 for the 700 μm cavity filter and 9.15 for the 110 μm cavity filter.

Figure 8 Characterization results of the 700 μm filter under a constant current of 450 mA
(a) Variations of photodiode signal and average temperature over time
(b) Correlation between light intensity and temperature
(c) Transmission wavelength shift versus temperature
The 700 μm filter presents an excellent linear relationship between temperature and transmission wavelength, with a wavelength shift of 5.7 pm/°C and a free spectral range (FSR) of 137.1 pm. The finesse is calculated to be 7.665 based on the transmission peaks acquired during the cooling cycle near room temperature.

Figure 9 Variation of linewidth with transmission peak wavelength for the 700 μm cavity filter

Figure 10 Comparison between the initial and final thermal cycles after an interval of 364 days
(a) Heating phase
(b) Cooling phase
Long-term stability tests demonstrate that the device shows no obvious performance degradation when operated within the normal working temperature range.

Figure 11 Characterization results of the 110 μm filter under a constant current of 4.5 A
(a) Changes of photodiode signal and average temperature over time
(b) Correlation between light intensity and temperature
(c) Transmission wavelength shift with temperatureThe 110 μm filter failed to complete the long-term stability test, as the glass cracked due to excessively high operating temperature.

Figure 12 Variation of linewidth with transmission peak wavelength for the 110 μm cavity filter
The finesse of this filter was calculated from the transmission peaks recorded during the cooling cycle near room temperature, yielding a value of 6.786.
3.3 Considerations for Optical Resonant Cavity
During operation, heating directly affects the performance of Fabry-Pérot filters. Uneven distribution of thermal expansion and thermo-optic effect inside the cavity will cause peak broadening and finesse reduction. Thermal gradients degrade filter performance, so optimizing resistor layout and geometric structure to minimize such gradients is a key focus of this work.

Figure 13 Thermal images of the optical cavity surface and the back side of glass substrates with different cavity diameters
(a), (c), (e), (g) Thermal distribution on the resistor side of cavities with diameters of 1 mm, 2 mm, 3 mm and 4 mm, respectively
(b), (d), (f), (h) Corresponding thermal images of the glass back side for cavities of the same sizes

Figure 14 Finite element thermal simulation of the filter geometry at a target resistor temperature of 70 °C
(a) Cross-section of the full filter geometry
(b) Cross-section of the 1 mm × 0.7 mm optical cavity

Figure 15 Thermal simulation of the effects of different resistor configurations on thermal gradients inside the optical cavity
(a) Single-resistor structure
(b) Double-sided annular resistor
(c) Sidewall annular resistor

Figure 16 Thermal simulation after replacing the top layer of the Bragg mirror with a transparent resistor
Double-sided heating using transparent conductors can reduce the maximum thermal gradient inside the cavity to 0.075 °C, significantly improving temperature uniformity.
4 Conclusion
This study presents a method for fabricating large-gap, monolithic, temperature-tunable Fabry-Pérot filters using standard unmodified glass substrates as resonant cavities. The proposed approach enables the preparation of filters with large effective areas and long cavity lengths, suitable for high-resolution spectroscopic applications.
Various types of standard glass substrates were tested, and a qualified component screening method based on interferogram analysis was developed. The fabrication process introduced herein yields tunable filters without moving parts or actuators, featuring simple preparation and operation, compactness, robustness, and compatibility with diverse applications.
Among the fabricated variants, the filter with a 700 μm-thick solid glass resonant cavity achieved a highly linear relationship between temperature and transmission wavelength (5.7 pm/°C, FSR = 137.1 pm) and maintained stable performance across the entire operating temperature range, confirming that the two-sided mirrors naturally retain parallelism.
In summary, this technology is suitable for spectrometer miniaturization, especially for high-resolution techniques such as Brillouin spectroscopy, and offers significant advantages over existing solutions: low R&D and fabrication costs, minimal maintenance requirements, and excellent performance.
Note: This paper was selected and translated by Tianjin JHBF Optoelectronic Technology Co., Ltd. to promote and share fundamental knowledge on semiconductor optical amplifiers (SOAs) and support the advancement and application of SOA technologies. While the company has made every effort to ensure translation accuracy, errors, omissions, or interpretive inaccuracies may exist. Readers are advised to consult the original text or use this translation for cross-reference. Feedback on any errors is welcome for mutual improvement.
Tianjin JHBF Optoelectronic Technology Co., Ltd. (https://www.soaamplifier.com/) is a high-tech enterprise dedicated to the R&D and manufacturing of domestic semiconductor optical amplifiers (SOAs). The company has launched a full range of SOA products (850 nm, 1060 nm, 1270 nm, 1310 nm, 1550 nm, 1625 nm) and gain chip RSOA products (850 nm, 1310 nm, 1550 nm). It operates a class-10,000 cleanroom laboratory equipped with comprehensive facilities for optical chip fabrication, testing, and packaging, as well as capabilities for hybrid integrated micro-packaging of photonic chips. Current R&D efforts focus on hybrid integrated devices (NLL/ECL + SOA) and high-power SOA components. The company also provides external services for optoelectronic device testing, packaging, and microfabrication.

anslation of the 2025 article by Bruno Esteves – **Therm

ally Tunable Fabry‑Pérot Filter for Miniaturization of High‑Resolution Spectrometers** ### Abstract This study presents a novel implementation of a large‑gap tunable Fabry‑Pérot interferometer for high‑resolution spectroscopy. The device employs a solid resonant cavity made of common, unmodified glass substrates and leverages the **thermo‑optic effect** and **thermal expansion** to control the transmission wavelength, instead of complex mechanical systems. This simplifies miniaturization and enhances device integration. Experimental results show that with a **700 μm solid glass cavity**, a wavelength tuning shift of **5.7 pm/°C** is achieved over a **free spectral range (FSR) of 137.1 pm**, exhibiting excellent linearity for precise, predictable wavelength control. Designed to meet the miniaturization needs of Brillouin spectral signal acquisition—applications requiring ultra‑high spectral resolution filters—the proposed design addresses the limitations of conventional tunable Fabry‑Pérot filters, which rely on complex piezoelectric actuators to adjust mirror spacing and alignment, compromising practicality. This work promises high‑precision, high‑resolution, low‑maintenance filters ideal for miniaturized spectral measurements. **Keywords**: Fabry‑Pérot; Tunable Optical Filter; Brillouin Spectroscopy; Glass Resonant Cavity; Thermal Modulation ### 1 Introduction Brillouin scattering is an inelastic scattering phenomenon that occurs when photons interact with acoustic phonons and magnons in materials, inducing wavelength shifts. The resulting frequency shift ranges from **0.1 to 100 GHz**, providing information on the viscoelastic properties of target materials. Brillouin scattering signals lie adjacent to the Rayleigh peak and are orders of magnitude weaker, making their detection and quantification extremely challenging. State‑of‑the‑art Brillouin spectrometers offer sufficient resolution to probe viscoelastic properties of materials and tissues with high quality, finding applications in materials science, food, healthcare, and other industries. However, traditional spectral measurement systems, while versatile and practical, often require bulky, complex filtering setups to achieve the spectral resolution needed for precise measurements. In these systems, cascaded air‑gap Fabry‑Pérot filters deliver the highest resolution and contrast via precision piezoelectric actuators that adjust mirror spacing and alignment, but this renders them highly vibration‑sensitive. Combined with the operational challenges of complex actuators, miniaturization and integration remain difficult. These limitations are particularly pronounced in medical diagnostics and other size‑constrained applications where device integration and usability are critical. In recent years, significant progress has been made in the development of miniaturized devices based on Fabry‑Pérot interferometers, showing great potential for spectrometer miniaturization. Air‑gap and liquid‑gap filters based on low‑order, small‑gap designs have been successfully fabricated, typically adopting piezoelectric‑based cavity length modulation systems. While effective, piezoelectric solutions still suffer from numerous drawbacks, including structural complexity, vibration sensitivity, and high maintenance requirements. As an alternative, tunable solid‑cavity Fabry‑Pérot filters based on the thermo‑optic effect (refractive index changes with temperature) and thermal expansion have been investigated. Thermal tuning offers advantages such as structural simplicity, compactness, and low maintenance, which are crucial for applications like miniaturized spectroscopy. However, challenges remain, especially in heat‑constrained environments such as high vacuum, requiring additional design considerations, e.g., integrated heat sinks. Despite remarkable progress, miniaturization of high‑resolution filters required for Brillouin spectroscopy remains challenging. One major obstacle is maintaining parallel mirror alignment across the required cavity length range, particularly in tunable designs that typically demand mirror position adjustment. This study proposes a new method to achieve tunability in large‑gap Fabry‑Pérot interferometers. The core is a **solid glass resonant cavity** fabricated from common glass substrates, with transmission wavelength controlled via thermal modulation (material expansion and refractive index changes). The result is a **monolithic, moving‑part‑free** device with mirror alignment guaranteed during fabrication, making it suitable for use outside laboratory environments. Using such substrates as resonant cavities enables much longer cavity lengths than traditional thin‑film‑deposited solid resonators, achieving higher resolution. The proposed device structure is illustrated in Figure 1. It consists of a solid glass plate serving as the resonant cavity, a pair of Bragg mirrors deposited on both sides, and a metal layer on top of one mirror. The metal layer functions as a heating resistor to control device temperature and as an optical mask to block stray light transmission. 需要我把这段英文再统一成期刊投稿格式(术语斜体,单位规范,关键词加粗)吗?