1 Introduction
With the advancements in infrared sensing technology, infrared cameras have found widespread applications in environment monitoring [1,2], process monitoring [3], medical diagnostics [4], and camouflage identification [5]. Simultaneously, there is a growing demand for versatile mid-wave infrared (MWIR) devices, accompanied by a strong emphasis on reducing the size, weight, and power (SWaP). Conventional MWIR spectral sensors rely on the use of prisms or filter wheel to project different spectral signals on the sensors [6–8]. External dispersive elements generally require the necessary optical path and complex setup, which results in a bulky system and mounting manufacturing costs. Integrating narrowband filter arrays with broadband photodetectors offers an advantage in simultaneous capture of multiple spectral components and achieving compact hyperspectral imagers [9]. Decades of intensive research on nano-patterned structures and their optical characteristics have revealed that subwavelength structures exhibit unique optical features, serving as perfect absorbers [10], polarizers [11], and optical filters [12,13] capable of manipulating light beyond the diffraction limit. Hybrid integration of subwavelength structure arrays with sensing devices holds promise for addressing the inherent limitations of conventional optical components, which are often not well-integrated and result in bulky devices [14]. The development of wafer-scale processing and advanced nanofabrication methods now enables the fabrication of high quality nanostructures which may replace conventional optical components to realize ultra-compact devices.
In recent years, there has been a significant focus on optical resonance in nanostructures for the development of ultra-thin filters [15–19]. Subwavelength structures typically function as planar arrays of unit cells on a scale comparable to the target wavelength. The properties of subwavelength optical structures are predominantly determined by material properties and subwavelength geometries in ultra-thin films [20]. Consequently, subwavelength structures hold great potential for direct integration onto focal plane arrays (FPAs). The application of subwavelength structures not only enhances the performance of MWIR devices but also facilitates the creation of compact and efficient systems. The addition of distinctive optical properties of subwavelength structures makes them indispensable in achieving thin, lightweight, and powerful optical components, addressing the industry’s demand for improved performance and reduction in SWaP.
Guided-mode resonance (GMR) are leaky modes with sharp transmission or reflection resonances typically observed in waveguide structures with a grating on it, exhibiting remarkable sensitivity to optical parameters influenced by their shape geometry and the polarization of incident light [18,21]. GMR structures have been tailored to produce narrowband resonances as color filters [22–24]. The central transmission wavelength can be easily adjusted by modifying the grating period. However, GMR filters employing dielectric subwavelength gratings typically operate in the reflection mode, necessitating a complex optical setup [25–27]. Recent advancements have reported transmission filters operating within the visible and near-infrared spectra realized by incorporating metal gratings into GMR structures [13,28,29]. Leveraging their straightforward design, these filters hold promise for extending applications into the MWIR and terahertz bands, offering significant potential for multichannel integration and large-scale fabrication towards compact spectral sensing solutions.
We present a straightforward design of a GMR filtering structure aimed at realizing narrowband optical filters operating in the MWIR waveband. Systematic investigation on this structure has been conducted to unravel the influencing factors impacting its filtering performance. The center wavelength of transmission can be simply tuned by changing the period of gold gratings to achieve target narrowband transmission across the MWIR waveband (3 µm–5 µm). Furthermore, the full width at half maximum (FWHM) of transmission peaks is adjustable within a range from 5.7 nm to 101.0 nm depending on the thickness of the waveguide layer. This study offers a potential strategy for fabricating ultra-thin narrowband MWIR filters which may address the pressing need for compact MWIR spectral sensors.
2 Simulation and analysis of the GMR filters
2.1 Schematic of the GMR filtering structure
The proposed structure based on GMR, comprising a dielectric waveguide layer with an array of gold gratings, is under normal incidence of a transverse magnetic (TM)-polarized wave (the E-field is perpendicular to the grating direction) as depicted in Fig. 1. The filtering properties of the GMR filter are analyzed within the MWIR range from 3 μm to 5 μm. The modifiable design parameters include the gold layer thickness (da), waveguide layer thickness (dwg), grating period (p), and gold grating slit width (w). The periodic dielectric variation arises from the high absorbance at the visible region and high reflectance at infrared wavelengths of the Au gratings, along with the low refractive index of the ambient [30]. This creates high transmittance at the resonance location, and by modifying these parameters, a resonance transmission can be finely tuned across a broad wavelength range with the customized bandwidth.

Figure 1.Schematic of the GMR subwavelength structure, where I0 and It correspond to the incident and transmitted light intensities, respectively.
2.2 Effects of waveguide layer thickness and electric field distribution
Low refractive index material silica (SiO2) is chosen as the waveguide material for its ease of fabrication, and then we investigate the structure with varying waveguide thicknesses and different structural parameters. To examine the effect of the thickness of the SiO2 layer, we use a fixed value for the grating period (p = 3.4 µm). The parameters for the Au grating thickness and slit width are determined as da = 100 nm and w = 500 nm, respectively. By varying the dwg among the range from 0.2 µm to 0.8 µm, simulation results indicate a narrowing transmission bandwidth along with a blue shift as dwg decreases, as illustrated in Fig. 2(a). As shown in Fig. 2(b), FWHM of each condition decreases from 101.0 nm to 5.7 nm as dwg decreases, as well as a decrease in the peak transmission from 92% to 60%.

Figure 2.Simulated results under the specific condition of da = 100 nm, w = 500 nm, and p = 3.4 µm: (a) simulated transmission spectra of the designed structure with various waveguide layer thicknesses between 0.2 µm and 0.8 µm and (b) FWHM and peak transmittance of the filters with different waveguide thicknesses.
In order to enhance comprehension of the physical mechanism underlying the device performance, we simulate the electric field distributions at resonant wavelengths for the structures with different SiO2 thicknesses dwg of 0.2 µm, 0.5 µm, and 0.8 µm, respectively. Fig. 3 depicts the simulated electric field distributions at the corresponding transmission peaks in the reversed two-dimensional (2D) unit cells of the GMR filters with da= 100 nm and varying dwg. The incident light illuminates normally from the bottom of the structure, passing through the Au gratings with 500 nm slits and then the SiO2 waveguide layer successively. The locally enhanced electric field can be seen on the top surface of the waveguide layer, and with the reduction in the waveguide thickness, a stronger resonance is observed, which is in conformity with the narrowing bandwidth.

Figure 3.Electric field distributions in the GMR structure at the resonant wavelength with various waveguide layer thicknesses: (a) dwg = 0.2 µm, (b) dwg = 0.5 µm, and (c) dwg = 0.8 µm under the specific condition of da = 100 nm, w = 500 nm, and p = 3.4 µm.
2.3 Filtering performance across the wavelength range from 3 µm to 5 µm
The performance of the filters is primarily determined by the features of the main transmission peaks. In a comprehensive consideration of transmittance and bandwidth, we simulate several filters operating at different wavelengths across the MWIR waveband by simply adjusting the period of the Au gratings, while maintaining da= 100 nm, w = 500 nm, and dwg = 0.5 µm. The calculated transmission spectra of filters operating at 3.0 µm, 3.5 µm, 4.0 µm, 4.5 µm, and 5.0 µm are shown in Fig. 4. Inset table shows FWHM and peak transmittance (T) of the filters at operating wavelength (λ).

Figure 4.Simulated transmission spectra of filters with varying grating periods under the specific condition of da= 100 nm, w = 500 nm, and dwg = 0.5 µm.
All of the filters achieve a high transmittance exceeding 79%. However, the differences in performance persist among these filters, manifested in the variations in peak transmittance and FWHM attributable to structural parameters.
2.4 Filtering performance optimization
The filtering properties of the GMR filter is highly tunable depending on the material selection and its structural parameters. Although the optimized parameters for each filter aimed at different wavelengths may vary, relatively uniform filtering performance can be achieved for all filters by appropriately adjusting their respective structural parameters. Thus, to elucidate the effects of different slit widths (w) and Au grating thicknesses da, simulations are conducted to study the influence of varying parameters on the characteristics of the main transmission peak. The calculated results presented in Fig. 5(a) suggest that a wider slit, namely a low duty ratio, will lead to a higher transmittance accompanied by a blue shift and broadening of the transmission bandwidth. In the case of varying da from 50 nm to 150 nm, a red shift of the peak is observed with an increased thickness, albeit with the minimal impact on its transmittance and FWHM, as shown in Fig. 5(b).

Figure 5.Simulated transmission spectra of the filters with varying (a) slit widths w and (b) grating thicknesses da under the specific condition of p = 3.4 µm and dwg = 0.5 µm.
Since the waveguide layer thickness and slit width have a significant influence on the filtering performance. We proposed two methods to achieve relatively uniform performance for filters across the MWIR waveband. In Fig. 6(a), a varying grating slit is applied for filters operating at 3.0 µm (300 nm), 3.5 µm (500 nm), 4.0 µm (650 nm), 4.5 µm (800 nm), and 5.0 µm (950 nm), with the parameters da and dwg fixed at 100 nm and 0.5 µm, respectively. In Fig. 6(b), a gradient waveguide thickness dwg varying from 0.4 µm to 0.8 µm is applied for the filters. Both methods yield consistent performance across the filters, and they are compatible with the state-of-the-art fabrication technologies.

Figure 6.Two methods towards consistency in filtering performance with varying (a) slit widths and (b) gradient waveguide thicknesses.
3 Conclusion
In summary, this study presents a design of GMR filters operating in the MWIR waveband, harnessing subwavelength gold gratings along with a slab waveguide. This structure, distinguished by its processability and potential for compact integration with MWIR image sensors, offers remarkable tunability in spectral filtering performance by simply adjusting the structural parameters. It demonstrates an exceptional narrowband transmission across the wavelength range from 3 µm to 5 µm through the adjustment in the period of Au gratings. With meticulous consideration of waveguide material and structural configuration, this design affords facile tuning of filtering characteristics to suit diverse application contexts. Our work holds promise for advancing functional sensing and detection applications in the realm of MWIR sensing technology.
Disclosures
The authors declare no conflicts of interest.