1. Introduction

The 8–12 µm LWIR spectral region corresponds to an atmospheric window as well as to the peak terrestrial emission and is widely used for day/night sensing and imaging applications. Some of these applications require use of compact spectrally tunable notch or band-stop filters, which reflect narrow band(s) of incident light while transmitting the rest. Such filters cannot be fabricated using traditional multilayer thin film technology due to impractical processing requirements. In 1992, Magnusson and Wang [1] showed that small compact notch filters can be designed based on the guided-mode resonance (GMR) effect in dielectric WGG. Since then, such filters have been demonstrated from the visible to the LWIR spectral regions [1–17]. A GMRF based on one-dimensional (1-D) gratings only on one side of the substrate is polarization sensitive [1–10]. Recently, we demonstrated polarization insensitivity at normal incidence for a double-sided LWIR GMRF with orthogonal 1-D gratings on either side of a substrate [11], as well as a combination of two separate 1-D LWIR GMRFs with linear gratings in orthogonal orientations [9]. A polarization insensitive GMRF can also be designed using 2-D gratings at normal incidence of light [12–17]. So far 2-D GMRFs have been reported in the visible [12], the shortwave infrared [13–15], the midwave infrared [16], and part of LWIR ∼6–10 µm [17].

In this paper, we report on fabrication and experimental demonstration of two different sets of polarization-independent ebeam-written high-spatial-resolution GMRFs covering the 8–12 µm spectral region. The first set of GMRFs encompass a 2-D Ge WGG on a polished ZnSe substrate without an ARC and the second set comprises a 2-D Ge WGG on a polished ZnSe substrate with a broadband (7–12 µm) ARC applied on the backside. We achieved close to15% improvement in the filter transmittance by using the substrate with ARC. We designed, fabricated, and characterized 2-D ZC subwavelength WGG GMR notch filters operating from 8 to 12 µm using high-refractive index (n) transparent dielectric materials (i.e., amorphous Ge film with n = 4.1 and ZnSe substrate with n = 2.41). The size of the fabricated filters is 8×8 mm². At the normal incidence, the 2-D filter reflects the incident broadband light at two narrowband notches independent of incident light polarization while transmitting the rest of the incident light. We carefully chose the device parameters—grating period (P), fill factor (ff), grating thickness (t₁), and waveguide thickness (t₂)—for this spectral range of operation by scanning over parameter values to obtain the highest diffraction efficiency. We implemented the rigorous coupled-wave analysis (RCWA) algorithm [18] to carry out the modeling and design of the filters by using seven Fourier orders for convergence. Physical vapor deposition, e-beam lithography without a mask, and RIE techniques were used to deposit and fabricate high-spatial resolution, high-quality prototype 2-D GMRFs. We characterized the polarization-independent filtering performance at normal incidence of light for these filters with two separate experimental setups using coherent and incoherent incident light: (i) an automated room-temperature QCL system tunable from 8 to 12 µm and a thermal detector; and (ii) a modified commercial FTIR spectrometer with a collimated incident beam and a high-sensitivity, high-speed, liquid-nitrogen-(LN₂)-cooled mercury cadmium telluride (MCT) detector. We obtained an excellent agreement between the theoretical and experimental results.

2. Materials and methods

2.1 Modeling and simulation

To predict the wideband electromagnetic properties of the 2-D GMRFs, we implemented the RCWA to obtain the design parameters using Ge and ZnSe [18]. In our model, the input parameters are refractive indices of incident/exit regions, grating layer, waveguide (WG) layer, and the substrate; incidence angle; period (P), thickness (t₁), and fill factor (ff) of the grating; thickness of the planar WG (t₂); and thickness of the substrate (t₃) as schematically shown in Fig. 1 for a 2-D filter. We chose the following design parameters for the 2-D GMRF: P = 3.2 µm, square grating; ff = 0.55, t₁ = 0.4 µm; t₂ = 1 µm, with t₃ = 1 mm. In Fig. 2(a)–(d), we show computed contour color maps that display the spectral transmittance as a function of P, ff, t₁, and t₂ for both the transverse electric (TE) and transverse magnetic (TM) polarized—as well as unpolarized incident light for normal incidence of light—assuming an infinite thickness of the substrate. The color scale corresponding to the transmittance values from 0 to 1 is located on the right-hand side. Dark-blue regions in these plots correspond to near-zero transmittance corresponding to the notch wavelength(s) and red-orange regions correspond to high transmission of light. It has been shown that the modal behavior of a 2-D filter can be understood in terms of the TE and TM modes of two equivalent 1-D grating filters, where the polarization vector parallel to the linear grating corresponds to the TE case and perpendicular to the linear grating to the TM case, and the TE and TM modes for the equivalent 1-D filters gets blended in a 2-D filter resulting in shape and variability of the notches in the transmittance spectrum [14].

 

Fig. 1. Schematic drawings of a 2-D GMRF with parameter labels.

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Fig. 2. Color plots of spectral transmittance with color scale on the right for 2-D GMRF as a function of period, fill factor, grating thickness, and waveguide thickness (assuming the substrate thickness to be infinite) over 8 to 12 µm spectral interval for TE, TM, or unpolarized incident light. Here, we show the filter transmittance in (a) as a function of P and wavelength with ff = 0.55, t₁ = 0.4 µm, t₂ = 1 µm; (b) as a function of ff and wavelength with P = 3.2 µm, t₁ = 0.4 µm, t₂ = 1 µm; in (c) as a function of t₁ and wavelength with P = 3.2 µm, ff = 0.55; t₂ = 1 µm; and (d) as a function of t₂ and wavelength with P = 3.2 µm, ff = 0.55; t₁ = 0.4 µm.

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Figure 2(a) shows that for each value of the 2.5 to 3.2 µm period there are two wavelengths where the transmittance is low corresponding to the two notches in the spectrum that will be plotted for simulated and measured values of transmittance later. Figure 2(b) plots transmittance as a function of fill factor and wavelength and shows that for each value of ff from 0.4 to 0.9 there are two wavelengths corresponding to two minima of transmittance. In Fig. 2(c) we show a color plot of transmittance as a function of grating thickness and wavelength. Again, there are two transmittance minima for each value of t₁ from 0.3 to 1.5. It is interesting to note that the first minimum gets wider as the grating thickness increases; this implies that the full width at half maximum (FWHM) of the transmittance notch gets wider as grating groves become deeper. Figure 2(d) shows a color plot of transmittance as a function of the waveguide height and the wavelength and has two minima in transmittance for each value of t₂. We chose parameters that give us one of the transmission notches around 9 µm.

2.2 Device fabrication and characterization

We fabricated 2-D GMRF on two different types of 25.4-mm-diameter polished ZnSe substrates: (i) without and (ii) with broadband 7–12 µm ARC, Crystran Limited, UK [19] on the backside to see how much improvement in the spectral transmittance is achieved as well as to check if the coherent noise is lowered when used with lasers. For the fabrication of a 2-D GMRF, we followed the procedure as detailed in our earlier papers [10,11]. The main difference being that when we use the ZnSe substrate with one side coated with a broadband ARC, to protect the ARC side of the substrate, we first spin-coated it with polymethyl-methacrylate (PMMA) at 3000 RPM and then baked it at 180 °C for 10 min. We then proceeded by following the steps listed previously [10]. Briefly, the designed geometries were fabricated on the ZnSe substrates consisting of a 1.5-µm-thick Ge layer deposited by a physical vapor deposition method. Electron-beam lithography and an inductively coupled plasma RIE technique were used to transfer the grating patterns to the Ge layer. Afterward, to complete the fabrication process, the PMMA layer is removed yielding the fabricated filter as shown in the atomic force microscopy (AFM) and scanning electron microscopy (SEM) images (Fig. 3), which were used to measure the grating period, thickness, and fill factor.

 

Fig. 3. (a) AFM, (b) a photo, and (c) and (d) SEM images of 2-D GMRF. Focused ion-beam (FIB) milling was carried out by depositing a platinum layer on top to show the detailed shape of the grating structures and to confirm that the grating sidewalls are straight.

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The measured values of these parameters for the GMRF with substrate without ARC are as follows: P = 3.23 µm; ff = 0.54; t₁ = 320 nm; t₂ = 1.07 µm. These values are close to the values used in designing the GMRF. The values of these parameters for the fabricated GMRF with substrate with ARC were measured similarly: P = 3.15 µm; ff = 0.54; t₁ = 400 nm; t₂ = 1.01 µm. These values are slightly different than the values for GMRF without ARC, but still close to the values used in designing the GMRF. We used the measured values of the parameters in simulating the transmittance spectra for the two filters. In Figs. 4(a) and 5(a), we show the simulated transmittance spectra for 2-D GMRFs with both types of substrates. We carried out simulations using RCWA only for zero-order transmittance, due to the fact that for the chosen subwavelength parameter values, all other orders are evanescent. We used the measured value n = 4.1 for a thin film of e-beam-grown amorphous Ge on a ZnSe substrate using an LWIR ellipsometer. Since these filters will be used with both laser and incoherent source light experiments, we characterized the filter transmittance using two separate experimental setups: (i) an automated air-cooled QCL system (Daylight Solutions model 2300) and an uncooled broadband thermopile detector power meter (Ophir-Spiricon model Vega-B power meter with a 16-mm-diameter 10A-PPS detector) over the spectral range of 8 to 12 µm where the laser is vertically polarized and transmittance is directly measured using coherent light; and (ii) a modified commercial FTIR spectrometer (Bruker 70) with a collimated incident beam (a traditional FTIR spectrometer could not be used because the incident beam on the sample is focused and does not meet the plane wave incidence requirement to correspond to RCWA simulations) and a high-sensitivity, LN₂-cooled, 1-mm-diameter MCT detector with 20-kHz scan speed for incoherent light measurement [11].

 

Fig. 4. Simulated and measured transmittance spectra of 2-D GMRF without ARC on the backside of substrate: (a) simulation with measured parameters, (b) QCL measurement, and (c) modified FTIR measurement.

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The QCL system consists of three QCLs and runs in a quasi-continuous-wave mode at 100 kHz. Each of the three separate QCLs in this system is single mode with very small sidelobes and is vertically polarized (TE polarization). We can rotate the filter about the optical axis to precisely line up the GMRF grating-groove direction with the incident light polarization orientation. For the 2-D filter we first align the grating grooves in one direction parallel to the QCL polarization for the TE and then rotate the filter by 90° relative to the laser polarization orientation for the TM polarization measurements. In the modified FTIR setup, we used a 45° turning mirror to reflect the light from the interferometer inside the FTIR to get a collimated incident beam propagating along the optical axis coming out through a ZnSe side window of the spectrometer in a custom measurement chamber. After the collimated beam is incident on the sample and gets transmitted through, it is focused by a parabolic mirror on an MCT detector. In the FTIR setup, the incident light polarization is changed using an LWIR wire grid polarizer before the sample to carry out measurements with either TE or TM incident polarization by rotating the polarizer and keeping the filter orientation fixed. We first orient the polarizer for vertical polarization and align the grating grooves with this orientation for the TE and rotate the polarizer by 90° for the TM measurements. By removing the wiregrid polarizer we can also carry out measurements with unpolarized incident light. Both these experimental setups have been described in detail previously in Gupta and Song [11]. For both types of GMRFs (without and with ARC), we measured the spectral transmittance by both the QCL and FTIR when the light is incident at 0° for either the TE or TM polarization measurement. We found that measurements with both these incident polarizations yielded the same spectrum. We show the measured spectrum by QCL in Fig. 4(b) and by FTIR in Fig. 4(c) for the filter without ARC, and similarly in Fig. 5(b) and (c) for GMRF with ARC. A spectral resolution of 0.01 µm was used in the QCL and 1.5 cm^-1 in the FTIR measurements.

 

Fig. 5. Simulated and measured transmittance spectra of 2-D GMRF with ARC on the backside of substrate: (a) simulation with measured parameters, (b) QCL measurement, and (c) modified FTIR measurement.

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3. Discussion

We found that the spectral transmittance of the 2-D GMRFs is polarization independent for normal incidence of light as shown in Figs. 4 and 5. Next, we will discuss the spectral details for the 2-D GMRFs without ARC and with ARC based on our simulations, QCL and FTIR measurements and compare the filter performances.

As shown in Fig. 4(a)–(c), for the simulated, QCL measured and FTIR measured transmittance spectrum for the GMRF without ARC, the first notch is at 9 µm (FWHM 100 nm, transmittance varies from 0% to 87%) and the slightly narrower second notch at 10.6 µm (FWHM 30 nm, transmittance varies from 7% to 90%); 9 µm (notch width 220 nm, transmittance varies from 2% to 72%) and the slightly narrower and shallower notch is at 10.64 µm (notch width 100 nm, transmittance varies from 18% to 72%); and 9.0 µm (notch width 220 nm, transmittance varies from 0% to 78%) and the slightly narrower notch is at 10.62 µm (notch width 90 nm, transmittance varies from 14% to 76%), respectively. For the 2-D GMRF with ARC, the simulated, QCL measured and FTIR measured transmittance spectrum are shown in Fig. 5(a)–(c) with the wider notch at 8.75 µm (FWHM 170 nm, transmittance varies from 0% to 90%) and the slightly narrower notch is at 10.26 µm (FWHM 50 nm, transmittance varies from 0% to 90%); 8.84 µm (FWHM 280 nm, transmittance varies from 4% to 90%) and the slightly narrower and shallower notch is at 10.22 µm (FWHM 110 nm, transmittance varies from 15% to 87%); and 8.82 µm (notch width 290 nm, transmittance varies from 0.7% to 90%) and the slightly narrower notch is at 10.19 µm (notch width 100 nm, transmittance varies from 7% to 87%), respectively. The measured notch wavelengths from both measurements are close to the simulated values within experimental uncertainties.

There are differences in the notch values for GMRF without ARC and with ARC due to the difference in the measured values of grating and waveguide thicknesses caused by a slight variation in the RIE process carried out to form the grating grooves. For the filters with ARC on the backside of substrate, the measured maximum transmittance from QCL measurements is ∼87%, which is slightly smaller than the predicted value. For the FTIR measurements, it is the same as the predicted value. For the filters without ARC on the backside of substrate, the measured maximum transmittance from QCL measurements is ∼72% and with FTIR it is 78%. Therefore, it is clear that the ARC on the backside of substrate improves the filter transmission as much as 15%. Also, the QCL measured spectrum for GMRF with ARC is less noisy than without ARC as shown in Figs. 4(b) and 5(b).

Using a 2-D GMRF eliminates need for orthogonally aligning two separate cascaded 1-D GMRFs required in our earlier work to achieve polarization independence [9]. The fabrication process for a 2-D GMRF is much easier than a polarization-independent monolithic double-sided orthogonal linear grating GMRF [11] as it requires only half the fabrication steps without the need to precisely align two sides of the substrate during ebeam lithography. Also, the 2-D filters with ARC yield higher maximum transmission (90% vs 84%) with much less coherent noise when used with lasers than the double-sided GMRFs [11].

4. Summary and conclusion

We designed and fabricated high-quality 2-D GMRFs on ZnSe substrates with and without ARC applied on the backside to determine whether the filter transmission can be improved and to see if coherent noise in laser experiments can be reduced. We observed ∼15% expected transmittance improvement with ARC than without ARC. We used e-beam lithography with RIE to achieve high spatial resolution in the subwavelength features. The size of the fabricated filters is 8×8 mm². We used an RCWA algorithm with optimized parameters to design the 2-D GMRF filters with the best spectral performance. A room-temperature tunable QCL system was used to carry out direct transmittance measurements. Additionally, a modified FTIR spectrometer with normal incidence of light was used to carry out traditional filter transmittance measurements. As expected, the 2-D GMRFs are insensitive to the incident light polarization at normal incidence of light. Our simulation and measurement results clearly illustrated this independence. Also, we showed that there are two notch wavelengths at normal incidence. Such filters facilitate notch filtering at either of the two notches for fixed-wavelength light emitters in the LWIR. We found that using a substrate with ARC as compared to a substrate without ARC reduces noise caused by the coherent light when used with a laser. Based on close agreement between the theoretical and experimental spectral transmittance for the fabricated GMRFs, it is clear that a 2-D GMRF is a valuable optical component when polarization-independent, fixed-wavelength notch filtering is required including for removal of laser sidebands. The 2-D filters with ARC are much easier to fabricate than our earlier work with double-sided 1-D monolithic filters and yield higher transmittance with lower coherent noise. We are working on 2-D GMRFs with high sidebands to further improve performance of polarization-independent notch filters. We are also working on understanding the detailed modal behavior of the 2-D filters.