1. Introduction

Guided-mode resonance (GMR) effects originating in quasi-guided, or leaky, waveguide modes induced on patterned films with subwavelength periods are well known [1–5]. On account of their versatility and large attendant parametric spaces, new aspects and attributes continue to appear. It has been shown that a single periodic resonance layer with one-dimensional (1D) periodicity enables narrow-line band-pass and band-stop filters, polarizers, and reflectors [6]. Applications including ultrasensitive biosensors [7], absorption-enhanced solar cells [8], and tunable filters [9] have been demonstrated. Most recently, efficient GMR color filters were realized experimentally [10].

Color filters are key elements for display devices including televisions, computers, mobile phones, digital cameras, e-readers, and multimedia projectors. They can be transmissive or reflective to suit the display technology of interest. Dye-based transmissive color filters, common in liquid crystal displays (LCD) [11], are limited by low efficiency, heating, absorption, and imperfect color selectivity. Thus, grating-based color filters [12–20] are of growing interest on account of high efficiency and improved band selection. Feasible grating materials include semiconductors (e.g., silicon) [12,13], metals (aluminum) [14–17], dielectrics (nitride/oxide) [18,19], or polymers [20]. Among these materials, Al and Si transmissive color filters exhibit relatively low efficiency [12–17] due to inherent high absorption in the visible spectral region. On the other hand, dielectric reflective filters [18,19] can provide high efficiency with reasonably narrow bandwidths improving input light utilization and color purity.

In reflective displays, the color filters must be highly efficient to utilize the available illumination well. Dielectric GMR reflection filters can have high efficiency with reasonably narrow bandwidth [5]. Recently, we reported resonant color filter arrays in which subpixels with different grating periods generate the red, green, and blue (RGB) color components in a single polarization state [10]. Angle-tuned color filters applying a single pixel to achieve the RGB primary colors were also demonstrated experimentally [19]. In both cases, high efficiency was achieved [10,19]. Prior to that, Kanamori et al. [20] reported polymer-based reflective color filters with experimental efficiency of 50%, whereas Cho et al. [21] showed reflective filters with efficiencies of 30%, 75%, and 85% for blue, green, and red colors, respectively. Using localized surface plasmons on metallic nanoantennas, a polarization-dependent color filtering was demonstrated [22]. These authors provided a blue-to-yellow color shift in transmitted light with a change of polarization. Finally, polarization-dependent transmission color filters with experimental efficiency up to 75% using a two-dimensional metal (Al) grating along with a Si₃N₄ core were illustrated [23].

In this paper, we report the design and fabrication of guided-mode resonant polarization-controlled tunable color filters (PCTCFs) based on subwavelength Si₃N₄ gratings. Our polarization-tuned filters work in reflection, and they are fabricated in lossless dielectric materials. We report experimental efficiency up to 99% with a 12-nm bandwidth and provide a good match between theory and experiment. These results exceed the performance of metal-based transmission devices [22, 23] in terms of efficiency and color purity. Polarization-tunable GMR color filters operating in reflection have not been reported previously.

2. Device structure and design

The filters under consideration consist of a partially etched silicon nitride layer on a glass substrate as illustrated in Fig. 1. The grating parameters are optimized to achieve a particular resonance wavelength with low sidebands for the unwanted part of the spectrum. The position of the resonance wavelength can be tuned by changing the structural and material properties such as refractive index, period, thickness, and incident angle as discussed in [5,24]. The resonance wavelength also depends on the polarization of the input light [5]. In this study, we control the resonance wavelength (output color) by controlling the input light polarization, thus implementing an active filter.

 

Fig. 1 Basic GMR color filter structure showing materials and device parameters with d_g = grating depth, d_h = thickness of homogeneous layer, F = fill factor, Λ = period, I = incident light wave, T₀ = zero-order transmittance, and R₀ = zero-order reflectance. The input light wave with electric-field vector (E) has TE and TM polarization components as indicated.

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We design the device using numerical methods based on rigorous coupled-wave analysis [25]. To facilitate fabrication, we keep all pixel parameters the same except the period. The optimized design parameters for both pixels are d_g = 55 nm, d_h = 110 nm, and F = 0.5. The optimized pixel periods are 300 nm for the green-blue filter and 370 nm for the red-yellow filter. The substrate is made of plain microscopic glass with a nominal refractive index of 1.48.

We change the polarization state of the input light to obtain different colors from the same physical filter. In general, on varying the polarization angle φ, we obtain the superposition of the TE and TM polarized reflectance. As noted in Fig. 1, TE polarization refers to the electric field vector being normal to the plane of incidence (along the grating grooves); it is associated with a polarization angle of 90° as defined here.

Figure 2(a) shows the computed spectral response of a green-blue polarization-tunable filter. For TE-polarized input light, the output color is green centered at 516.5 nm, and for TM polarized light, the output color is blue centered at 483.5 nm. At φ = 45°, we obtain 50% green and 50% blue that generates a cyan output color. Figure 2(b) shows the computed spectral response for the red-yellow polarization-tunable color filter. TM-polarized input light provides an output yellow color centered at 575 nm, whereas TE-polarized light yields an output red color centered at 619 nm. At φ = 45°, we get 50% red and 50% yellow color that generates an orange output color. Using the experimental reflectance of the color filters, the displayable red, green, and blue primary colors can be computed [10].

 

Fig. 2 (a) Computed spectral response of the green-blue polarization-controlled tunable color filter; design parameters are d_g = 55 nm, d_h = 110 nm, F = 0.5, and Ʌ = 300 nm. (b) Computed spectral response of the red-yellow filter; design parameters are d_g = 55 nm, d_h = 110 nm, F = 0.5, and Ʌ = 370 nm. We use n = 2.02 and n_s = 1.48 in both cases.

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In practical applications, light is not necessarily normally incident on a pixel; we assume it is normally incident in the current study for the sake of simplicity. To show that these assumptions hold under small angular deviations, we treat an example representative pixel under oblique incidence. It is well-known that as the input angle deviates from zero, the resonance peak splits due to counter propagating positive and negative first-order diffraction [5]. In the present case at small off-normal incidence, these split resonances remain spectrally close preserving the perceived color. Figure 3(a) shows an example for TM-polarized incident light with the design parameters representing the blue-green filter in Fig. 2(a). It is evident that even though we change the incident angle from 0° to 5° (total input cone angle being 10°), the split resonances remain in the blue-color region and a viewer will not see much difference in the perceived color as expressed in Fig. 3(b). The detailed method for calculating perceived colors from reflectance values can be found in [10].

 

Fig. 3 (a) Spectral response of a blue pixel with TM-polarized obliquely incident light. (b) Effect of off-normal incident light on the perceived color emanating from the pixel.

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3. Device fabrication and characterization

To fabricate the filters, we deposit a Si₃N₄ thin film on a cleaned glass substrate using a sputtering system. Thereafter, we spin-coat a 300-nm-thick positive photoresist (PR) layer on the film. To increase the adhesion between PR and Si₃N₄, we spin-coat a thin layer of hexamethyldisiloxane (HMDS) on the film before applying the PR. Then we record a 1D grating pattern on the PR using a laser interferometric lithography system that is based on a classic Lloyd-mirror geometry with a pattern period conveniently controlled by a simple stage rotation. The exposing laser has a 266-nm wavelength; it is well-polarized and provides up to 200 mW output power in a narrow spectral band. To etch the nitride film, we use reactive ion etching (RIE) involving a gas mixture of trifluromethane (CHF₃) and oxygen (O₂). After RIE, a thin PR film still adheres to the grating; it is stripped using O₂ plasma. Finally, we use wet cleaning with nanostrip (90% H₂SO₄ and 5% H₂O₂) followed by O₂ plasma ashing to ensure that no PR remains on the nitride grating. A step-by-step summary of the fabrication details is given in Fig. 4.

 

Fig. 4 Summary of the fabrication steps of the color filter.

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We characterize the device using an atomic force microscope (AFM), a scanning electron microscope (SEM), and an ellipsometer. From the AFM measurement, we verify the period, grating thickness, and fill factor. Thus, we find the fabricated device parameters as d_g ≈54 nm, Λ ≈301 nm, and F ≈0.49. The ellipsometric Si₃N₄ film thickness is 150 nm, specifying the homogeneous film thickness as 96 nm. The film has a refractive index of n = 2.05 at the wavelength of 550 nm. The AFM image of a fabricated green-blue filter is shown in Fig. 5. An SEM image of a similar green-blue filter is given in Fig. 6, which closely matches the parameters obtained from AFM and ellipsometry.

 

Fig. 5 AFM image showing the grating profile of a green-blue PCTCF. Device parameters are d_g ≈54 nm, d_h ≈96 nm, Ʌ ≈301 nm, and F ≈0.49.

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Fig. 6 SEM image of the green-blue PCTCF (a) top view and (b) cross-sectional view. Device parameters from SEM measurements are d_g ≈55 nm, d_h ≈90 nm, Ʌ ≈306 nm, and F ≈0.45.

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From the AFM measurement of the fabricated red-yellow tunable filter, the device parameters are d_g ≈60 nm, Λ ≈369 nm, and F ≈0.46. The ellipsometric measurement shows that the total Si₃N₄ film thickness is 165 nm, determining the homogeneous layer thickness of 105 nm. The refractive index of Si₃N₄ is found to be n = 2.02 at a wavelength of 550 nm. The parameters are verified using an SEM measurement of the device.

The fabricated devices parameters found from AFM, SEM, and ellipsometry measurements are close to the design parameters. The fabricated pixels presented here are very large (5 × 5 mm²) for convenience in characterization and spectral measurements. To apply this technology in devices, the pixels should be much smaller. The effective pixel size can be calculated using the decay length of the leaky waveguide mode. The decay length is approximately L_d ≈Λλ/4πΔλ, where Δλ is the spectral linewidth of the filter [3]. Using this equation, we estimate the decay length as ~2 μm. Thus, this pixel should work well with, for example, 10 × 10 μm² lateral dimensions, which significantly exceed this decay limit.

4. Results and discussion

The reflectance of the fabricated filters as a function of wavelength is measured using a spectrum analyzer. A tungsten halogen lamp with a wavelength range of 360–2000 nm serves as the light source. A polarizer is mounted in front of the light source to select a specific polarization state. We can change the polarization angle φ from 0° to 90° using our measurement setup. First, we measure the reflected light intensity as a function of wavelength from a reference aluminum mirror. Then, we measure the reflected light intensity from the color filter. Finally, we calculate the reflectance of the filter by taking the ratio of the intensity reflected from the sample to the intensity reflected from the reference mirror for each wavelength.

Figure 7 shows the experimental and theoretical reflectance of the blue-green tunable filter. For φ = 0°, the output color is blue and the center wavelength is 480 nm for both theory and experiment. For φ = 90°, the output color is green and the center wavelength is 518 nm for experiment and 520 nm for theory. The measured full-width-at-half maximum (FWHM) spectral width is ~12 nm for the green and 10 nm for the blue pixel. The theoretical spectral width is 10 nm for green and 8 nm for blue. The fabricated device parameters are Λ = 301 nm, d_g = 54 nm, d_h = 96 nm, F = 0.49. The parameters used for simulation are Λ = 305 nm, d_g = 51 nm, d_h = 96 nm, F = 0.45, n = 2.05, n_s = 1.48; these are close to the fabricated device parameters.

 

Fig. 7 Spectral response of the green-blue PCTCF. For TM (φ = 0°) polarization, we have a blue filter with R₀ = 80% at λ_c = 480 nm. For TE (φ = 90°) polarization, we have a green filter with R₀ = 90% at λ_c = 518 nm. We denote λ_c = center wavelength of a pixel, where the efficiency is maximum.

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Figure 8 compares the experimental and simulated reflectance of the red-yellow tunable pixel. For φ = 0°, the output color is yellow and the center wavelength is 573 nm for both theory and experiment. For φ = 90°, the output color is red and the center wavelength is 607 nm for experiment and 616 nm for theory. The measured FWHM spectral width is ~12 nm for the red and 8 nm for the yellow pixel. The theoretical spectral width is 10 nm for red and 6 nm for yellow. The fabricated device parameters are Λ = 369 nm, d_g = 60 nm, d_h = 105 nm, F = 0.46. For simulation, we used the fabricated device parameters.

 

Fig. 8 Spectral response of the red-yellow PCTCF. For TM polarization, we have a yellow filter with R₀ = 80% at λ_c = 573 nm. For TE polarization, we have a green filter with R₀ = 90% at λ_c = 607 nm. We denote λ_c = center wavelength of a pixel, where the efficiency is maximum.

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Figure 9(a) shows the CIE chromaticity diagram displaying the color gamut of the PCTCF. Due to the availability of four RGYB colors from two pixels, it shows a quadrilateral color gamut instead of the conventional triangular color gamut from RGB pixels. From the experimental reflectance values, standard RGB components (sRGB) values are calculated. The sRGB values are 105, 107, and 133 for the blue pixel; 0, 145, and 85 for the green pixel; 162, 85, and 27 for the red pixel; and 128, 123, and 27 for the yellow pixel. Figure 9(b) shows the perceived colors using the sRGB values of the pixels calculated from the experimental reflectance values.

 

Fig. 9 (a) CIE chromaticity diagram showing the color gamut of the prototype tunable color filters. (b) Perceived colors constructed from the experimentally observed reflectance values.

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5. Conclusions

Efficient reflective polarization-controlled tunable color filters are designed and fabricated using subwavelength Si₃N₄ resonant ratings. A red color filter for TE-polarized light produces a yellow color with TM-polarized light. A green filter for TE-polarized light produces a blue color with TM-polarized light. Therefore, the two pixels successfully generate four colors without any intermediate mixing. The fabricated filters possess narrow bandwidth with experimental efficiencies in excess of 90% for TE- and 80% for TM-polarized light. We find a reasonable match between the experimental data and theoretical results. The device has potential for applications in displays, image sensors and biomedical imaging technologies.