1. Introduction

Guided-mode resonance (GMR) effect of subwavelength waveguide grating (SWG) occurs when the diffracted light from the grating structure is phase matched with the leaky mode supported by the waveguide [1], leading to a sharp resonant reflection peak or transmission dip in diffraction spectrum. Among the numerous applications based on GMR effect, GMR filter is a basic type [2, 3]. Owing to its high efficiency, low sideband and controllable bandwidth, GMR filter has potentials to be further developed as high-sensitivity sensors [4, 5] or color filters [6, 7]. The polarization of the incidence can affect the resonant effect of GMR filter, especially for one-dimensional (1D) resonant grating. Generally, the sensitivity against the polarization can be well used in polarizer [8, 9] or polarization-controlled tunable color filter [10], but under certain applications such as dense wavelength division multiplexing [11] and laser devices [12], polarization-insensitive filter plays a critical role.

A variety of designs have been proposed to realize polarization-insensitive filters, mainly focusing on GMR filters with 2D grating structure to eliminate the polarization sensitivity under normal [13] or oblique incidence [14]; and designs with 1D grating under full conical incidence [15, 16]. In the classic incident plane, Muhammad et al. presented two types of 1D GMR gratings with non-polarizing resonance properties at normal incidence [17, 18]. Hu Xu-Hui et al. presented a theoretical polarization-independent GMR filter at oblique incidence in the infrared range [19]. Among most of reported structures, the grating bars are fully surrounded by low-index materials; resulting in a large refractive index contrast, herein referred to as high-contrast gratings (HCGs) [20]. In contradistinction to substantial refractive-index discontinuity at the grating/substrate interface for HCG, zero-contrast grating (ZCG) refers precisely to the same interface without ambiguity; thereby eliminating local interface reflections and phase changes [21, 22].

In this paper we experimentally demonstrate a polarization-insensitive ZCG filter operating in the visible range. The oblique incident angle where the polarization-insensitive resonance occurs is directly observed in the angular-resolved spectrum. Moreover, the identical structure can also act as a polarization-tunable color filter when the incident light is normal to the grating surface [10]. This free-standing multi-functional device is implemented on an HfO₂/Silicon platform. Experimental results are in good agreement with the simulations obtained by rigorous coupled-wave analysis (RCWA) method [23].

2. Design and fabrication

Figure 1 illustrates the schematic structure of the proposed free-standing ZCG device. The device is fully surrounded with air, and the higher refractive index of HfO₂ film, which is set to be 1.95 for simplicity, endows the thin-film system the capability to support optical modes. The sub-wavelength grating period Λ allows the device work in the zero-order diffraction regime. Filling factor refers to the ratio of the grating width with respect to the grating period, i.e., η = w/Λ. Classic incidence is the precondition in this paper, which means the incident wave vector is in the xz-plane (azimuthal angle = 0°). θ is the incident angle measured from z-axis in the xz-plane. The polarization of the E vector is oriented in a polarization (p-s) plane normal to the direction defined by the wavevector K. Within this plane, the polarization angle ϕ sets the orientation of E, where a value of 0 corresponds to the s-polarization, and 90 specifies the p-polarization.

 

Fig. 1 Schematic structure of the free-standing ZCG filter, where t_g is the grating thickness, t_m is the HfO₂ film thickness, Λ is the grating period and w is the grating width.

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The total HfO₂ membrane consisting of HfO₂ grating and HfO₂ waveguide layer is evaporated on silicon substrate by electron beam evaporation with a thickness t_m of 200nm. When HfO₂ grating thickness increases, the thickness of HfO₂ waveguide layer correspondingly decreases, leading to different optical characterizations of the filter. There is a trade-off between the thickness of HfO₂ grating and HfO₂ waveguide layer where optimal optical response can be obtained. Based on RCWA method, the optimized design parameters where low sideband and narrow line-width can be achieved are filling factor η = 0.5, grating thickness t_g = 70nm and the HfO₂ waveguide layer thickness (t_m-t_g) = 130nm. The grating period Λ used in this paper is 400nm.

The free-standing polarization-insensitive ZCG filter is implemented on a prepared HfO₂/Silicon film by combining ion beam etching (IBE) of HfO₂ film with deep reactive ion etching (DRIE) of silicon substrate from backside [24, 25]. The structure morphology of fabricated ZCG filter is characterized by scanning electron microscope (SEM) and atomic force microscope (AFM). The free-standing ZCG filter consisting of 29 grating lines is well shaped without any cracking of grating lines, as shown in Fig. 2(a). Figure 2(b) shows the geometry parameters of grating, including period of 400nm, thickness of 70nm and filling factor of 0.5. The cross section depth of the fabricated ZCG filter is shown in Fig. 2(c).

 

Fig. 2 (a) SEM image of the fabricated polarization-insensitive ZCG filter, with the magnification of the grating line inset; (b) and (c) AFM images of the grating structural profile.

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3. Results and analysis

By a combination of homogeneous waveguide eigenfunction and the phase-matching condition of periodic structure, dispersion relations of leaky guided mode in the waveguide grating can be plotted for locating the resonance loci [1, 26]. Intrinsic and straightforward approaches have been taken to obtain the dispersion relations [27, 28]. In this paper, the incident angle where the polarization-insensitive resonance occurs can be determined by calculating the reflectance of ZCG filter as a function of wavelength and incident angle using commercially available software, RSoft’s Diffract-MOD, which is based on RCWA method. The RCWA method can provide reliable simulation results when the number of grating lines is large enough [26]. Figure 3 illustrates the simulated angular-resolved reflectance for the linear HfO₂ ZCG filter under different polarization angles. Figures 3(a) and 3(d) provide the particular optical response corresponding to s- and p-polarization, respectively. The difference between which is caused by the different eigenfunctions. Varying the polarization angle ϕ by the step of 30°, the angular-resolved reflectance of the ZCG filter with an intermediate polarization angle shown in Figs. 3(b) and 3(c) have clearly revealed that they are composing from the superposition of Figs. 3(a) and 3(d). Owing to the angle symmetry, we only analyze the positive incident angle. Varying ϕ from 0° to 90° can generate a continuously transition from Fig. 3(a) to Fig. 3(d). During this continuously transition, there are two distinct crossing points labeled p1 and p2 (θ_p1 = 7.8°, θ_p2 = 12.1°) which can be easily obtained from Fig. 3(b) or Fig. 3(c) remaining existing, where both s- and p-polarizations have the same propagation constant, resulting in polarization-insensitivity. These polarization-insensitive locations can be induced from angular-resolved reflectance plot with an intermediate polarization angle to the same position. Once the polarization-insensitive θ are determined, with a corresponding θ_p1 and θ_p2 white dash lines drawn in Figs. 3(a) and 3(d), we can get the crossing points p1 and p2 referring as polarization-insensitive locations marked by ellipse boxes in the particular optical response corresponding to s- and p-polarization, respectively. As for other oblique incident angle, along with either s- or p-polarization, no overlap causes polarization sensitivity. When the incident light is normal to the grating surface, resonant locations p3 and p4 occur with different polarization angles, corresponding to different wavelengths, which can be well used as polarization-controlled tunable color filter [10].

 

Fig. 3 Simulation results of angular-resolved reflectance for the linear HfO₂ ZCG filter with Λ = 400nm, η = 0.5, and t_g = 70nm under different polarization angles: (a) ϕ = 0° (s-polarization); (b) ϕ = 30°; (c) ϕ = 60°; (d) ϕ = 90° (p-polarization).

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Figures 4(a) and 4(b) show the spectral reflectivity of the proposed ZCG filter under incident angle of θ = 7.8° and θ = 12.1°, respectively. In order to demonstrate the polarization-insensitivity, four different polarization angles (ϕ = 0°, 30°, 60°, 90°) are used to obtain the spectral reflectivity. Simulation results show that the resonant wavelengths (λ_p1 = 595nm and λ_p2 = 499nm) are insensitive to polarization under the oblique incidence of θ_p1 and θ_p2. The reflectance spectrum of the ZCG filter under normal incidence with four different polarization states is illustrated in Fig. 4(c). For p-polarized (ϕ = 90°) incidence, the output color is yellow centering at 546nm; and for s-polarized (ϕ = 0°) incidence, it is red centering at 638nm. When the polarization angles ϕ are 30° and 60°, the device reflects light with orange color due to the superimposition of yellow and red color, indicating its potential application in polarization-controlled tunable color filter.

 

Fig. 4 Reflectance spectra with different polarization angle ϕ under incident angle: (a) θ = θ_p1 = 7.8°, (b) θ = θ_p2 = 12.1°, (c) normal incidence θ = 0°.

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The optical characterizations of the fabricated HfO₂ ZCG filter are performed by an angular-resolved micro-reflectance measurement system [29]. Figure 5(a) shows the simulated angular-resolved reflectance spectra of the proposed HfO₂ ZCG filter under polarization angle ϕ of 45°. The two distinct crossing points labeled as p1 and p2 (θ_p1 = 7.8°; θ_p2 = 12.1°) indicate the incident angle and resonance wavelength where the polarization-insensitivity occur. Figure 5(b) illustrates the measured angular-resolved reflectance spectra of the fabricated HfO₂ ZCG filter under ϕ = 45°. The polarization-insensitive incident angles are θ_p1’ = 12.8° and θ_p2’ = 14.2°, corresponding to the incident angles θ_p1 = 7.8° and θ_p2 = 12.1° in Fig. 5(a), respectively. The angle shifts may be caused by the deviations between the fabricated gratings and the ideal element. Figure 5(c) shows the simulated and experimental reflectance of the HfO₂ ZCG filter under incident angle relating to the first crossing point (p1, p1’). The polarization-insensitive center wavelength is ~595nm for both theory and experiment, corresponding to the incident angle θ_p1 = 7.8° and θ_p1’ = 12.8°. Figure 5(d) compares the theoretical and experimental reflectance of the HfO₂ ZCG filter under incident angle relating to the second crossing point (p2, p2’). The calculated polarization-insensitive resonant wavelength locates at ~499nm wavelength under the incident angle θ_p2 of 12.1°, and the measured polarization-insensitive resonant wavelength locates at ~500nm under the incident angle θ_p2’ of 14.2°. The relatively lower efficiency in experimental result may be caused by rough side wall of the fabricated grating or the deviation in grating profile against the ideal model. It can be improved by optimizing the parameters during the fabrication process.

 

Fig. 5 (a) Simulated, (b) measured angular-resolved reflectance for the linear HfO₂ GMRF under polarization angle ϕ of 45°; reflectance spectrum under incident angles: (c) θ_p1 and θ_p1’, (d) θ_p2 and θ_p2’

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Figure 6 shows the measured angular-resolved reflectance spectra of the fabricated HfO₂ ZCG filter under four different polarization angles ϕ with the step of 30°. The two crossing points labeled as p1’and p2’ in each of the angular-resolved reflectance spectra corresponding to the incident angle and resonance wavelength where the polarization-insensitivity occur. Under the incident angle θ_p1’ and θ_p2’, the reflectance spectra with different polarization angles are plotted in Figs. 7(a) and 7(b), respectively. Polarization-insensitive resonances are observed at ~595nm in Fig. 7(a) and ~500nm in Fig. 7(b), which agree well with the simulated resonant wavelengths ~595nm in Fig. 4(a) and ~499nm in Fig. 4(b). Figure 7(c) illustrates the reflectance spectra under normal incidence with different polarizations. The resonant peak locates at ~ 560nm when the incident light is p-polarized and at ~ 656nm when the incident light is s-polarized; corresponding to the 546nm for p-polarized and 638nm for the s-polarized incidence in Fig. 4(c). These results indicate the color of the reflected lights can be tuned at normal incidence by changing the polarization of the incident light.

 

Fig. 6 Measured angular-resolved reflectance for the fabricated HfO₂ ZCG filter with different polarization angle (a) ϕ = 0°; (b) ϕ = 30°; (c) ϕ = 60°; (d) ϕ = 90°.

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Fig. 7 Measured reflectance spectrum under different incident angles (a) θ = θ_p1’ = 12.8°, (b) θ = θ_p2’ = 14.2°, (c) normal incidence θ = 0°.

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4. Summary

In this paper, a free-standing ZCG filter implemented on HfO₂/Silicon platform is presented. When the incidence angle θ is 12.8°, the HfO₂ ZCG filter demonstrates the polarization-insensitive resonance at 595nm, and for incidence angle θ of 14.2°, polarization-insensitive resonance occurs at 500nm, suggesting its potential application in polarization-insensitive filter. The identical structure can also serve as a polarization-controlled tunable color filter when the incidence light is normal to the grating surface; reflecting the light with yellow and red colors under p- and s-polarization, respectively. The spectral properties are calculated by the RCWA method and measured by angular-resolved micro-reflectance system. Experimental results agree well with the simulations, which indicate that the proposed ZCG structure is promising for polarization-insensitive filter and polarization-controlled tunable color filter.