Dispersion Engineered Metastructures Enabling Broadband Angular Selectivity

Abstract

Angle-selective optical devices are of importance to several applications such as photovoltaics, high-sensitivity photodetectors and displays. There are several approaches to realizing angular selectivity, but it remains challenging to obtain isotropic responses over large spectral bandwidths in optically thin structures. We introduce a dispersion engineering approach coupled with topology optimization to design 2D metastructures, leveraging guided-mode resonances (GMRs), that exhibit isotropic angular selectivity over relative bandwidths of approximately 20%. We experimentally demonstrate metastructures with complementary angular selectivities, either scattering light strongly near normal incidence and transmitting efficiently at higher incident angles, or vice versa. A key finding is that these designs enable operation over spectral bandwidths greater than the GMR linewidths would suggest, a result of carefully tailored interactions between the Fabry-Perot background and resonantly scattered light. This work marks a significant step forward for the realization of broadband, angle-selective scattering in readily fabricated structures of subwavelength thickness, and enables new possibilities in sensing, analog information processing, high-efficiency photovoltaics, and displays.

Figures (4)

• Figure 1: a) The left panel shows an ideal angle-selective response while the right one represents what one typically encounters in practice. The color scale can indicate either transmittance or reflectance. b) The two kinds of angular selectivity under consideration. On the left is a situation where light exhibits specular transmission near normal incidence and strong scattering at higher angles. On the right, the opposite case is shown.
• Figure 2: Dispersion engineering in 1D dielectric gratings. a) Transmittance predicted by coupled-mode theory for two non-orthogonal modes of odd symmetry coupled to a Fabry-Perot background. The $\omega_{\mathrm{FP}}$ labels represent the first two FP modes of the slab, which is parameterized by a thickness of 0.45 $\mu m$ and an effective index of 3.5, similar to silicon. The resonances are both tuned to $\omega_{\mathrm{FP,1}}$ when $k_x=0$ The predicted transmittance of the same modes but instead tuned to $\omega_{\mathrm{FP,2}}$ for b)$Q_{\mathrm{mode}}=31.7$ and c)$Q_{\mathrm{mode}}=6.3$. d) Cross section of the extruded grating geometry consisting of patterned Si on a glass substrate illuminated with a plane wave. e) Simulated $E_x$ profiles of the upper and lower branches of the lowest order GMR band at $k_x=0$ in a structure with $w_{\mathrm{air}}=0.02$$\mu m$. The field amplitudes are normalized to their respective largest absolute value. f) Simulated transmittance with FDTD of the grating with $w_{\mathrm{air}}=0.02$$\mu m$ (left) and $w_{\mathrm{air}}=0.29$$\mu m$ (right). In the left panel, the resonant modes of the structure are shown as white circles overlaid on the transmittance; they are calculated by analyzing the decaying tail of the field amplitudes after exciting the grating with a point source. g) The angular width over which transmittance is strongly suppressed, defined as the angle where $T(k_x)=T_{\mathrm{max}}/2$ for each $\omega$ in the spectral band of interest. The average value is 18.1°.
• Figure 3: Isotropic angular selectivity with topology optimization. a) Forward designed 2D grating structure obtained through a "naive" extension of the 1D version. On the left, a bird's eye view of the unit cell is shown with a period of 0.76 $\mu m$ and $w_{\mathrm{air}}=0.29$$\mu m$. The transmittance calculated with RCWA is shown on the right. b) Topology-optimized unit cell and an SEM of the fabricated metastructure. The thickness and period are 0.475 $\mu m$ and 0.705 $\mu m$, respectively. Simulated c) and experimentally measured d) transmittance of the topology-optimized structure as a function of wavelength and incident polar angle for $\phi=0\degree$ and $\phi=45\degree$. e) Simulated transmittance as a function of $k_x$ and $k_y$ for four wavelengths.
• Figure 4: Band-pass angular selectivity. a) Simulated transmittance (RCWA) for a 1D grating structure with a thickness and period of 0.4 $\mu m$ and 0.45 $\mu m$, respectively, for two different values of $w_{air}$. b) Nominal and fabricated unit cell of 2D metastructure. c) Simulated transmittance along $\phi=0\degree$ and $\phi=45\degree$. d) Line cuts along $\theta_{inc}$ of transmittance for three wavelengths. e) Experimentally measured transmittance for the structure in b).