Angular Dispersions in Terahertz Metasurfaces: Physics and Applications

Angular dispersion—the response of a metasurface strongly depending on the impinging angle—is an intrinsic property of metasurfaces, but its physical origin remains obscure, which hinders its applications in metasurface design. We establish a theory to quantitatively describe such intriguing effects in metasurfaces, and we verify it by both experiments and numerical simulations on a typical terahertz metasurface. The physical understanding gained motivates us to propose an alternative strategy to design metadevices exhibiting impinging-angle-dependent multifunctionalities. As an illustration, we design a polarization-control metadevice that can behave as a half- or quarter-wave plate under different excitation angles. Our results not only reveal the physical origin of the angular dispersion but also point out an additional degree of freedom to manipulate light, both of which are important for designing metadevices facing versatile application requests.

Figure 1

(a),(b) Manifestation of angular dispersion in metasurfaces (MS) represented by resonant frequency shift ($f_1\ne f_2$) of a metasurface seen at different incidence angles (${\theta }_1\ne {\theta }_2$). (c),(d) Schematics of an incident-angle-dependent multifunctional metadevice for polarization control on a reflective beam. Here, the metadevice can convert a linearly polarized (LP) wave to a right-handed (RCP) or left-handed circular-polarized (LCP) wave under different incidence angles.

Figure 2

(a) Optical picture of part of the fabricated terahertz metasurface sample. (b) Schematics of our experimental characterizations on angular dispersion of the terahertz samples. The incident light lies in the $x\text{−}z$ plane, while the in-plane $\mathbf{E}$ field is polarized along the direction, as shown in the inset. (c),(d) Measured (scatter) transmittance spectra of the metasurfaces with different incident angles for the TM ($\alpha =0°$) and TE ($\alpha =90°$) polarizations, respectively. (e),(f) Computed rescaled transmittance $\delta T$ (color map) of two metasurfaces (with $\alpha =0°$ and $\alpha =90°$) versus the frequency and incident angle, with stars representing the measured resonant-mode positions. Geometrical parameters of the SRR: inner and outer radius, $R_1=20\mu \mathrm{m}$ and $R_2=30\mu \mathrm{m}$; gap width, $g=6\mu \mathrm{m}$. Lattice constant of the array, $P=70\mu \mathrm{m}$.

Figure 3

(a) Resonant frequency shifts versus incident angles for metasurfaces with different values of $\alpha$ obtained through experiments (the stars), FEM simulations (the solid lines), and TBM calculations (the dashed lines). (b) $J_1$ and $J_2$ calculated with the TBM for samples with different $\alpha$ values. (c) Nearest-neighbor coupling strength $t_{(0,0)}^{(1,0)}$ as a function of $\alpha$, obtained through direct TBM calculations (scatters) and through the effective model Eq. (5) (the red line). (Inset) $E_z$-field distribution on the structure surface calculated with FEM simulations at frequency 0.63 THz.

Figure 4

(a) Side and top views of the designed meta-atom. (b) $E_z$-field distributions on the structural surfaces in two different cases, obtained with FEM simulations at 0.54 THz under normal incidence. (c) FEM-simulated reflection-phase spectra of the designed metasurface shined by terahertz waves at different incident angles with TE (solid lines) and TM (dotted lines) polarizations. (d) Resonant frequency versus incident angle as the metasurface is shined by oblique incident waves taking TE (red) and TM (blue) polarizations, obtained with FEM simulations (the circles) and theoretical calculations based on the TBM (the solid lines). (e) FEM-simulated reflection-phase difference between TE and TM cases for our metasurface versus incident angle and frequency. (f) TE-TM reflection-phase difference (the solid line) as a function of incident angle, calculated with FEM simulations at 0.55 THz, showing that the reflected beam can exhibit different polarization states if the input wave is linearly polarized as depicted in the inset. The geometrical parameters are $P=100\mu \mathrm{m}$, $L_c=92\mu \mathrm{m}$, $L_b=40\mu \mathrm{m}$, $w=8\mu \mathrm{m}$, $h_m=1\mu \mathrm{m}$, and $h_i=4\mu \mathrm{m}$.