Time-modulated Metasurfaces Research Articles

Electrically tunable harmonics in time-modulated metasurfaces for wavefront engineering

Modulation of metasurfaces in time gives rise to several exotic space–time scattering phenomena by breaking the reciprocity constraint and generation of higher-order frequency harmonics. We introduce a new design paradigm for time-modulated metasurfaces, enabling tunable engineering of the generated frequency harmonics and their emerging wavefronts by electrically controlling the phase delay in modulation. It is demonstrated that the light acquires a dispersionless phase shift regardless of incident angle and polarization, upon undergoing frequency conversion in a time-modulated metasurface which is linearly proportional to the modulation phase delay and the order of generated frequency harmonic. The conversion efficiency to the frequency harmonics is independent of modulation phase delay and only depends on the modulation depth and resonant characteristics of the metasurface, with the highest efficiency occurring in the vicinity of resonance, and decreasing away from the resonant regime. The modulation-induced phase shift allows for creating tunable spatially varying phase discontinuities with 2π span in the wavefronts of generated frequency harmonics for a wide range of frequencies and incident angles. Specifically, we apply this approach to a time-modulated metasurface in the Teraherz regime consisted of graphene-wrapped silicon microwires. For this purpose, we use an accurate and efficient semi-analytical framework based on multipole scattering. We demonstrate the utility of the design rule for tunable beam steering and focusing of generated frequency harmonics giving rise to several intriguing effects such as spatial decomposition of harmonics, anomalous bending with full coverage of angles and dual-polarity lensing. Furthermore, we investigate the angular and spectral performance of the time-modulated metasurface in manipulation of generated frequency harmonics to verify its constant phase response versus incident wavelength and angle. The nonreciprocal response of the metasurface in wavefront engineering is also studied by establishing nonreciprocal links with large isolations via modulation-induced phase shift. The proposed design approach enables a new class of high-efficiency tunable metasurfaces with wide angular and frequency bandwidth, wavefront engineering capabilities, nonreciprocal response and multi-functionality.

Finite-Difference Time-Domain Modeling of Space–Time-Modulated Metasurfaces

A finite-difference time-domain modeling of finite-size zero thickness space–time-modulated Huygens’ metasurfaces based on generalized sheet transition conditions is proposed and numerically demonstrated. A typical all-dielectric Huygens’ unit cell is taken as an example and its material permittivity is modulated in both space and time, to emulate a traveling-type spatio-temporal perturbation on the metasurface. By mapping the permittivity variation onto the parameters of the equivalent Lorentzian electric and magnetic susceptibility densities, $\chi _{\text {ee}}$ and $\chi _{\text {mm}}$ , the problem is formulated into a set of second-order differential equations in time with nonconstant coefficients. The resulting field solutions are then conveniently solved using an explicit finite-difference technique and integrated with a Yee-cell-based propagation region to visualize the scattered fields taking into account the various diffractive effects from the metasurface of finite size. Several examples are shown for both linear and space–time varying metasurfaces which are excited with normally incident plane and Gaussian beams, showing detailed scattering field solutions. While the time-modulated metasurface leads to the generation of new collinearly propagating temporal harmonics, these harmonics are angularly separated in space, when an additional space modulation is introduced in the metasurface.