Electrically tunable harmonics in time-modulated metasurfaces for wavefront engineering

Abstract

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 timemodulated 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 modulationinduced 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.

A Dynamically Modulated All‐Dielectric Metasurface Doublet for Directional Harmonic Generation and Manipulation in Transmission

“…The main drawback of such a quasi‐static metasurface in wavefront engineering is the relatively high variations in the amplitude during phase modulation (changing between 1 and 0.4) which can give rise to spurious scattering. In the rest of this manuscript, we study the time‐modulated performance of the metasurface which is able to circumvent this shortcoming owing to the maintained constant amplitude of higher‐order frequency harmonics by varying the modulation phase delay while covering full 2π phase span . Furthermore, the time‐modulated metasurface can increase the functionality bandwidth through dispersionless modulation‐induced phase shift of higher‐order frequency harmonics.…”

“…A high‐speed continuous tuning mechanism for all‐dielectric metasurfaces not only allows for real‐time control over the optical response but also enables realization of time‐modulated metasurfaces by applying time‐varying external stimuli. Despite their linearity, time‐modulated metasurfaces exhibit frequency‐mixing property and lead to generation of higher‐order frequency harmonics which are consisted of fundamental frequency up‐ and down‐modulated by the frequency of biasing . Unlike frequency conversion in nonlinear metasurfaces which requires high optical intensities and operates for one excitation at a time, frequency conversion in time‐modulated metasurfaces can be achieved for simultaneous excitations with arbitrary intensities.…”

“…Time modulation also renders a 4D design space and provides new degrees of freedom in light manipulation which can be used to overcome several limitations associated with quasi‐static tunable metasurfaces. In particular, the light acquires a dispersionless phase shift upon undergoing frequency conversion in a time‐modulated metasurfaces which is linearly proportional to the harmonic order and modulation phase delay, while maintaining a constant amplitude . This creates a new paradigm for designing dynamic metasurfaces with 2π phase span and uniform amplitude.…”

Theory and Design of Multifunctional Space-Time Metasurfaces

“…In this way, the total reactance is inductive and modulated in time, producing the same effect as time-varying inductance. In the terahertz and mid-infrared band, graphene is a good candidate to implement the tunable component of space-time modulated metasurfaces due to its tunable electrical conductivity and the compatibility with the advanced nanofabrication technologies [29,30,38,39,42]. Considering that graphene is a lossy material, in this section we show how one can use space-time modulated graphene sheets to create tunable wave isolators in the terahertz range.…”

Space-Time Modulation: Principles and Applications

“…It provides asymmetric interband photonic transitions [7]- [14], subluminal and superluminal phase velocities, and asymmetric dispersion diagrams [4], [11], [13], [14], and holds potential for energy accumulation [15]. Various enhanced-efficiency magnet-free microwave and optical components have been recently realized by taking advantage of the unique properties of ST modulation, including isolators [9], [11], [16]- [19], circulators [20]- [23], Manuscript pure frequency mixer [24] metasurfaces [25]- [28], one-way beam splitters [12], [14], nonreciprocal antennas [29]- [31], and advanced wave engineering [32].…”