Phase-Induced Frequency Conversion and Doppler Effect With Time-Modulated Metasurfaces

Abstract

Metasurfaces consisting of electrically thin and densely packed planar arrays of subwavelength elements enable an unprecedented control of the impinging electromagnetic fields. Spatially modulated metasurfaces can efficiently tailor the spatial distribution of these fields with great flexibility. Similarly, time modulated metasurfaces can be successfully used to manipulate the frequency content and time variations of the impinging field. In this paper, we present time-modulated reflective metasurfaces that cause a frequency shift to the impinging radiation, thus realizing an artificial Doppler effect in a non-moving electrically thin structure. Starting from the theoretical analysis, we analytically derive the required time modulation of the surface admittance to achieve this effect, and present a realistic timevarying structure, based on a properly designed and dynamically tuned high-impedance surface. It is analytically and numerically demonstrated that the field emerging from the metasurface is up-/down-converted in frequency according to the modulation profile of the metasurface. The proposed metasurface concept, enabling a frequency modulation of the electromagnetic field "on-the-fly", may find application in telecommunication, radar, and sensing scenarios.

High‐Efficiency Synthesizer for Spatial Waves Based on Space‐Time‐Coding Digital Metasurface

“…Recently some transmission‐type time‐modulated metasurfaces are proposed and demonstrate good nonlinear effects, they still suffer from the limitations like the system complexity and large loss toward practical applications. [ 16–20 ]…”

Topological Space‐Time Photonic Transitions in Angular‐Momentum‐Biased Metasurfaces

“…As it has been recently shown, [ 70,78,79,82,83 ] adjusting the temporal modulation waveform can be used to control the spectral diversity of generated frequency harmonics by a TMM in the adiabatic modulation regime ( f m << f 0 ) through engineering the temporal evolution of the phase and amplitude of steady‐state scattered fields which can be mapped to the quasistatic response corresponding to the external bias at each instant of time. By setting modulation phase delay dependent on the azimuthal angle as α = U (φ), we can express the spatiotemporal modulation waveform of an angular‐momentum‐biased metasurface as a truncated Fourier series in the form of which is a representative of an arbitrary periodic signal with a temporal periodicity of T m = 1/ f m and an azimuthal phase delay profile of U (φ).…”

“…This leads to the n th frequency harmonic exhibiting a topological charge of l = nq , according to Equation (). Particularly, engineering the temporal profile of modulation waveform in such a way that it yields serrodyne frequency conversion (pure frequency mixing) through a linear modulation of quasi‐static phase over 2π span at each cycle of modulation [ 70,78,82,83 ] will yield a frequency shift in the reflected light which is proportional to the change in the orbital angular momentum ( n = l / q ). In such a case, the angular‐momentum‐biased metasurface mimics the unidirectional spinning of a q ‐plate and the result complies with the phenomenon of rotational Doppler shift, [ 80,81 ] which has been demonstrated using mechanically spinning q ‐plate metasurfaces utilizing geometric phase shift and spin‐orbit coupling.…”

“…A desired spectral distribution of frequency harmonics dictates the temporal profiles of amplitude and phase (∠ r ( t ) and |r( t )|) which depend on the resonant dispersion of the metasurface as well as the modulation waveform. [ 70,78,79,82,83 ] The key to ideal realization of a desired output spectrum of frequency harmonics is dynamic and independent control over phase and amplitude of the quasi‐static response by engineering the modulation waveform which proves to be prohibitive in tunable metasurfaces due to limited phase span and inevitable correlation between amplitude and phase. While the modulation waveform can be engineered by merely considering the temporal evolution of the phase (similar to the phase‐only spatial holograms) to arrive at a nonideal output spectrum, adopting an evolutionary algorithm for optimizing the modulation waveform can yield a more desired response by taking into account the correlation and trade‐offs between phase and amplitude.…”

“…In the case of pure frequency mixing, the optimized modulation waveform in Figure 4a exhibits a sawtooth‐like pattern as an ideal serrodyne frequency translation is induced by a sawtooth temporal phase profile modulating the quasi‐static phase linearly over 2π span at each cycle of modulation (∠ r ( t ) = ω m t ). [ 70,78,82,83 ] The output spectrum in Figure 4b indicates that most of the reflected power is residing at the first up‐modulated frequency harmonic (i.e., f = f 0 + f m ). The normalized frequency conversion efficiency is calculated as 59%.…”