Fig. 1. Conceptual demonstration of light interaction with space–time gradient nonreciprocal metasurface. The metasurface comprises a periodic arrangement of a-Si SWG over the SiO2 substrate that is backed by a four-layer DBR. The optimized dimensions are as follows (units in nm): w=853, h1=684, h2=749, h3=104, h4=266, and Λ=1007. The incoming TE-polarized light with the frequency ωc (electric field along the SWG) from port 1 is coupled to port 2 upon upconversion, whereas the incident light coming from port 2 is strongly suppressed after upconversion when coupled to port 1. Therefore, the free-space ports 1 and 2 are isolated. Close-up: the SWG that is configured as three pairs of p–n junctions and the multigate biasing scheme. The modulation is enabled by applying the time-varying signal with the modulation frequency ωm and RF phase shifters to induce the required phase gradient across the metasurface.

Fig. 2. Simulated characteristics of all-dielectric high-Q time-invariant metasurface under normal illumination of TE-polarized light. The spectral distribution of the metasurface reflection amplitude as functions of (a) width (w) when h1 is fixed at 684 nm and (b) height (h1) when w is set to 853 nm. The peak positions and the Q-factors of the two anticrossing modes are shown by black (high-Q mode) and red (low-Q mode) circles. The size of the circles is proportional to the Q-factor levels such that larger circles correspond to high-Q resonances. The insets show the magnetic near-field maps within the SWG cross section for different dimensions at their operating wavelengths over the low-Q and high-Q branches. (c) The amplitude (red) and phase (blue) of the reflected light as a function of incident wavelength when w and h1 are fixed to 853 and 684 nm, respectively. The alternative x and y axes correspond to the real and imaginary parts of the complex reflection coefficient that illustrates a circle trajectory while covering all four quadrants that ensure 2π phase swing. (d) Multipolar contribution of the scattering cross section of the SWG. (e) Near-zone distribution of the magnetic field within the metasurface cross section at the resonant wavelength of 1548 nm, which confirms excitation of higher-order Mie mode corresponding to the magnetic octupole.

Fig. 3. Space–time modulation of the high-Q metasurface. (a) The profile of the sinusoidal modulation waveform with time-reversal symmetry that is applied to the metasurface. The spatial distributions of the (b) electron and (c) hole carrier concentrations inside the multijunction p–n layers as functions of time depicted in one modulation cycle. (d) The real and (e) imaginary parts of the refractive index within the multijunction p–n layers as functions of time and space in one modulation cycle obtained at the operating wavelength of 1548 nm. The refractive index is sinusoidally modulated between 3.7295 and 3.7325. The white dashed lines demarcate the boundaries between the p-type and n-type regions.

Fig. 4. Nonadiabatic frequency conversion performance of the normally illuminated ultrahigh-Q spatiotemporal metasurface under time reversal. (a) The output spectrum of the reflection coefficient at the generated sidebands as a function of sideband order (n) and the incident wavelength. (b) The reflection amplitude at the fundamental (n=0), first-order upconverted (n=+1), and first-order downconverted (n=−1) sidebands as functions of incident wavelengths. (c) The normalized output spectrum of the reflected light when the space–time metasurface is under normal (θi=0deg) and oblique (θi=20deg) illuminations. An isolation level more than 35 dB is observed.

Fig. 5. Optical power isolation in free space. The wavefronts of the reflected light from the gradient space–time metasurface at the fundamental and first-order upconverted sidebands when the metasurface is illuminated by (a), (b) normal light coming from port 1 and (c), (d) oblique incidence coming from port 2. At resonant frequency (ω=ωr), the upconverted normally incident light is steered toward port 2 (θ=20deg). The light incoming from port 2 at ωr+ωm is bent toward port 1 at θ=0deg upon upconversion, while its amplitude is strongly suppressed. The color bars are rescaled to provide a fair comparison. The magnetic field level in (d) varies between −0.01 and 0.01.