Quasi‐Static and Time‐Modulated Optical Phased Arrays: Beamforming Analysis and Comparative Study

Abstract

Herein, design procedures of the quasi‐static and time‐modulated optical phased arrays (OPAs) operating at near‐infrared spectrum are proposed and a comparative analysis over their dynamic beam‐steering functionalities is conducted. A metal–insulator–metal configuration integrated with indium tin oxide is considered as a building block of the reflective OPA. First, beamforming performance of the quasi‐static OPA, designed using the intuition‐based forward approach, is analytically studied and its main shortcomings posed by nonideal unit cell performance are highlighted. To surmount these limitations, an optimization‐based inverse design algorithm using multiobjective evolutionary optimization technique is proposed, which outputs non‐intuitive amplitude and phase profiles of the metal–insulator–metal supercells and identifies optimal beamforming tradeoffs between gain and sidelobe ratio of the quasi‐static OPA. Then, beam‐steering functionality of the time‐modulated OPA is investigated. Time‐modulated OPA affords 2π dispersionless phase shift, and constant amplitude at the sidebands, which lead to enhanced spectral and angular bandwidth, wide angle‐of‐view, and suppressed sidelobes. Following the fact that amplitude and phase of the sideband signals can be independently controlled through depth and phase delay of modulation, Taylor one‐parameter distribution is used to implement amplitude tapering for engineering the beamforming tradeoffs between gain and sidelobe levels of the time‐modulated OPAs.

High-quality-factor space–time metasurface for free-space power isolation at near-infrared regime

“…(14) in Ref. 84, which shows the imprinted phase gradients at the sidebands with the opposite orders are conjugate. The spatiotemporal permittivity change of the a-Si SWG, which results from the sinusoidal modulation waveform, can be described as ϵSWG=ϵdc+Δϵ sin[ωmt+α(x)], where Δϵ is the modulation depth and defines the deviation of the permittivity with respect to the unbiased configuration, which is set to 0.008 in accordance with Fig.…”

“…In order to achieve the desired nonreciprocal response at the output spectrum, the inverse design and optimization methods should be employed for obtaining the complex modulation waveforms with strong time-reversal asymmetry (i.e., a sawtooth-like pattern). 83,84 However, these methods are time-consuming, and, as discussed earlier, the spatial pathway of light at different sidebands cannot be sufficiently changed to impart nonreciprocity. Lifting the adiabaticity of modulation offers a pathway to attain a noticeable conversion from the fundamental to higher-order frequencies under time reversal and substantially change the spatial pathway of light, without making any effort to optimize the modulation waveform.…”

“…As is clearly observed, for the incoming light from port 1 and at resonant frequency (ω r ), the light is reflected back to port 1, since the direction of the fundamental frequency is governed by the specular reflection and cannot be actively tuned by changing the modulation-induced phase shift. 84 However, the reflected light at the upconverted sideband (ω r þ ω m ) is steered toward port 2 at θ ¼ 20 deg. The perturbations in the wavefront of the magnetic field in Fig.…”

“…For the sake of simplicity, the normal and oblique directions at θ=0 deg and θ=20 deg are called port 1 and port 2, respectively. As is clearly observed, for the incoming light from port 1 and at resonant frequency (ωr), the light is reflected back to port 1, since the direction of the fundamental frequency is governed by the specular reflection and cannot be actively tuned by changing the modulation-induced phase shift 84 . However, the reflected light at the upconverted sideband (ωr+ωm) is steered toward port 2 at θ=20 deg.…”

Microwave Space-Time-Modulated Metasurfaces

“…Appropriate elements may be envisioned at terahertz and optics for the realization of time modulation, for example, using dielectric slabs doped to create p–i–n junction schemes responding to a modulation wave and operating as voltage-controllable capacitors. Furthermore, indium–tin-oxide (ITO) has been recently utilized for dynamic modulation of light at the NIR frequency regime, as it offers a short response time (of the order of a nanosecond), continuous tunability, negligible hysteresis, low power consumption, a large refractive index variation range, and epsilon-near-zero capability. − The experimental realization of ITO-integrated modulators at optical telecommunication wavelengths has been demonstrated, whose modulation speeds are only limited by the RC time constant governed by the driver electronics and wiring, and typical achievable space-time modulation frequency values are estimated to be more than 100 GHz. , Considering the high speed of ITO, it represents a promising candidate for the realization of space-time metasurfaces at optical frequencies. The extraordinary wave processing and transformation through space-time-modulated metasurfaces opens new opportunities in biomedicine, wireless communications, radars, cloaking, and beyond.…”