A design method of broadband metalens using time-domain topology optimization

Abstract

Flat metalenses have attracted attention due to an increasing demand for compact electromagnetic devices. For such applications, broadband metalenses are highly desirable; however, conventional metalenses show relatively narrow band operation. Here, we propose a design method of free-form metalenses using topology optimization to operate with enhanced bandwidths. In contrast with preceding reports of topology optimization methods for metalenses, we developed a topology optimization method based on the time domain formulation to deal with broadband frequencies simultaneously. For this purpose, a group delay of optical pulses in the time domain, which is equivalent to the broadband phase matching condition in the frequency domain, is employed in the objective function. A level set based topology optimization method is applied to obtain a clear optimal configuration. To demonstrate the effectiveness of the proposed method, we provide design examples of metalens unit cells at millimeter frequency. We confirm that optimized unit cells of metalenses show superior performance compared to the conventional unit cells for both transmittance efficiency and phase error in broadband wavelength.

Time Reversal Differentiation of FDTD for Photonic Inverse Design

“…Such nanostructures are designed through dispersion engineering, in which the transmission phase is designed to have a specific dependence on the illumination frequency, a process that typically entails the simulation of a nanostructure behavior over a dense set of frequencies, followed by polynomial regression on the transmitted spectral phase profile. ,, A linear phase dependence in the spectral phase represents a group delay on the pulse envelope, enabling such behavior to be engineered more directly in the time domain. To our knowledge, such time-domain group delay topology optimization has only been done in the context of metasurfaces by Yasuda and Nishiwaki . To simulate an array of nanostructures, we replace the TFSF and PML boundary conditions in the transverse y – z directions with periodic boundary conditions (Figure a).…”

Time-Domain Topology Optimization of Arbitrary Dispersive Materials for Broadband 3D Nanophotonics Inverse Design

“…Density-based topology optimization (TopOpt) for inverse design originally introduced in mechanical engineering is an iterative design process that allows us to optimize the distribution of a given material in a specified domain in order to optimize a certain objective function. − This method has been applied to a variety of engineering problems in photonics, such as the optimization of metasurfaces to control certain properties of light (polarization, phase, angular momentum, and achromatic focusing), − photonic crystals to find optimal omnidirectional band gaps, nanoantennas for broad-band enhancement, small-scale particle accelerators, quantum emitter and (de-)­multiplexers as important components for photonic quantum computers, − and nonlinear photonic devices for, e.g., second- and third-harmonic generation. , …”