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

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.