Multi-objective time-domain adjoint via temporal convolution for band-selective electromagnetic topology optimization

Abstract

Adjoint-based topology optimization enables gradient computation for electromagnetic design from only two simulations, independent of problem size. Conventional frequency-domain adjoint methods suit single-frequency objectives but incur computational costs scaling linearly with spectral resolution for broadband design. Time-domain adjoint methods efficiently capture broadband responses, however, their native gradients integrate over the entire excitation bandwidth, preventing independent control of multiple spectral bands. Consequently, multi-band optimization requires separate forward-adjoint simulation pairs per band, eliminating the computational efficiency advantage. We present a multi-objective time-domain adjoint method that computes band-selective gradients via temporal convolution of stored electromagnetic fields. By the convolution theorem, post-processing with band-pass filters isolates designated spectral content without additional simulations. We validate the method on three nanophotonic systems. First, a wavelength-division demultiplexer achieves 8.74 s per iteration, outperforming conventional time-domain (14.32 s) and frequency-domain (120 s) methods. Second, a metalens demonstrates independently prescribed numerical apertures across four spectral bands with less than 5% focal length error. Third, a spectral router achieves 70%–75% routing efficiency, approximately 2× the theoretical limit of absorption-based designs. These results establish that convolution-enabled, band-selective gradients restore the computational advantage of time-domain adjoint optimization for multi-band electromagnetic design.