Nyquist-Sampled Time-Domain Adjoint FDTD for Memory-Efficient Broadband Nanophotonic Inverse Design

Abstract

Adjoint optimization is a cornerstone of broadband nanophotonic inverse design, but conventional time-domain implementations face a severe memory bottleneck because they retain forward-field histories at every finite-difference time-domain (FDTD) time step. Here, we show that this full time-step storage is unnecessary for broadband design objectives because the underlying fields are band-limited. By storing forward fields only at Nyquist intervals and using the resulting sparse fields during the adjoint pass, the proposed method enables on-the-fly gradient accumulation without retaining full forward-field histories. This Nyquist-sampled adjoint FDTD framework preserves the two-simulation scaling of time-domain adjoint optimization while substantially reducing the dominant field-storage. Because the broadband gradient is evaluated directly in the time domain, with no spectral discretization, the per-iteration cost is independent of the number of frequencies---in contrast to frequency-sampled adjoint formulations, whose cost grows with spectral sampling density. Gradient verification confirms that Nyquist sampling reproduces conventional full-storage adjoint gradients with negligible error, whereas undersampling beyond the Nyquist limit produces aliasing-induced gradient degradation. Across four two-dimensional broadband nanophotonic benchmarks and a fully three-dimensional metalens, the method maintains gradient fidelity and optimized device performance while reducing dominant field-storage memory by more than $100\times$ relative to full-history storage in a prototypical example. These results suggest that the principal memory barrier in broadband time-domain adjoint FDTD is not an intrinsic requirement of gradient evaluation but rather a consequence of redundant temporal field storage, thereby opening a practical route to large-scale three-dimensional nanophotonic inverse design.