An Efficient Framework for Simulating Optical Responses of Dynamically Evolving Periodic Nanoarrays

Predicting and controlling the optical response of dynamically evolving nanoarrays are crucial for advancing applications in sensing, photonics, and optoelectronics. Discrete dipole approximation (DDA) under periodic boundary conditions (PBCs) has been widely used, but it becomes prohibitively expensive for structurally evolving systems, as each structural or compositional change requires resolving a large electromagnetic problem. Recently, we introduced the rank-one decomposition DDA (RD-DDA) to accelerate the simulation for isolated nanostructures, and here, it is extended to periodic boundary conditions, establishing an efficient and accurate framework for modeling the optical behavior of nanoarrays with dynamically evolving lattice units. Using this RD-DDA-PBC framework, we continuously tracked the spectral evolution of plasmonic nanoarrays during etching and coating, capturing simulated intermediate configurations and associated transient spectral features that are difficult to sample efficiently with repeated full DDA-PBC calculations. By coupling RD-DDA-PBC with kinetic Monte Carlo (KMC) simulations, we investigated the etching kinetics of nanoarray structures under a localized electric field enhancement. Furthermore, integration with reinforcement learning (RL) enables inverse optical geometry design, allowing the autonomous generation of nanoarray structures with prescribed spectral features. Overall, this work establishes an efficient framework for updating periodic DDA calculations during lattice evolution and demonstrates its use in forward spectral tracking, coarse-grained field-biased KMC simulations, and the proof-of-concept inverse design of periodic nanoarrays.