Nonlinear Maxwell's Equations as a Boundary Value Problem in Multilayer Nanophotonics

Abstract

Calculating strong-field, broadband nonlinear phenomena in complex nanophotonic structures remains difficult because it requires simultaneous handling of non-perturbative dynamics, impulsive processes, and structural complexity. Here, we introduce a unified framework that combines the transfer matrix method with an iterative Green's function approach. The linear multilayer response is incorporated as boundary conditions into a nonlinear boundary value problem, which is then solved self-consistently, naturally accommodating broad spectra and arbitrary nonlinearity. The framework is validated with two examples in the transparent and resonant regimes, respectively. The first demonstrates an impulsive spectral modulation in second harmonic generation that is captured only by a full-structure broadband treatment. The second demonstrates the entire dynamical evolution of exciton-polaritons in a pump-probe experiment reproduced by a unified simulation. This framework directly links nanophotonic design with ultrafast nonlinear dynamics.