Graphics processing unit‐based solution of nonlinear Maxwell's equations for inhomogeneous dispersive media

Abstract

SummaryA new approach is developed for fast solution of complex dynamic problems in nonlinear optics. The model consists of the nonlinear Maxwell's equations coupled with time‐dependent electron density equation. The approach is based on the Finite‐Difference Time‐Domain and the auxiliary differential equation methods for frequency‐dependent Drude media with a time‐dependent carrier density, changing due to Kerr, photoionization, avalanche, and recombination effects. The system of nonlinear Maxwell‐Ampere equations is solved by an iterative fixed‐point procedure. The proposed approach is shown to remain stable even for complex nonlinear media and strong gradient fields. Graphics‐processing‐units technique is implemented by using an efficient algorithm enabling solution of massively 3‐dimensional problems within reasonable computation time.