Method of field expansions for doubly layered media with a quasiperiodic interface

Periodic structures play a crucial role in applied optics; however, generalized forms of periodicity are becoming increasingly important in electromagnetics. Due not only to their importance but also to the high cost and great difficulty in producing these at the nanoscale required, numerical simulation of these devices is of extraordinary importance. In this contribution, the author derives, implements, and validates the generalization of a high-order perturbation of surface (HOPS) algorithm (the method of field expansions-FE) for the numerical simulation of layered media scattering to account for quasiperiodic interfaces. Due to their interfacial character, these HOPS approaches are substantially faster than their volumetric counterparts such as finite difference or finite element methods. Additionally, our approach can address structures that the classical FE method would find onerous (for interfaces with widely disparate periods) or impossible (for profiles of incommensurate periods) due to its enhanced capability of simulating quasiperiodic interfaces. Beyond validating the implementation, the author also investigates the (nonlinear) dispersion relation of surface plasmon resonances on a sequence of increasingly challenging vacuum-silver structures featuring a quasiperiodic interface.