The Rapid Analysis of Scattering from Periodic Dielectric Structures Using Accelerated Cartesian Expansions (ACE)

TL;DR

This paper introduces the ACE algorithm for fast, accurate analysis of electromagnetic fields in periodic dielectric structures, significantly reducing computational cost from quadratic to linear time.

Contribution

The paper presents a novel application of the Accelerated Cartesian Expansions (ACE) method to volumetric electric field integral equations in doubly periodic dielectric structures, enabling rapid computations.

Findings

Achieved O(N) computational complexity for field evaluations.

Validated the method's accuracy against traditional approaches.

Demonstrated effectiveness in photonics applications.

Abstract

The analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap (PBG) structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral equation based methods, for which traditional iterative methods require O(N^2) operations, N being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the ACE algorithm, which is used to evaluate the requisite potentials in O(N) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.