FDTD Modeling of Periodic Structures: A Review

TL;DR

This review comprehensively discusses the mathematical principles, implementation techniques, and applications of periodic boundary conditions in 3D FDTD simulations, highlighting their robustness and efficiency in modeling periodic structures.

Contribution

It provides a systematic overview of PBC techniques in FDTD, including new insights into their implementation and application for analyzing periodic structures.

Findings

Demonstrates robustness and utility of PBCs in FDTD simulations

Provides a unified view of various PBC approaches

Shows efficiency of PBCs in modeling complex structures

Abstract

This paper reviews the state of the art of periodic boundary conditions (PBCs) in Finite-Difference Time-Domain (FDTD) simulations. The mathematical principles and 3D FDTD implementation details are systematically outlined. Techniques for extracting scattering parameters, Brillouin diagrams and attenuation constants are presented, along with the Array Scanning Method (ASM) used to model the interaction of non-periodic sources with periodic structures. Through these techniques, the robustness, utility and efficiency of PBCs are demonstrated and a unified view of the various approaches to the FDTD implementation of PBCs is presented.