Finite-Difference Modeling of Nonlinear Phenomena in Time-Domain Electromagnetics: A Review

Nonlinearities are likely to emerge in a wide range of electromagnetic (EM) problems, commonly described by Maxwell’s equations, which can be encountered in several real-world applications, in areas such as optical communications, etc. The necessity for efficiently analyzing this type of problems has led to the development of suitable computational approaches, among which schemes based on the finite-difference time-domain (FDTD) method play a prominent role. Unlike other numerical methods that perform reliably only if specific approximations are valid (e.g. wave propagation along a dominant direction), FDTD-based techniques can be applied in more generalized frameworks, and are capable of computing credible outcomes without requiring very complex algorithmic implementations. In the present chapter, we report various key contributions presented over the years regarding the nonlinear FDTD analysis of EM problems, as the original algorithm is suitable for linear cases only, and describe their basic formulation, features, and range of applicability. In essence, this work aspires to provide an updated look on existing finite-difference models for nonlinear problems, and offer to those not familiar with the subject a solid starting point for studying the corresponding electromagnetic phenomena.