Abstract

This chapter deals with numerical simulation in photonics. It provides an overview of the most widely used methods, explains their concepts, and gives some details, as long as it is necessary for a qualitative understanding. It is far from being complete but tries to describe the landscape of simulation tools. Parts of this review are closely related to the book Numerical Methods in Photonics [1], which itself is a comprehensive representation of the field covered by many very detailed monographs. The methods we describe in the following are the finite-difference time-domain FDTD method, closely related to the finite integration technique (FIT), the Fourier modal method (FMM), the finite element method (FEM), and the discontinuous galerkin (DG) method. We omit other very useful methods often specialized to certain applications, in particular:

Beam propagation method (BPM), for simulation of paraxial beam propagation [2]

Integral methods such as boundary integral methods, for simulation problems in grating design [3]

Plane wave expansion (PWE) for simulations of band structures [4]

and refer the reader to the given monographs.