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. There are many aspects to consider if one has to choose a numerical method to solve a particular problem in photonics. Finite difference time domain, discontinuous galerkin, and finite element method are general methods for solving electromagnetic problems; they are not specially tailored to photonics. In the most general case, the numerical methods of photonics solve time-dependent Maxwell's equations with general media. Maxwell's equations take different forms depending on the different modeling situations. In the case of time-dependent problems, these are the different types of linear and nonlinear scattering problems. For a direct discretization of Maxwell's equations, it is not necessary to consider the discrete approximation of the gradient but it completes the insight into the structure of the subsequent discretization process.