ABSTRACT
This chapter describes how light propagation in straight dielectric waveguides can be modelled in the frequency domain (FD) by the finite-difference approach. By a straight waveguide, we understand a waveguide structure which is invariant in the direction of light propagation. Important examples of such waveguides are optical fibres, including microstructured fibres, and (the straight sections of) various slab and planar waveguide structures. Understanding and designing the properties of such waveguides are important in areas such as signal transmission (telecommunication), nonlinear signal processing, fibre lasers, and waveguide-based sensors. Therefore, efficient tools for numerical modelling are of great importance for both university and industry researchers in these fields. The finite-difference methods are simple and versatile techniques, which allow to expose the tricks and approximations involved in modelling on a real-space grid without getting lost in details of mathematics and coding. They rely on discretizing the electromagnetic fields of the waveguide modes on a uniform real-space grid, using simple interpolation formulas to evaluate numerical derivatives.
