Photonic devices operate on the phenomenon of light guiding along optical waveguides. Optical waveguides are used in laser diodes, directional couplers, fibre lasers, amplifiers, and so on [1-3]. For the study of light propagation in the waveguiding structures that are used in photonic devices, the numerical techniques that were discussed in Chapter 3 are often insufficient. This is because the waveguiding structures used in photonic devices are neither perfectly straight nor infinitely long. For instance, the typical length of an edge emitting laser diode is around several hundreds of micrometres while in the case of a fibre laser the length of the optical waveguide can equal several metres. Furthermore, an optical beam whilst propagating along an optical waveguide can encounter abrupt air-dielectric interfaces. For  example, cleaved semiconductor mirrors are commonly used in laser diodes to provide a feedback mechanism for the generation of the optical radiation.