Chapter 7 - Beam propagation method

Abstract

This chapter describes the beam propagation method (BPM), which is the most powerful technique to investigate linear and nonlinear light wave propagation phenomena in axially varying waveguides such as curvilinear directional couplers, branching and combining waveguides, S-shaped bent waveguides, and tapered waveguides. BPM is also important for the analysis of ultra short light pulse propagation in optical fibers. The two kinds of BPM procedures described in the chapter are based on the fast Fourier transform (FFT) and the finite difference method (FDM). In BPM analysis, the electric field is first propagated in free space over a distance. Then phase retardation of the entire length is taken into account at the center of propagation. The electric field is again propagated in the latter free space. The basic procedure of BPM is formulated over the small distance to relate the transmitted field to the initial field. BPM wave propagation analysis is similar to light propagation in a linear medium and the influence of the nonlinear optical effect can be separated in the pulse propagation analysis by BPM.