Parallel numerical methods for analysing optical devices with the BPM
In this work, some developments in the theory of modelling integrated optical devices are discussed. The theory of the Beam Propagation Method (BPM) to analyse longitudinal optical waveguides is established. The BPM is then formulated and implemented numerically to study both two and three-dimensional optical waveguides using several Finite-Difference (FD) techniques. For the 2-D analysis, comparisons between the performance of the implicit Crank Nicholson (CN), the explicit Real Space (RS) and the Explicit Finite-Difference (EFD) are made through systematic tests on slab waveguide geometries. For three-dimensional applications, two explicit highly-parallel three-dimensional FD-BPMs (the RS and the EFD) have been implemented on two different parallel computers, namely a transputer array (MIMD type) and a Connection Machine (SIMD type). To assess the performance of parallel computers in this context, serial computer codes for the two methods have been implemented and a comparison between the speed of the serial and parallel codes has been made. Large gains in the speed of the parallel FD-BPMs have been obtained compared to the serial implementations; both methods, in their parallel form, can execute, per propagational step, a large problem containing 106 discretisation points in a few seconds. In addition, a comparison between the performance of the transputer array and the Connection Machine in executing the two FD-BPMs has been discussed. To assess and compare the two methods, three different rib waveguides and three different directional couplers have been analysed and the results compared with published results. It has been concluded from testing these methods that the parallel EFD-BPM is more efficient than the parallel RS-BPM. Then, the linear parallel EFD-BPM was extended to model nonlinear second harmonic generation process in three-dimensional waveguides, where the source field is allowed to deplete, using the transputer array and the Connection Machine.