Three-dimensional analysis of a tapered waveguide structure by a doubled-grid finite-differences method

In this work 3D techniques based on finite difference (FD) schemes will be introduced to efficiently simulate the wave propagation in both longitudinally variant and invariant InP based devices. For a longitudinally invariant medium whose refractive index does not vary along propagation direction, we have chosen a step-index channel waveguide and determined the intensity distribution of the fundamental mode. As a longitudinally variant integrated optic structure, a tapered waveguide is selected which is commonly used as a beam transformer for butt-joint coupling of the above mentioned rectangular waveguide to a fibre. According to both structures two different FD techniques are chosen to permit a numerically more effective investigation as against the split-operator fast- Fourier transform (FFT) method, also known as the Beam-Propagation-Method (BPM). This paper consists of three sections. In the first chapter the FD method will be investigated in comparison with the BPM and its capability for solving a variety of integrated-optics problems will be emphasized. The second chapter describes the analytical background of the propagation algorithms used in this paper. Numerical results obtained by the application of the developed algorithms to the above mentioned two devices will be given in the last chapter. investigation of perhaps most complex integrated optics structures in order to finally determine the optimized design of the optical device before going into production. Since none of the existing methods is universal, one must choose a simulation method according to the given problem or think of developing something new. In this work we show that for two different structures two different FD methods are capable to tackle the given simulation problem. Each method has its advantages and disadvantages.