Finite Difference Beam Propagation Method

With the development of integrated optics, all kinds of optical wave guide devices with different function and structure have appeared. Designing a wave guide with CAD method can not only save time but also analyze the characters of it. Then numerical algorithm are used to analyze integrated optical wave guide, beam propagation method (BPM) is a good method which is widely used in the study of guided wave optics and the mode properties of optical fibers largely owing to its numerical speed and simplicity. Many wave guide simulation software using BPM have appeared now, so it's important to study the source code to improve the software. Finite difference beam propagation method (FD-BPM) is introduced; two new wide-angle finite difference beam propagation methods (WA-FD-BPM) are presented to improve on precision.Start with introducing the present situation and development of BPM,this thesis labors BPM which has been performed by solving the Helmholtz equation under the paraxial approximation and wide-angle approximation. Based on slowly varying envelop approximation, finite difference equation is used to replace partial differential equation. This thesis derived the formula needed in calculating scalar two and three dimensional FD-BPM systematically and built theoretical model. On the foundation of the theoretical model, this thesis exert the matrix function of MATLAB, completed the program of alternating direction implicit beam propagation method which is used to simulate three dimensional Y branch wave guide. The results of directional coupler simulation using scalar two and three dimensional FD-BPM are exactly the same which prove the correctness of the program, besides, the thesis analyze the influence of the number of grid points on algorithm precision.After introducing the formula used in WA-FD-BPM, both paraxial approximation and wide-angle approximation algorithm are simulated by MATLAB using an oblique wave guide. From the result, we can see WA-FD-BPM is improved on precision. For the purpose to obtain higher precision and shorter calculation time, two trial methods which expand from the square root operator for WA-FD-BPM are proposed, and the numerical simulations show that the coefficients of those new second order formulas are more precise than that of the conventional one while the calculation time isn't change. It's important to improve the wave guide simulation software.