Scalar Finite-Difference BPM For Gauss Beam Propogating Though 2D And 3D Waveguide

With the development of integrated optics, all kinds of optical wave-guide devices with different function and structure have appeared. Designing wave-guide completely by experimental method is complicated, while designing a wave-guide with CAD method can not only overcome such difficulty but also analyze the characters of optical wave-guide and thus lead to a quick designation. Then numerical algorithms are used to analyze integrated optical wave-guide and beam propagation method is a good method which is widely used.First, we introduced the present situation and development of integrated optics, and the analysis of geometrical optics and electromagnetism of planar wave-guide, the fluctuation equations of planar wave-guide and other frequent types. We also analyzed the application of 2D finite difference beam propagation method in embranchment wave-guide, discussed the Transparent Boundary Condition(TBC) , Absorb Boundary Condition(ABC) and Perfect Matching Layer Boundary Condition(PML).Based on Maxwell equations and envelope approximate theory, we derived the formula needed in calculating scalar 3D FD-BPM systematically, and built a theoretical model for it, with finite difference in stead of partial differential. On a foundation of the theoretical model, we exert the matrix function of MATLAB, completed the program of scalar 3D FD-BPM, which is more complex than 2D FD-BPM.We studied the propagation of Gauss beam, described the light field of Gauss beam in different position. Though the simulation we observed that for an arbitrary initial field, extrinsic field would have a striking change after a long distance. At last, the stable field is the wave-guide mode.We analyzed the propagation of Gauss beam with different waist in the same rectangular wave guide. From the propagation field, we would get the propagation field at any position. At a short range, the propagation field would be influenced by input field;at a long range, the propagation field would be influenced by wave-guide layer.