Optical Waveguide Finite Element Beam Propagation Method Analysis In Time Domain

Along with the development of optical network communication technology, the structures and functions of optical components based on optical waveguides become more and more novelty. Naturally the analysis and design of optical waveguides and study on the propagation of light-wave become a focus. And following the appearance of new optical waveguides such as photonic crystal and photonic crystal fiber, some methods of numerical analysis used before can't reach the desired demand. So we need methods of numerical analysis which is more effective, for example the finite element method. Because of its adaptation to shape and high precision, the finite element method has a more and more important role in the analysis of optical waveguides. The study on the application of the finite element method in analysis on optical waveguide must have an instructive function to the analysis and study on optical waveguides.In chapter two, we derive the field distribution functions of two-dimension planar optical waveguides from Maxwell functions, and then receive the Euler function, this is the basis of the finite element method for the analysis of two-dimension optical waveguide. Subsequently, by dividing the compute field by linear element and combining with analytical solution, we receive the propagation functions of two-dimension optical waveguides and simulate numerically. Then using linear triangular-element node auto-division arithmetic, we receive the result of field distribution and compare it with that before. Then we simulate by ANSYS and receive the field distribution diagram. These demonstrate the validity of the finite element method. In chapter three, we analyze three-dimension optical waveguides in scalar finite element method and vector finite element method. Then we present the method to avoid spurious solutions, receive the propagation functions of three-dimension optical waveguides. Due to the importance of axis-symmetry optical waveguides, here we analyze the axis-symmetry optical waveguides in scalar method and vector method, respectively. We receive the propagation functions of axis-symmetry optical waveguides. How to divide grids is an important ring in the finite element method, so in the chapter four we discuss and compare the question in the analysis of optical waveguides. On the base on front chapters, the chapter five presents the finite element analysis result of photonic crystal fibers and demonstrates the front theoretical mode by compare and analysis. In the chapter six, first we derive the 3D-FETD-BPM and discretize the time-domain wave function of optical wave field based on single-mode optical fiber described by slow-variety envelope approximate. In the end , the theoretical mode of three-dimension time-domain beam propagation method is established.After the derivation and numerical simulation of the finite element method, the validity of the finite element method in the simulation of photonic crystal fiber is demonstrated. This has an instructive meaning to the study on the propagation characteristic of photonic crystal fiber.