The Analysis Of Microstructure Optical Waveguide Mode-Field Based On Boundary Element Method

Solving the transfer constant and mode-field distribution of complex cross-section microstructure optical waveguide is the basis of theory about microstructure optical waveguide, while the solution to micro-structure optical waveguide mode-field can often be attributed to electromagnetic field boundary value problems. In recent years, because of the boundary element method in numerical solution of electromagnetic field boundary value problems can get higher accuracy in the premise of reducing the space dimension, the number of equations and the amount of input data, it has aroused more attention. In this paper, how to use the boundary element method for numerical solution of electromagnetic field boundary value problems is studied theoretically.The boundary element method is a numerical method, which attributes the differential equation which describe fields to the boundary integral equation through the method of weighted residuals, then as the finite element method, the boundary segmentation and interpolation of this integral equation can be done to get approximate results. The boundary element method is a combining product of the boundary integral method and discrete pattern of the finite element method, which is provided with both the strengths of these two methods. In this paper, the process of using boundary element method for solving the electromagnetic field boundary value problems is studied deeply.Firstly, the mathematical foundations of obtaining boundary integral equation of the Helmholtz equation - Weighted Residual Method is studied, the weighted residual expressions of approximate solution in case of meeting different boundary conditions are discussed, and the boundary integral equations of the direct boundary element method and the indirect boundary element method are derived.Secondly, the boundary integral equation of the Helmholtz equation is derived based on the general weighted residual expression. Then, how to use the boundary element method for getting the numerical solution of this boundary integral equation is considered.Finally, using the derived results, the cut-off frequencies of transmission modes which exist in the uniform circular waveguide are calculated by programming, and this article also discusses the effect of uniform circular waveguide parameters and the number of selected boundary nodes on calculation accuracy and computing time.