Analysis Of Slab Waveguide Modes Based On The Finite Element Method

Dielectric waveguides are used into limiting the way and the spread of optical components in integrated optical circuits and waveguide devices,which includes with a circular section of waveguide (optical fiber) and the slab waveguide, rectangular waveguide, etc.The Research on the optical waveguide is usually based on the theory of electromagnetic and the optical characteristic of dielectric materials. The Maxwell's equations and boundary conditions ,which dominant the phenomenon of optical waveguide ,have deduced the wave equation which is the theoretical basis of Optical waveguide.Due to the complex structure and parameters, optical waveguide can get strict exact solutions except for several limited structure and refractive rate distribution, and most non-uniform waveguide has no exact solutions,only soluted by the approximate method and numerical method.In the approximation method, the light approximation and WKB approximation are extensively applicated because of the feature of clear and simple analysis, which, however, are only suitable for the slow changed refractive rate distribution and the mode of waveguide.The Finite Element Method(FEM) is one of the important ways to find optical waveguide modes. In FEM ,the domain of the problem is discretized into small elements . The solution of the problem is approximated in each element ,and it is connected at the nodal points to form the solution model in the entire analysis domain.FEM is suitable for the mode analysis of optical waveguides with arbitrary refractive-index profiles and complicated sructures.It's one of the most widely used numerical method in engineering analysis.Scalar node finite element method is applied in this paper ,from which linear equations are derived with boundary conditions.The slab optical waveguides modes are analyzed in the paper. Simulation results coincide with existing literature theory and the experimental data, are useful reference for other devices finite element numerical analysis.The calculated numerical results show that FEM based on the Variational Principle is an approach for analysis of waveguide eigenvalue problems.FEM is an effective computational method.