Validity Analysis Of Mode Expansion In Optical Waveguide With PML

This paper discusses the validity of application of model expansion method in the waveguide with perfectly matched layer. In the waveguide of three-tier structure with PML, according to the symmetry of wave distribution, we divided the waveguide propagation mode into odd mode and even mode. Then based on the eigenvalues, they correspond to guided mode, leaky mode and PML mode respectively. Specially, in the two-tier structure waveguide with PML, there is only the odd mode accordingly. This paper studies the variation of corresponding coefficients in a variety of models and the convergence and effectiveness of model expansion method in optical waveguide structure.In this paper, with the reference of asymptotic methods and Chebyshev pseudospectral method, we try to find the eigenvalue of high precision. From asymptotic methods, the bigger the accurate values is, the higher the precision, while Chebyshev pseudospectral methods show the smaller the accurate values is, the higher the precision. This paper uses the eigenvalue from these two methods as the initial value to obtain a more accurate one through Newton iteration, and then we compare it with exact eigenvalue. Since waveguide structure with PML destructs the symmetry of the operator, making the characteristic functions corresponding to different eigenvalues no longer orthogonal, this paper constructs conjugacy function systems, which are from three-tier waveguide structure with PML and orthogonal with characteristic function, to facilitate solving the coefficients of corresponding model and the variation of the coefficients. Finally, in the numerical examples, we discussed the effectiveness of mode expansion method in different types of incident wave.