Pseudospectral Frequency-Domain Formulae Based on Modified Perfectly Matched Layers for Calculating Both Guided and Leaky Modes

We propose a new pseudospectral frequency-domain (PSFD) formulation within the modified perfectly matched layer (MPML) for absorbing both radiation losses and evanescent waves. By applying the improved PSFD method on Chebyshev-Gauss-Lobatto mesh points, both guided and leaky modes of optical waveguides can be solved from Helmholtz's equations for the transverse-magnetic components. To ensure the global accuracy of the PSFD-MPML method, new and appropriate boundary conditions are derived at each subdomain in the MPML region. By comparing the analytic solution of a step-index single-mode fiber and the results by adopting our method, the convergence behavior of the proposed method on the guided modes is examined. To demonstrate the validity and usefulness of our method on the leaky modes, the one-ring triangular holey fiber is taken as another example.