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Numerical mode matching (NMM) methods are widely used for analyzing wavepropagation and scattering in structures that are piece-wise uniform along onespatial direction. For open structures that are unbounded in transversedirections (perpendicular to the uniform direction), the NMM methods use theperfectly matched layer (PML) technique to truncate the transverse variables.When incident waves are specified in homogeneous media surrounding the mainstructure, the total field is not always outgoing, and the NMM methods rely onreference solutions for each uniform segment. Existing NMM methods havedifficulty handing gracing incident waves and special incident waves related tothe onset of total internal reflection, and are not very efficient at computingreference solutions for non-plane incident waves. In this paper, a new NMMmethod is developed to overcome these limitations. A Robin-type boundarycondition is proposed to ensure that non-propagating and non-decaying wavefield components are not reflected by truncated PMLs. Exponential convergenceof the PML solutions based on the hybrid Dirichlet-Robin boundary condition isestablished theoretically. A fast method is developed for computing referencesolutions for cylindrical incident waves. The new NMM is implemented fortwo-dimensional structures and polarized electromagnetic waves. Numericalexperiments are carried out to validate the new NMM method and to demonstrateits performance.

A numerical mode matching method for wave scattering in a layered medium with a stratified inhomogeneity