  Numerical mode matching (NMM) methods are widely used for analyzing wave
propagation and scattering in structures that are piece-wise uniform along one
spatial direction. For open structures that are unbounded in transverse
directions (perpendicular to the uniform direction), the NMM methods use the
perfectly matched layer (PML) technique to truncate the transverse variables.
When incident waves are specified in homogeneous media surrounding the main
structure, the total field is not always outgoing, and the NMM methods rely on
reference solutions for each uniform segment. Existing NMM methods have
difficulty handing gracing incident waves and special incident waves related to
the onset of total internal reflection, and are not very efficient at computing
reference solutions for non-plane incident waves. In this paper, a new NMM
method is developed to overcome these limitations. A Robin-type boundary
condition is proposed to ensure that non-propagating and non-decaying wave
field components are not reflected by truncated PMLs. Exponential convergence
of the PML solutions based on the hybrid Dirichlet-Robin boundary condition is
established theoretically. A fast method is developed for computing reference
solutions for cylindrical incident waves. The new NMM is implemented for
two-dimensional structures and polarized electromagnetic waves. Numerical
experiments are carried out to validate the new NMM method and to demonstrate
its performance.
