Validity of Modal Expansion Method for the optical waveguide with PML

The perfectly matched layer (PML) is a widely used technique for the numerical simulations of the unbounded wave propagation problems. When unbounded waveguide is terminated by a finite PML, it gives rise to three classes of modes, i.e., propagation modes, leaky modes and Berenger modes (PML modes). The classical Modal Expansion Method only involves propagation modes and a continuous spectrum of radiation modes, but the infinite integral is sophisticated. In this paper, we study the validity of Modal Expansion Method with these three classes of modes. All the discrete modes of the finite PML-truncated waveguide are computed by the asymptotic approximation combining with the Chebyshev pseudospectral method.