Asymptotic solutions of eigenmodes in slab waveguides terminated by perfectly matched layers

For numerical modeling of optical wave-guiding structures, perfectly matched layers (PMLs) are widely used to terminate the transverse variables of the waveguide. The PML modes are the eigenmodes of a waveguide terminated by PMLs, and they have found important applications in the mode matching method, the coupled mode theory, and so on. In this paper, we consider PML modes for two-dimensional slab waveguides. It is shown that the PML modes consist of perturbed propagating modes, perturbed leaky modes, and two infinite sequences of Berenger modes. High-order asymptotic solutions for the Berenger modes are derived using a systematic approach.