Propagating modes in optical waveguides terminated by perfectly matched layers

For numerical simulations of optical waveguides, perfectly matched layers (PMLs) are widely used to truncate the unbounded transverse directions. However, a PML induces some undesired side effects to the propagating modes in the waveguide. In general, the propagation constant becomes complex, so that the mode may grow or decay exponentially along the waveguide axis. Through a perturbation analysis, we obtain approximate formulas for the propagation constants of PML-terminated planar waveguides.