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Leaky modes are useful to partially represent the continuous spectrum in open waveguides. The perfectly matched layer (PML) is a widely used technique for truncating unbounded domains in numerical simulations of wave propagation problems. When a Pekeris waveguide is terminated by a finite PML, it gives rise to three classes of modes corresponding to the trapped modes, the leaky modes and the modes...
A numerical method is developed for solving the two-dimensional Helmholtz equation in a region bounded by a flat top and a curved bottom. A local orthogonal transformation is first used to flatten the curved bottom of the waveguide. The one-way re-formulation based on the Dirichlet-to-Neumann map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation...
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