Normal mode solutions for absorbing boundary conditions

Wave propagation problems with radiation boundary conditions are non‐hermitian and therefore typically cannot be solved by expanding in terms of eigenfunctions that correspond to real eigenvalues. We present a method for solving such problems entirely in terms of a superposition of normal modes, using the "shifted eigenvalue" method outlined by Lanczos. In effect, the desired system with an outgoing radiation boundary condition is coupled to a system which is identical, but has an incoming radiation boundary condition. The combined system is hermitian, and thus has real eigenvalues. We present numerical computations for a one‐dimensional, semi‐infinite, homogeneous continuum.