On the Transparent Boundary Conditions (TBC) for the Parabolic Wave Equation

For the simulation of the propagation of electromagnetic waves is in certain situations the parabolic approximation of the scalar wave equation commonly used. It is important to have well-performing transparent boundary conditions applied on the boundaries of the finite computational window, to enable the superfluous portion of the propagating wave to radiate away from the e.g. wave guiding structure. Four different formulations (continuous, two kinds of semi-discrete and one fully-discrete) of the non-local transparent boundary conditions are described and their performance compared.