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On the three formulations of transparent boundaries for the beam propagation method

Šumichrast, Ľubomír; Ehrhardt, Matthias

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

For the simulation of the propagation of optical waves in the open waveguiding structures of the integrated optics the beam propagation method of solution of the parabolic wave equation is commonly used. It is of paramount importance to have well-performing transparent boundary conditions applied on the boundaries of the computational window, to enable the superfluous portion of the propagating wave to radiate away from the waveguiding structure. Three different formulations (continuous, semi-discrete and fully-discrete) of the non-local transparent boundary conditions are introduced and compared here.