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Explicit Wideband Time-Domain Beam Propagation Algorithm Based on Faber Polynomials

A novel explicit algorithm based on a wideband time-domain beam propagation approach for the solution of Maxwell's equation in the time domain is presented. The algorithm utilizes a Faber polynomial expansion to approximate the time-domain propagator. The expansion allows the usage of time steps exceeding the Courant–Friedrichs–Lewy stability condition. The approach enables the conceptual formulation of time stepping schemes featuring a more accurate approximation of the time dependent propagation for band limited signals than the classical finite difference time-domain method at the same computational effort.