Beam propagation method based on a Fourier series approximation of the propagation operator

An efficient beam propagation method based on a finite difference scheme is proposed for photonic devices. As the eigenvalue spectrum of the discretization matrix is compact, the propagation operator can be periodically extended. Afterwards the periodically approximated propagation operator is expanded into a Fourier series. Due to well known ringing effects a window function has to be introduced. Then each of the Fourier exponentials is expanded into a Taylor series. The resulting approximation of the propagation operator is investigated and the method is applied to an example to demonstrate the efficiency of the concept.