An Efficient Finite Element Scheme for Highly Nonlinear Waveguides

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Abstract
Since the late 70's the Beam Propagation Method (BPM) or Split-Step Fourier Method (SS/FM), has been widely used for solving the nonlinear partial differential equations which describe the propagation of spatial pulses through waveguide structures. By applying the Split-Step technique, the paraxial wave equation can be split in two propagating equations, one involving only linear terms and another including nonlinear ones. These two equations describe diffraction and nonlinear refraction respectively. In the SS/FM, diffraction is integrated by using the Fourier transform. However, the performance of this method is known to be seriously affected when abrupt variations of the refractive index are taken into account [1], and the problem tends to become even worse in the high nonlinear regime [2].