Non-iterative bi-directional wave propagation method for treating reflections

We describe a bi-directional wave propagation method based on the split-step non-paraxial collocation method. The method is non-iterative and does not require any matrix inversion or diagonalization. The method is applied to reflections from waveguide discontinuities, terminations as well as multilayer reflecting structures. The results obtained compare very well with those obtained using computationally intensive methods such as the finite element method (FEM) and the finite-difference time-domain (FDTD) method.