On a Novel Mode-Solver and Beam Propagation Method Based on Galerkin Approach and Arnoldi Iteration Technique

In this work a modified Galerkin method is used to study the modal and propagation behaviour of generic integrated optical structures. The paraxial propagation equation is solved through non-linear mapping of the transverse plane and subsequent Galerkin approach. The differential equation is thus transformed into a specific finite-dimension linear problem. The field evolution is then calculated step-wise by approximating the exponential propagator through an Arnoldi iterative procedure. A similar approach is applied to the corresponding eigenproblem.