COMPUTATION OF WAVE-PROPAGATION IN INTEGRATED OPTICAL-DEVICES USING Z-TRANSIENT VARIATIONAL-PRINCIPLES

As an alternative to the classical beam propagation method (BPM), a variational method is presented to solve the TE and TM Helmholtz equations in the paraxial approximation for the propagation of polarized beams through optical waveguides. Using the method of local potentials the paraxial wave equations are first converted into equivalent z-transient variational principles. These functionals are minimized using a combination of the Rayleigh Ritz Finite Element procedure and a Crank-Nicholson-like Finite Difference scheme. Solutions in anisotropic material are obtained by applying standard Galerkin Finite Element and Finite Difference methods to a variational formulations derived from the coupled TE/TM paraxial Helmholtz equations. Error comparisons with the BPM show that the presented variational method is more accurate, unconditionally stable and overcomes the restrictions to low contrast media, uniform sampling and TE-propagation. In addition, the new approach allows for mesh refinement during propagation.