AN IMPROVED FINITE-DIFFERENCE VECTOR BEAM-PROPAGATION FORMULATION FOR GRADED-INDEX WAVE-GUIDES

An improved finite-difference vector beam propagation formulation for graded-index waveguides is presented. The modification over the existing version involves a more accurate representation of the Fresnel operator in finite-difference form that accounts for the gradient of the refractive index in the vector Helmholtz equation. The modified scheme is assessed by calculating the TM mode propagation constants of single-mode planar guides that yield better agreement to the exact values over the existing scheme. Furthermore, the calculated coupling lengths of a vertical directional coupler show improved comparison to experimental data.