An improved finite-difference vector beam propagation formulation for graded-index waveguides

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Abstract
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 Hehmholtz 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.