Vector and quasi-vector solutions for optical waveguide modes using efficient Galerkin´s method with Hermite-Gauss basis functions

An efficient vector formulation and a corresponding quasi-vector formulation for the analysis of optical waveguides are presented. The proposed method is applicable to a large class of optical waveguides with general refractive index profile in a finite region of arbitrary shape and surrounded by a homogeneous cladding. The vector formulation is based on Galerkin´s procedure using Hermite-Gauss basis functions. It is shown that use of Hermite-Gauss basis functions leads to a significant increase in computational efficiency over trigonometric basis functions. The quasi-vector solution is obtained from the standard scalar formulation by including a polarization correction. The accuracy of the scalar, vector, and quasi-vector solutions is demonstrated by comparison with the exact solution for the fundamental mode in a circular fiber. Comparison of the modal solutions obtained with the various methods for optical waveguides with square, rectangular, circular, and elliptical core demonstrate the accuracy and advantage of the quasi-vector solution