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

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4 Author(s)
Weisshaar, A. ; Dept. of Electr. & Comput. Eng., Oregon State Univ., Corvallis, OR, USA ; Li, J. ; Gallawa, R.L. ; Goyal, I.C.

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

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Lightwave Technology, Journal of  (Volume:13 ,  Issue: 8 )