Title :
Solution of the scalar wave equation for arbitrarily shaped dielectric waveguides by two-dimensional Fourier analysis
Author :
Henry, Charles H. ; Verbeek, Bart H.
Author_Institution :
AT&T Bell Lab., Murray Hill, NJ, USA
Abstract :
A method for calculating the modes of arbitrarily shaped dielectric waveguides is presented. It consists of expanding the field in a two-dimensional Fourier series. The expansion is used to convert the scalar wave equation into a matrix eigenvalue equation. To facilitate calculation of the matrix elements, the waveguide geometry is approximated by a number of rectangles of constant refractive index. The accuracy of the method is demonstrated by calculating the dominant mode of a circular optical fiber and comparing it with the exact solution. The method well-fitted the experimental data on dielectric film waveguides on silicon, including data on waveguide-to-fiber butt-coupling loss, waveguide far-field angles, and the coupling length of directional couplers.<>
Keywords :
matrix algebra; optical modulation; optical waveguide theory; refractive index; Fourier analysis; circular optical fiber; coupling length; dielectric waveguides; matrix eigenvalue equation; refractive index; scalar wave equation; waveguide far-field angles; waveguide-to-fiber butt-coupling loss; Dielectrics; Eigenvalues and eigenfunctions; Fourier series; Geometrical optics; Matrix converters; Optical waveguides; Partial differential equations; Rectangular waveguides; Refractive index; Transmission line matrix methods;
Journal_Title :
Lightwave Technology, Journal of
