Modal properties of circular and noncircular optical waveguides |
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Authors: | R L Gallawa I C Goyal A K Ghatak |
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Institution: |
a Electromagnetic Technology Division, National Institute of Standards and Technology, Boulder, Colorado, 80303
b Department of Physics, Indian Institute of Technology, New Delhi |
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Abstract: | We give a review and a comparison of recent methods of analyzing circular and noncircular optical waveguides. Comparison among competing methodologies is made as follows: Galerkin's method is used with Laguerre-Gauss basis functions in circular geometry to examine the modal solution in a step index fiber, and comparison with the exact solution is made. A W-fiber, which has no exact solution, is then examined. Rectangular geometry is considered, and discussion centers on the use of Galerkin's method using trigonometric basis functions and Hermite-Gauss basis functions. Re difficulty arising from the use of basis functions that do not decay exponentially for large argument (trigonometric functions) is illustrated. Finally, a square step index waveguide is used to illustrate a comparison between a variational method that uses the Gaussian approximation as the starting point, and Galerkin's method using Hermite-Gauss basis functions. We conclude that the variational method does well in predicting the propagation constant β but does not do well in predicting the modal field. |
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