Gaussian approximation for noncircular fibers

17-1 The Gaussian approximation 17-2 Example Infinite power-law profiles 

17-3 Slight eccenticity 17-4 Example Step profile 17-5 Example Gaussian profile 

The Gaussian approximation was introduced in Chapter 15 to provide simple, but accurate, analytical expressions for fundamental-mode quantities of interest on circular fibers of arbitrary profile. Here we show how to generalize this approximation and describe fundamental-mode propagation on weakly guiding fibers of arbitrary cross-section. 

The basis of the Gaussian approximation for circular fibers is the observation that the fundamental-mode field distribution on an arbitrary profile fiber is approximately Gaussian. Coupled with the fact that the same field on an ihfinite parabolic-profile fiber is exactly Gaussian, the approximation fits the field of the arbitrary profile fiber to the field of an infinite parabolic-profile fiber. The optimum fit is found by the variational procedure described in Section 15-1. Now in Chapter 16, we showed that the fundamental-mode field distribution on an elliptical fiber with an infinite parabolic profile has a Gaussian dependence on both spatial variables in the cross-section. Accordingly, we fit the field of such a profile to the unknown field of the noncircular fiber of arbitrary profile by a similar variational procedure, as we show below [1, 2], 

The two fundamental modes on a weakly guiding fiber of nondrcular cross- 

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Section 17-3 Gaussian approximation for noncircular fibers 371 17-3 Slight eccentricity... 

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