Abstract
Averaged coupled wave equations are derived for a fibre Bragg grating with Gaussian noise added to the refractive index. The corrections to reflection and transmission coefficients are expressed in terms of a Green matrix of the unperturbed grating. The explicit formula for the Green matrix is derived for the uniform grating. The average reflectivity is calculated analytically. The noise is shown to increase reflectivity outside the Bragg reflection band and to smooth out the oscillations in the spectrum.
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