Rayleigh backscattering theory for single-mode optical fibers

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Abstract
The theory of backscattering in single-mode optical fibers is described through use of a correlation function for the refractive-index fluctuation in the fiber. A simple formula for the backscattered power is derived using two correlation functions for the Booker–Gordon and Gaussian models. The zeroth-order approximation of the formula, in which the correlation length is much smaller than the spot size of the waveguide mode, coincides with Brinkmeyer’s model. The backscattered power at the input end of single-mode fiber is compared with that for multimode fiber. It is also shown that the backscattered power level at the input end is lower by approximately 55 dB than the input power level.