Modeling of Brillouin scattering in long-distance fiber optic link with bi-directional optical amplifiers

For the dissemination of precise signals from atomic clocks (like e.g. cesium clocks/fountains, H masers or optical clocks) an optical link operating in both forward and backward directions over the same optical fiber is essential. In such a link stimulated Brillouin scattering is one of the non-linear effects that may reduce the forward optical signal power and convert it into the noise that propagates in the backward direction. When triggered, this usually prohibits a stable operation of the link or at least seriously degrades the parameters of delivered signals. In the link that uses a number of bi-directional optical amplifiers, the conditions that trigger the Brillouin scattering process may occur relatively easily because the effective length for the scattering process is substantially increased comparing to a typical telecommunications link. Thus in the design phase of the link, checking the conditions for Brillouin scattering should be a part of the link optimization procedure (i.e. optimizing bi-directional amplifiers gains and determining the localization of wavelength-selective isolators).
In the paper we consider the mathematical model of the stimulated Brillouin scattering in the long distance, fiber optic links with multiple bi-directional optical amplifiers. The model was implemented in Matlab and consists of the coupled differential equations describing the propagation of pump and scattered signals that develop due to spontaneous scattering. The presence of bi-directional optical amplifiers at some points of the fiber is modeled as a point-like discontinuity of the α parameter that is used to represent the attenuation of the fiber. These discontinuities create an extra level of difficulty when solving the coupled equations numerically (the problem is stiff) so a special algorithm is presented that searches iteratively for the solution. The obtained results were compared with the measurements of the real link to confirm the correctness of the solution.

Author: Karol Salwik
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