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Modeling of Brillouin scattering in long-distance fiber optic links with bidirectional 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 bi-directionally over the same fiber is essential. In such a link stimulated Brillouin scattering is one of the non-linear effects that may reduce the power of forward optical signal and convert it into the noise that propagates in the backward direction. 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 of large effective length for the scattering process. Thus in the design phase of the link, checking of the conditions for Brillouin scattering should be a part of optimization procedure (i.e. optimizing bi-directional amplifiers gains). In the paper we consider the mathematical model of the stimulated Brillouin scattering in the long distance, fiber optic links with multiple bidirectional optical amplifiers. The model was implemented in Matlab and consists of the coupled differential equations describing the propagation of pump and scattered signals that develops due to spontaneous scattering. The presence of bi-directional optical amplifiers is modeled as 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 numerically solving the coupled equations (the problem is stiff) so special algorithm is presented that iteratively searches for the solution. The obtained results were compared with the measurements of the real link to confirm the correctness of the solution.