Iterative method for Brillouin fiber ring resonator

Abstract

The interest for Brillouin fiber ring lasers has significantly increased due to the large spectrum of their applications: the large scale of their peak power, the ultra-narrow linewidth and the low threshold power are the most exploited features. At the same time, their application is limited because of the important peak-power fluctuations which are mainly due to the stochastic nature of the Spontaneous Brillouin Scattering that initiates the Stimulated Brillouin Scattering (SBS). Therefore, it is of great interest to develop new models and methods for controlling these amplitude fluctuations. Several analytical and numerical solutions are often proposed to describe the steady state of the SBS in single mode optical fibers but, for instance, the general form of the non-linear equations system of the SBS is difficult to solve. Models start typically from the classical system [1] which couples the evolution of two optical fields with the acoustic field through the electrostriction process and propose several improvements to obtain a better agreement with experimental data or predict new behaviors.In the present paper we show that, in dynamical regime, experimental [ Fig. 1 (b)] and simulation results [Fig. 1(c)] for the transmitted pump and Stokes waves from the ring resonator are concordant for the same conditions. A hyperbolic secant periodic modulation signal is applied on the ring cavity formed by a directional fiber coupler (10/90) and by L = 2 m of SM optical fiber [ Fig. 1(a)]. For each period of the incident signal, one pulse is emitted by SBS inside the ring resonator. For the both situations, experimental and simulation, we can observe a small depletion in the transmitted pump that corresponds in the SBS signal emission. This pulse with Gaussian shape presents a FWHM of about 1µs and its repetition period is 200µs, which is in agreement with the repetition period of the pumping signal. Fig. 1 (a) Experimental setup of the Brillouin fiber ring laser. (b) Experimental results. (c) Simulation results. Transmitted signals (black) and SBS signals (red).In our iterative simulation method, we simplify the spatio-temporal system of the coupled equations including a noise source [2] by neglecting the time derivatives of the complex field amplitudes and by considering for the acoustic wave an expression no longer depending on time. The obtained approximation is generally valid for a continuous-wave pumping but also for a regime where the incident pulse duration is much longer than the roundtrip time in the ring cavity and superior to the phonon life time in this environment. Such a model, usually used to obtain the solutions in the steady-state regime, can be also used in the transient regime, when the time scales are much longer than the round-trip time. Assuming that the pump and the Stokes waves propagate with the same velocity, we can consider that during the forward-propagation of the pump on the first half of the resonator, the Stokes wave is backward-propagated on the other half of the resonator. These two...

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