An exact soluble equation for the steady state probability distribution in a nonlinear system: application to the noise reduction in Raman Ring Laser

In this paper, we consider the model of a nonlinear system subjected simultaneously to a random telegraph noise and a white noise. By using the formulae of differentiation introduced by Shapiro and Loginov (Physica 91:563–574, 1978), an exact equation for the steady state probability distribution of fluctuation in this system is derived. As an example of its application, we calculate analytically the steady state probability distribution of fluctuation and show the existence of noise induced phase transitions (Wodkiewicz et al. in J. Opt. Soc. Am. 1:398–405, 1984a) in Raman Ring Laser. Moreover, we show explicitly the so-called noise reduction considered in Lewenstein and Rzązewski (Opt. Commun. 63:174–178, 1987) for this system. It follows that the Stokes output of this laser tends to the stabilization under influence of the broad-band telegraph pump. This phenomenon could be realized experimentally in a much easer manner than for the case of Gaussian pump, because the construction of the injected telegraph pump signal is much easer than in the case of Gaussian signal. The recent paper is an extended version of Doan and Van (1991).