tailieunhanh - An exactly soluble equation for the stationary probability distribution in a nonlinear system under the influence of two- telegraph noise: application to the noise reduction in a raman ring laser

In this paper, we will consider a nonlinear system with random telegraph noises in a Raman ring laser by modeling the laser pump light as a pre-Gaussian process and find an exactly soluble equation for the stationary probability distribution of fluctuations in this nonlinear system under the influence of two-telegraph noise. | Communications in Physics, Vol. 26, No. 1 (2016), pp. 75-82 DOI: AN EXACTLY SOLUBLE EQUATION FOR THE STATIONARY PROBABILITY DISTRIBUTION IN A NONLINEAR SYSTEM UNDER THE INFLUENCE OF TWO-TELEGRAPH NOISE: APPLICATION TO THE NOISE REDUCTION IN A RAMAN RING LASER DOAN QUOC KHOA† Quang Tri Teacher Training College, Quang Tri, Vietnam CHU VAN LANH Vinh University, Nghe An, Vietnam PHAN XUAN SANH Phan Boi Chau High School for The Gifted, Nghe An, Vietnam NGUYEN THI HONG SANG Tran Quoc Toan High School, Dong Thap, Vietnam LE THI HOA, NGUYEN THI THU, AND BUI VAN DUNG Hong Duc University, Thanh Hoa, Vietnam † E-mail: khoa dqspqt@ Received 04 March 2016 Accepted for publication 24 June 2016 Abstract. In this paper, we will consider a nonlinear system with random telegraph noises in a Raman ring laser by modeling the laser pump light as a pre-Gaussian process and find an exactly soluble equation for the stationary probability distribution of fluctuations in this nonlinear system under the influence of two-telegraph noise. As a consequence, we will obtain the so-called noise reduction in this system: the Stokes output of this laser tends to stabilize under the influence of the broad-band two-telegraph pre-Gaussian pump and compare this result with that obtained in our previous paper (Cao Long Van, Doan Quoc Khoa, Opt. Quant. Electron. 43 (2012) 137) for the case of one-telegraph noise. Keywords: Raman ring laser, two-telegraph noises, noise reduction, nonlinear system. Classification numbers: ; ; ; ; . c 2016 Vietnam Academy of Science and Technology 76 DOAN QUOC KHOA et al. I. INTRODUCTION Laser lights are never perfectly monochromatic so they generally have fluctuations in phase and amplitude. To simplify the complicated microscopic nature of all the relevant relaxation mechanisms, we model the laser lights by classical time-dependent random processes. The dynamical equations that contain .