Origin of uniform pump-to-Stokes relative intensity noise (RIN) transfer in Raman fiber lasers. A. A. Fotiadi*, S. A. Babin, D. V. Churkin, S. I. Kablukov, and E. V. Podivilov *Service d'Electromagnétisme et de Télécommunications, Faculté Polytechnique de Mons, 31 Boulevard Dolez, B-7000, Mons, Belgium Tel: +32 65 374198; Fax: +32 65 374199; E-mail: Fotiadi@telecom.fpms.ac.be Also with Ioffe Physico-Technical Institute of RAS, St.Petersburg, Russia Institute of Automation and Electrometry, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia Recently, the uniform pump-to-Stokes relative intensity noise (RIN) transfer has been discovered for cascaded Raman fiber lasers [1]. It was found that peaks of the radio- frequency (RF) spectrum associated with longitudinal mode beating in the pump laser cavity almost uniformly transfer to the 1st and 2nd Stokes RF-spectra. Here we present a detailed derivation of the analytical expression that explains this effect. We show that interaction between the intensity noise fluctuations related to counter-propagating waves in the Raman cavity is negligible comparing with the interaction of co-propagating fluctuations. This feature results in a simple relation between the fluctuation intensities. Introduction Continuous-wave-pumped Raman fiber lasers operating in the spectral range between 1.1 and 1.6 μm are of great interest for many applications in telecommunications, medicine, and other research areas. Although steady-state properties of the Raman lasers have been extensively considered from their early experimental demonstrations in the 1970’s, only a limited number of theoretical works has been devoted to the analysis of the dynamical behavior of the Raman lasers. Recently we proposed a simple dynamical model to explain the unexpected effect observed on Raman lasers [1]. The effect is the following. A Raman laser, for simplicity a one-stage one, is pumped with a fiber laser source. The length of the Raman laser cavity is assumed to be much longer than the length of the pump laser cavity: . The pump laser is multimode. Therefore, its RF-spectrum L l L >> l ( ) PC S ν presents a continuous chain of peaks associated with the longitudinal mode beating in the pump laser cavity. These peaks are observed in the MHz-frequency domain and have a spacing 2 PC c ln ν ∆ = . The Raman laser is also multimode. Accordingly its RF-spectrum is expected to present a similar peak chain associated with the mode beating in the Raman laser cavity, with a spacing 2 RC c Ln ν ∆ = . However, instead of that the RF-spectrum of the Raman laser, surprisingly, has a peak periodicity corresponding to the mode beating in the pump laser cavity, i.e. a spacing of PC ν ∆ . Inside these peaks the spectrum is modulated with a spacing RC PC ν ν ∆ << ∆ determined by the Raman cavity length. Our model completely explains this effect predicting the following dependence between the pump and Raman laser spectra: ( ) ( ) ( ) 1 2 ~ 1 2 cos 2 RL PL RC S S a a ν ν πν ν − ⎡ ⎤ + + ∆ ⎣ ⎦ 1 , a < is a model parameter (1) Since our analysis provoked some objections before its recent publication [1], we present here a detailed mathematical derivation of the last dependence (1). Proceedings Symposium IEEE/LEOS Benelux Chapter, 2005, Mons 209