Extreme-value statistics in supercontinuum generation by cascaded stimulated Raman scattering

Abstract

We study experimentally the statistical fluctuations observed in a supercontinuum generated in the normal dispersion regime through cascaded stimulated Raman scattering. Specifically, we show that the statistical distribution of shot-to-shot spectral variations evolves from a quasi-Gaussian in the saturated regime for Stokes orders near the pump to a long-tailed extreme-value distribution for Stokes orders at a large separation from the pump in the unsaturated regime.

Extreme statistics in Raman fiber amplifiers: From analytical description to experiments

“…2(b). Let us stress that for the range of power / fiber length considered here, it is not necessary to take into account the cascading of the Raman process: such a spontaneous cascading will ultimately lead to a depletion of the central part of the signal wave [7,14,36,37].In these conditions, we can express the longitudinal evolution of the gain G(z) that we define as the ratio of the peak power of the amplified signal and the initial average power (note that with such a definition, our gain differs from the ratio of the initial and output average powers).…”

“…More recently, it has also been demonstrated that the supercontinuum generation of picosecond pulses or continuous waves in a highly nonlinear microstructured optical fiber can be characterized by an "extreme" statistics deviating strongly from usual Gaussian statistics : under the combined effects of spontaneous modulational instability and intrapulse Raman response, rogue solitons can emerge and be significantly shifted towards long wavelengths where they can then be adequately isolated by an adequate filtering [4][5][6]. Other studies have outlined that such statistics are not restricted to soliton-supporting systems and that the Raman effects is a key ingredient that promotes non-Gaussian statistics, either through cascaded Stokes generation [7], through a turbulent behaviour recorded in ultralong Raman fiber cavities [8] or through pulse-topulse collisions and energy exchanges as observed in telecommunication systems [9,10]. In this contribution, we focus on discrete Raman amplifiers where extreme statistics have also been numerically and experimentally highlighted [11][12][13].…”

Weak Langmuir optical turbulence in a fiber cavity

“…One may wonder whether the spectral pattern of SIS reported here can be explained by a mechanism of cascaded Raman scattering, a well-known process that has been widely studied in both single pass propagation [94,95], or in cavity systems, e.g., in cw fiber lasers [96], in mode-locked fiber lasers [97], or in passive microresonators [98,99]. Cascaded Raman scattering refers to the generation of several Stokes orders, the 1st order subsequently leading to the generation of the 2nd order, which in turn generates the 3rd one, and so on several orders are generated in cascade.…”

Elementary field representation of supercontinuum

“…In order to compare more quantitatively the elementary field representation with the time-domain coherent-mode expansion, we define an error function with respect to the overall degree of coherenceμ calculated from the ensemble Δμ jμ −μ e;c j; (16) whereμ e (μ c ) is the overall degree of coherence as evaluated from the elementary-field (coherent-mode) construction. The value of the error function is given in Table 2 for the three ensembles obtained for different input peak power.…”

“…The recent interest into the statistical representation of SC fields has also been motivated by the observation that the initial noise present on the pump pulses can behave like an optical wind that can trigger the generation of waves with extreme amplitudes during the turbulent phase of SC formation in the long-pulse regime [12][13][14][15][16]. Because the elementary field construction is particularly useful to model SC ensembles with large fluctuations initiated by modulation instability, we anticipate that the representation introduced here may provide useful insight and find applications in physical systems where noise instabilities and amplification play a central role, including, e.g., Bose-Einstein condensates, hydrodynamic systems, or plasma physics.…”