Noise characteristics and statistics of picosecond Stokes pulses generated in optical fibers through stimulated Raman scattering

The growth of the Stokes pulse from spontaneous noise during stimulated Raman scattering of picosecond pump pulses in optical fibers, is investigated by using a Langevin-noise term in the coupled nonlinear Schrodinger equations, which include pump depletion, group-velocity mismatch, fiber dispersion, and self- and cross-phase modulation. The model makes use of the actual Raman-gain spectrum of optical fibers. Numerical simulations are used to examine the average behavior of the Stokes pulse, and shot-to-shot fluctuations that are likely to occur in practice. It is shown that the Raman-induced energy transfer is significantly affected by group-velocity dispersion for pump-pulse widths shorter than 5 ps. Examination of the average temporal width shows that the Stokes pulse is initially as wide as the pump pulse, undergoes a gain induced compression and then rebroadens for distances longer than a walk-off length. The effect of varying pump and fiber parameters is to change the minimum value of the Stokes-pulse width, and the distance at which the minimum occurs. The shot-to-shot energy and pulse-width fluctuations initially increase before being reduced at fiber lengths longer than the walk-off length. The primary effect of dispersive and nonlinear effects is to change the distance beyond which fluctuations decrease