Raman random laser in one-dimensional system

The probability of occurrence of random cavities' resonance frequency in the Stokes bandwidth of the Raman active medium can cause Raman laser oscillation in the random structures. Due to the small bandwidth of Raman line shape, the probability of the simultaneous appearance of random cavity resonance frequencies in the cascade Stokes line shapes is small. As a result, the cascade Raman laser oscillation effects on the saturation behavior are negligible. The nonlinear transmission matrix method is employed to determine the statistical behavior of a Raman random laser. Our results showed that the statistical behavior depends on the position of the Stokes line shape relative to the center of the stopband and the edge of the passband of the corresponding nondisorder system.