Split-step methods for numerical modeling of synchronously pumped crystalline Raman laser

Raman lasers based on stimulated Raman scattering are attractive sources of laser radiation in a visible and an infrared spectral range. Synchronously pumped crystalline Raman lasers present interesting possibility to obtain effective generation in picosecond or femtosecond time-scale. According to semiclassical theory, their dynamic process can be described by a system of partial differential equations for optical and phonons fields. In the case of picosecond or femtosecond regime the set of equations has to be solved numerically. This is especially valid for synchronous pumping. The formal form of formulas is very similar to the task of optical parametrical process. The optical parametrical process is described by coupling of three optical waves. In the case of stimulated Raman scattering coupling is between the two optical fields and phonon field. Otherwise, the sets of equations are analogous. For this reason, the behavior is the same and the output properties of synchronously pumped Raman lasers have similar characteristics as a synchronously pumped optical parametrical oscillator. In this contribution, the split-step methods for numerical solution of synchronously pumped crystalline Raman lasers are presented and compared. In addition, the fundamental behavior of these systems is described.