Theory and numerical simulation of nth-order cascaded Raman fiber lasers

Using the classical treatment of the stimulated Raman-scattering process, we use a theoretical model to simulate the operation of an nth-order cascaded Raman fiber laser. We introduce the partial differential equations employed to describe the propagation and time dependence of the forward and reverse-propagating fields of an rath-order cascaded Raman fiber laser. Under steady-state conditions, these equations form the well-known system of first-order, nonlinear boundary-value ordinary differential equations, with separated boundary conditions. We solve this system of equations numerically with the use of mono-implicit Runge-Kutta methods within a defect-control framework. We consider cascaded Raman fiber lasers of orders 2 through 5 and examine the parameters that influence the operation of these devices. We also provide preliminary results on the investigation of a time-dependent model in which the pump power is assumed to vary periodically with time. The associated system of first-order, hyperbolic, partial differential equations is treated by employing a transverse method-of-lines algorithm; the time derivatives are discretized with a finite-difference scheme, yielding a large system of boundary-value ordinary differential equations. We establish that for sinusoidal modulation of the pump the Stokes cavity modes exhibit antiphase dynamics typical of a system of locally coupled nonlinear oscillators.