Modulational instability of nonlinear electromagnetic waves in plasma Bragg grating

The nonlinear propagation of electromagnetic waves in a plasma Bragg grating is considered. In a weakly relativistic regime, by means of the Maxwell’s equations along with a plasma fluid model, two coupled equations are found that govern the evolution of the envelopes of forward and backward propagating waves in a cold unmagnetized plasma undergoing an ambient density modulation in the form of gratings. Then, the nonlinear plane wave solutions with constant amplitude are obtained and the stability of them against a small perturbation is investigated. The dependence of the growth rate and instability window on relevant parameters of the system is addressed.