The plasma density grating induced by intersecting intense laser pulses can be utilized as an optical compressors, polarizers, waveplates and photonic crystals for the manipulation of ultra-high-power laser pulses. However, the formation and evolution of the plasma density grating are still not fully understood as linear models are adopted to describe them usually. In this paper, two nonlinear theoretical models are presented to study the formation process of the plasma density grating. In the first model, a nonlinear analytical solution based on the fluid equations is presented while in the second model a particle-mesh method is adopted to investigate the kinetic effects. It is found that both models can describe the plasma density grating formation at different stages, well beyond the linear growth stage. More importantly, the second model can reproduce the phenomenon of ion wave-breaking of plasma density grating, which eventually induces the saturation of plasma density grating. Using the second model, the saturation time of the plasma density grating is obtained as a function of laser intensity and plasma density, which can be applied to estimate the lifetime of the plasma density grating in experiments. The results from these two nonlinear models are verified using particle-in-cell simulations.
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