  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.
