Formation and properties of spatially inhomogeneous plasma density gratings

Volume plasma density gratings receive increasing interest since, compared to solid-state optical media, they posses significantly higher damage thresholds. The gratings are produced by counterpropagating laser pulses in underdense plasma. When analyzing their optical properties, usually they are assumed to be homogeneous in space. The latter assumption, however, breaks down, especially when the gratings are produced by short high-power laser pump pulses. Then, generically the plasma grating posses an inhomogeneous envelope which results from the superposition of the pump pulses envelopes. The present paper discusses the effect of grating inhomogeneity on reflection and transmission of probe pulses. A Gaussian plasma density grating becomes an apodized grating which offers significant improvement over homogeneous gratings due to side-lobe suppression while maintaining reflectivity and a narrow bandwidth. On the other hand, the reflected probe pulses receive a chirp which depends on the spatial scale. For a Gaussian grating a cubic spectral phase appears. Numerical particle-in-cell simulations are supported by theoretical analysis based on coupled mode equations as well as an effective medium approach.