Non-ideal relativistic plasma mirrors

Relativistic plasma mirrors formed in the wake of intense laser pulses propagating in underdense plasmas can provide an efficient mechanism for generating attosecond pulses, and for enhanced focusing towards ultra-high intensity fields. We derive the reflection coefficient of a laser pulse interacting with relativistic mirrors, assuming different density profiles for the mirror. Analytical expressions are obtained for flat-top and parabolic density mirrors, and in the Dirac-delta limit, demonstrating the strong dependence of the reflectivity on the plasma mirror density profile. Fully kinetic multi-dimensional particle-in-cell simulations and our analytical model confirm that the density spike at the rear of the plasma bubble exhibits an approximately parabolic profile. Our results show that a laser wakefield setup can be optimized to maximize the reflection coefficient under specific laser driver conditions, determined by the balance between the moving plasma mirror proper density, thickness, and relativistic momentum carried by the mirror.