Ultra-strong attosecond laser focus produced by a relativistic-flying parabolic mirror

The reflection of a laser pulse by a relativistic-moving mirror is one of fundamental problems encountered in the high-power laser and plasma interactions. It is well known that a laser pulse reflected by a relativistic-flying mirror experiences the intensification of its intensity, frequency up-shift, and shortening of pulse duration. Thus, it is of fundamental interest to have a mathematical solution expressing the intensity distribution of a laser pulse reflected by a relativistic-flying parabolic mirror. In this paper, we present analytical and mathematical formulae describing the electromagnetic field of a laser pulse reflected and focused by the relativistic-flying parabolic mirror.