Toward superstrong fields with a relativistic curved plasma mirror

The laser pulse reflected and focused by the relativistically moving curved plasma mirror can exceed the laser intensity obtained by focusing high-power laser pulses with conventional physical optics. In the ultrarelativistic limit where the Lorentz $\ensuremath{\gamma}$ factor is large ($\ensuremath{\gamma}\ensuremath{\gg}1$), the general field configuration focused by the relativistic curved plasma mirror is calculated using the $4\ensuremath{\pi}$-spherical focusing scheme in the boosted frame of reference. The calculated field strength and distribution can be applied to investigate nonlinear quantum electrodynamic effect (electron-positron pair creation from the vacuum via the Schwinger mechanism) under the two-beam colliding scheme, in which a high-intensity laser pulse collides with a focused field by the relativistic mirror. The benefit of using the relativistic mirror has been discussed in terms of the invariant field. Taking advantage of the mathematical expression for the focused field, the spatial distributions of the pair creation rate have been calculated as functions of time and the carrier envelope phase of the laser pulse. The calculation predicts that creating $\ensuremath{\approx}2.2\ifmmode\times\else\texttimes\fi{}{10}^{6}$ electron-positron pairs is possible by colliding a 25 PW laser pulse with a reflected and focused field by the relativistic mirror with $\ensuremath{\gamma}=100$. This attributes to the field enhancement by the double Doppler effect, a large geometrical factor of the relativistic mirror, and the increase in the reflectivity due to the oblique incidence.