High-density (>1023/cm3) relativistic electron plasma confined between two laser pulses in a thin foil

The nonlinear interaction of two counterpropagating high-intensity laser pulses in thin foil targets is investigated theoretically and by simulation. The two laser pulses have circular polarization and illuminate the foil normally from both sides. They create a spatially confined relativistic electron plasma. An analytical stationary solution is derived for the special case in which the polarization of the two beams rotates in the same direction. The solutions depend on the relative phase of the two pulses. In general, the foil oscillates as a whole; the oscillation frequency is derived analytically. High order harmonics are found when frequencies and/or polarizations are changed. For same polarization and frequencies ωL and 2ωL of the two incident pulses, a harmonics spectrum is found in which each third harmonic (third, sixth, etc.) is absent. Under certain conditions, an instability occurs which can destroy the foil.