Theory of high-order harmonic generation in relativistic laser interaction with overdense plasma

High-order harmonic generation due to the interaction of a short ultrarelativistic laser pulse with overdense plasma is studied analytically and numerically. On the basis of the ultrarelativistic similarity theory we show that the high-order harmonic spectrum is universal, i.e., it does not depend on the interaction details. The spectrum includes the power-law part I-n proportional to n(-8/3) for n <root 8 alpha gamma(3)(max), followed by exponential decay. Here gamma(max) is the largest relativistic gamma factor of the plasma surface and alpha is the second derivative of the surface velocity at this moment. The high-order harmonic cutoff at proportional to gamma(3)(max) is parametrically larger than the 4 gamma(2)(max) predicted by the simple "oscillating mirror" model based on the Doppler effect. The cornerstone of our theory is the new physical phenomenon: spikes in the relativistic gamma factor of the plasma surface. These spikes define the high-order harmonic spectrum and lead to attosecond pulses in the reflected radiation.