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 In∝n-8,n∼3 for n<√(8α)γmax3, followed by exponential decay. Here γmax is the largest relativistic γ factor of the plasma surface and α is the second derivative of the surface velocity at this moment. The high-order harmonic cutoff at ∝γmax3 is parametrically larger than the 4γmax2 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 γ factor of the plasma surface. These spikes define the high-order harmonic spectrum and lead to attosecond pulses in the reflected radiation