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∝n^-8/3 for n<8αγ_max³ , followed by exponential decay. Here γ_max 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 ∝γ_max³ is parametrically larger than the 4γ_max² 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.