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{sub n}{proportional_to}n{sup -8,}n{approx}3 for n<{radical}(8{alpha}){gamma}{sub max}{sup 3}, followed by exponential decay. Here {gamma}{sub 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}{sub max}{sup 3} is parametrically larger than the 4{gamma}{sub max}{sup 2} 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.