Coherent x-ray beams with a subfemtosecond ($<{10}^{-15}\mathrm{s}$) pulse duration will enable measurements of fundamental atomic processes in a completely new regime. High-order harmonic generation (HOHG) using short pulse ($<100\mathrm{fs}$) infrared lasers focused to intensities surpassing ${10}^{18}\mathrm{W}{\mathrm{cm}}^{-2}$ onto a solid density plasma is a promising means of generating such short pulses. Critical to the relativistic oscillating mirror mechanism is the steepness of the plasma density gradient at the reflection point, characterized by a scale length, which can strongly influence the harmonic generation mechanism. It is shown that for intensities in excess of ${10}^{21}\mathrm{W}{\mathrm{cm}}^{-2}$ an optimum density ramp scale length exists that balances an increase in efficiency with a growth of parametric plasma wave instabilities. We show that for these higher intensities the optimal scale length is $c/{\omega }_0$, for which a variety of HOHG properties are optimized, including total conversion efficiency, HOHG divergence, and their power law scaling. Particle-in-cell simulations show striking evidence of the HOHG loss mechanism through parametric instabilities and relativistic self-phase modulation, which affect the produced spectra and conversion efficiency.

• Received 27 November 2012

DOI:https://doi.org/10.1103/PhysRevLett.110.175002