Phase-matched second- and third-harmonic generation in plasmas with density ripple

The generation of second and third harmonics by the interaction of an ultrashort laser pulse with underdense plasma having a density ripple is studied at intensities I lambda(2)=10(16)-10(19) W cm(-2) mu m(2) using fully relativistic two-dimensional particle-in-cell simulations with high spectral resolution. A theoretical model is developed for second- and third-harmonic conversion efficiencies. When the laser is plane polarized in the simulation plane even and odd harmonics are excited in the same polarization as the laser polarization. The highest efficiency of generation of a specific harmonic occurs when the ripple wave vector value k(q) satisfies phase-matching conditions. The efficiency of phase-matched harmonic generation is an order of magnitude higher than the one without phase matching. The efficiency increases rapidly in weak and moderate relativistic regime and tends to saturate in strong relativistic regime. At moderately relativistic intensities and low plasma densities, the simulation and recent experimental results are fairly reproduced by an analytical theory. (c) 2007 American Institute of Physics.