Effect of self-focusing on resonant third harmonic generation of laser in a rippled density plasma

Resonant third harmonic generation by a Gaussian laser beam in a rippled density plasma is studied. The laser ponderomotive force induces second harmonic longitudinal velocity on electrons that couples with the static density ripple to produce a density perturbation at 2ω,2k+q, where ω and k are the frequency and wave number of the laser and q is the ripple wave number of the laser. This density perturbation beats with electron oscillatory velocity at ω,k-vector to produce a nonlinear current driving the third harmonic generation. In the regime of quadratic nonlinearity, the self-focusing of the laser enhances the third harmonic power. However, at higher intensity, plasma density is significantly reduced on the axis, detuning the third harmonic resonance and weakening the harmonic yield. Self-focusing causes enhancement in the efficiency of harmonic generation.