The third harmonic generation of a self organized nonlinear laser Eigen mode of a two-dimensional plasma channel with complete electron evacuation from the inner region is investigated. The nonlinearities arise through the ponderomotive force and relativistic mass variations, while the ions are taken to be immobile. The second harmonic ponderomotive force produces electron density oscillations that beat with the oscillatory velocity due to the laser Eigen mode to create a nonlinear current, driving the third harmonic. As a0 increases up to the threshold value amin, at which complete electron evacuation begins in the inner region, the third harmonic amplitude rises rapidly. Above the threshold, as a0 increases, the width of the inner region where there is no third harmonic current, increases and third harmonic amplitude rises less rapidly. The conversion efficiency is found to be in reasonable agreement with the experimental results.
