Effect of ultrarelativistic laser beam filamentation on third harmonic spectrum

This paper investigates the generation of plasma wave and third harmonic generation in a hot collision less plasma by an intense laser beam. On the account of the V-vectorxB-vector force, a plasma wave at 2ω0 (here ω0 is the pump laser frequency) is generated. The solution of the pump laser beam has been obtained within the nonparaxial ray approximation. Filamentary structures of the laser beam are observed due to relativistic nonlinearity. By expanding the eikonal and the other relevant quantities up to the fourth power of r it is observed that the focusing of the laser beams become fast in the nonparaxial region. Interaction of the plasma wave with the incident laser beam generates the third harmonics. The mechanism of the plasma wave, third harmonic generation, and the parameters, which govern the third harmonic yield and hence the spectrum of third harmonics, have been studied in detail. Correlation of the third harmonic spectrum with the filamentation has been pointed out. Therefore, the broadening of the third harmonic spectra can be used as a diagnostic tool to study the presence of the filamentation of laser beams in laser plasma experiments.