Three-dimensional analysis of collective relativistic electron motion and coherent harmonic generation driven by an intense pulsed Gaussian beam

Collective electron motion driven by intense laser pulses can become highly nonlinear as results of the v×B term in the Lorentz force and the relativistic mass increase effect. These nonlinear effects are the bases of many nonlinear phenomena in high-field physics. Using paraxial expansion we analyzed the three-dimensional collective relativistic motion of electrons driven by an intense pulsed Gaussian beam. We solved the three-dimensional velocity field and density field of the electrons, as well as the scalar potential field resulting from the electron density modulation, in terms of the vector potential of the laser pulse in the highly relativistic regime. From the solutions we derived an analytical expression for the nonlinear oscillation of the electric current density. The results are applied to a systematical analysis of coherent relativistic harmonic generation as a demonstration of the applications. Extensive comparison with published experimental data is made, and the remarkable agreement provides a strong support to the analysis presented in this paper.