THz generation in plasmas using multiple color laser pulses

Experiments have demonstrated the generation of THz radiation when an intense, short laser pulse is mixed with its frequency-doubled counterpart in a gas. A number of mechanisms have been proposed to account for the observed THz radiation. Our analysis indicates that under the proper conditions the nonlinear coupling of the two short pulse lasers, one at frequency omega₀ and the other at 2omega₀ , in plasma can lead to the generation of THz radiation. The nonlinear coupling of the fundamental E₁(omega₀) and the frequency-doubled E₂(2omega₀) laser pulses is shown to lead to a third order susceptibility which has a time dependence characteristic of the laser pulse durations. Since the laser pulse duration is typically in the pico-second or sub-picosecond regime the resulting radiation is in the THz or multi-THz regime. The appropriate third order susceptibility is chi⁽³⁾(omega= 0; omega₀,omega₀,2omega₀) and is proportional to(E₁)² E₂. To obtain the third order susceptibility we solve the plasma fluid equations correct to third order in the laser fields, including both the relativistic and ponderomotive force terms. The relativistic and ponderomotive contributions to the susceptibility exactly cancel in the absence of electron collisions. Therefore, in this THz generation mechanism collisional effects play a critical role. In addition, THz generation depends on the relative polarizations of the lasers. We discuss the experimental observations and compare the results with our theoretical and numerical predictions.