Terahertz generation in plasmas using two-color laser pulses

We analyze the generation of terahertz radiation when an intense, short laser pulse is mixed with its frequency-doubled counterpart in plasma. The nonlinear coupling of the fundamental and the frequency-doubled laser pulses in plasma is shown to be characterized by a third order susceptibility which has a time dependence characteristic of the laser pulse durations. The terahertz generation process depends on the relative polarizations of the lasers and the terahertz frequency is omega approximately 1/tau(L), where tau(L) is the laser pulse duration. Since the laser pulse duration is typically in the picosecond or subpicosecond regime the resulting radiation is in the terahertz or multiterahertz regime. 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 nearly cancel in the absence of electron collisions. Therefore, in this terahertz generation mechanism collisional effects play a critical role. Consistent with recent experimental observations, our model shows that (1) the terahertz field amplitude is proportional to I(1) square root I(2), where I(1) and I(2) are the intensities of the fundamental and second harmonic laser pulses, respectively, (2) the terahertz emission is maximized when the polarization of the laser beams and the terahertz are aligned, (3) for typical experimental parameters, the emitted terahertz field amplitude is on the order of tens of kilovolts/cm with duration comparable to that of the drive laser pulses, and (4) the direction of terahertz emission depends sensitively on experimental parameters.