Far-field model of two-color laser driven terahertz radiation including field element interference and plasma response

The two-color laser field scheme for broad-band terahertz (THz) radiation from air has been intensively and broadly investigated due to the simplicity in technology and relative high yield efficiency. Experiments showed that the detected THz angular distribution is usually conical with a dip in the laser propagation axis which is unfavorable for its application, and the formation of an oscillating tail in the THz waveform has not yet been well understood. Here, we develop an electric field element interference model in which each local current source has a phase velocity determined by the laser pulse and a Gaussian temporal profile, rather than an ideal point source, as well as the current oscillation caused by the plasma dynamics is considered. By introducing the temporal interference, effects of the phase velocity and the Gaussian profile of the current can correct the THz angular distribution. Therefore, by adjusting the laser pulse duration and the group velocity, the THz angular distribution can be controlled and the dip could be even eliminated. Besides, the plasma dynamics can result in the formation of an oscillating tail in the THz waveform and sunken spikes in the corresponding spectrum. This is similar to the experimental results which are usually explained by the water vapor absorption. In turn, the spikes in the spectrum could provide a way to measure the plasma filament density.