Nonlinear phase shifts of bichromatic pump waves during terahertz wave generation in air

Generation of terahertz (THz) radiation in gaseous media by focused bichromatic femtosecond laser pulses is simple, efficient and well-established technique. However, despite the very high THz field strengths and extremely broadband spectral widths achieved by this method, THz generation efficiency strongly depends on the relative phase difference between two pump waves. Although this phase difference could be easily optimised by adjusting optical path length in the experimental setup, the exact value of this parameter is very useful both in theoretical modelling and in analysis of the experimental data. In the theoretical model, the input wave was a forward-propagating two-colour wave and the relevant Maxwell equations were solved numerically. Calculations show that the obtained maxima of the x-polarised THz wave do not depend on the phase difference. In contrast, significant shifts of the maxima positions have been obtained for the y-polarised THz wave. These findings have been confirmed experimentally, when dependencies of the THz field strength on pump polarisation angle for different fundamental pulse energies have been registered. Note that theoretically obtained results were found to be in good agreement with the experiment only when the nonlinear phase shifts of interacting waves were taken into account. In conclusion, it is shown that even at moderate pump powers the nonlinear Kerr-induced phase shifts of the fundamental and its second harmonic play an important role in THz wave generation from the laser-induced air plasma.