Kerr self-focusing of few-cycle terahertz pulses in dispersive media

Kerr self-focusing is one of the most common and fundamental nonlinear phenomena during high-power light pulses propagating through transparent media. It occurs usually when the pulse peak power exceeds a certain critical power and the Kerr nonlinearity overcomes the diffraction effect. In this paper, the nonlinear propagation of terahertz (THz) pulses in dispersive media is studied via numerical simulations. It is found that, for few-cycle THz pulses, the Kerr self-focusing is suppressed dramatically, and a substantially higher THz intensity than that defined by the well-known formula of self-focusing critical power is required to enable an observable spatial self-focusing behaviour. By theoretical modelling and numerically analysing the time-domain evolution of broadband THz pulses in media, the underlying physical cause is attributed to the dominance of the significant dispersion effect over the diffraction effect, resulting in that the Kerr nonlinearity competes with dispersion instead of diffraction. A modified analytical expression for the dispersion-mediated self-focusing critical intensity is derived and shows good agreement with simulation results. The influences of THz pulse and medium dispersion parameters on the THz propagation dynamics are systematically studied such as the THz cycle number, intensity, initial chirp and absolute phase as well as the medium group velocity dispersion, high-order dispersion and their sign. These results have important implications for the study of strong-field THz wave-matter interactions and THz nonlinear optics.