Numerical Study On High-order Kerr Effect For Ultrashort Laser Pulses

Ultrashort laser pulse propagation has many potential applications, such as the generation of terahertz wave, ultra wide-band laser radar, laser-triggered lightning and so on. The ultrashort laser propagation in the atmosphere has become a hot topic in recent years. When the ultrashort intense laser pulse propagates in the atmosphere, the self-guided propagation will happen due to the dynamic balance among the third-order Kerr self-focusing effect, the high-order Kerr effects and plasma defocusing effect. In this paper we apply the Split-Step Fourier Method and Crank-Nicholson difference (FCN) to simulate the propagation of the ultrashort laser pulses in the atmosphere, with the latest reported high-order Kerr indices in the literature. We investigate the effects of high-order Kerr effects and plasma defocusing effect on the propagation of laser pulses, and studied the influence of different initial powers of laser pulses on the propagation of the laser pulses given the fixed energy and peak intensity. The detail results in this paper are as follows:We use the full model, the full model without ionization, the classical model (not including high-order Kerr effect), vacuum model (not including the nonlinear effects) to simulate the ultrashort laser pulses propagation in atmosphere, respectively. Numerical simulations show that, the high-order Kerr effects plays a dominant role in the propagation of femtosecond laser pulse in air, and the plasma defocusing effect is very weak compared with the high-order Kerr effects, but it has an important impact on the energy distribution in the cross-section of the laser pulse. In the classical model, the peak intensity is higher than the result of the full model, and the plasma density in the classical model is one magnitude higher than that of the full model. Compared to the femtosecond laser pulse, the picosecond pulse produces larger plasma density, and the plasma defocusing effect is stronger. Therefore, the plasma defocusing effect can not be ignored for the picosecond or longer laser pulses.We adopt the full model to study the impact of different initial power on the propagation of the femtosecond laser pulse with the fixed energy and peak intensity. The results show that, with the increase of input power, the plasma defocusing effect increase, and the breakup of the pulse in time and space are more obvious, At the same time, the ionization effect is become stronger, and more energy of the pulse loses. With the decrease of the input power, the pulse duration becomes larger, and the pulse radius becames smaller, and the fluence of laser pulse is more concentrated in space, and the self-focusing effect is more obvious.