| The generation of the few-cycle pulse(FCP)has come of age.It has promoted the devel-opment of cutting-edge technology,such as the precision machining process,triggering and detection of ultrafast phenomena.In terms of nonlinear optics,the interaction of FCP and medium leads to many new nonlinear phenomena,such as the generation of supercon-tinuum spectrum and the generation of high-order harmonic generation.In recent decades,researchers have proposed many simplified theoretical model to describe the propagation of FCP in the nonlinear media,such as some universal model in nonlinear system(mKdV equation,sine-Gorden equation),the generalized nonlinear Schrodinger equation as the representative of the envelope model and the RSPE equation model.Based on the scalar RSPE equation and vector RSPE equation,the propagation properties of scalar FCP,cir-cularly polarized FCP in Kerr medium are studied in this paper.Firstly,the different aspects of FCP dynamics governed by the regularized short pulse equation(RSPE)are reported.It is shown that the RSPE provides an accurate description of the dynamics of the few-cycle pulse whose duration is larger than a single optical peri-od when the few-cycle pulse’s spectrum is in the medium’s anomalous dispersion regime.The approximate solutions of the RSPE are constructed from the soliton solutions of the nonlinear Schrodinger(NLS)equation.We demonstrate numerically that the stability of these few-cycle pulses strongly depend on their pulse duration.Furthermore,the interac-tions of the two and three few-cycle pulses are studied.When pulse parameters are suitably chosen,we show the elastic collision,inelastic collision and repulsive interaction between these multi few-cycle pulses.It is revealed that the interactions of the multi few-cycle pulses rely heavily on their pulse duration.Secondly,we study the different aspects of circularly polarization and linearly polar-ized FCP dynamics governed by the vector regularized short pulse equation.We derive the RSPE equation from the Maxwell’s equations,and demonstrate that this model can accurately describe the dynamic behavior of vector FCP larger than one optical cycle.Moreover,under the parameters of this model,the spectrum of vector FCP can range from the medium’s anomalous dispersion region to the normal dispersion region.By using the multi-scale method,we construct the approximate circularly polarized FCP solution of the vector RSPE equation from the soliton solution of the NLS equation.By the numerical evolution,we find that the FCP’s stability is dependent on whether the FCP’s spectrum is located in the normal-dispersion regime.And the FCP is more likely to be excited when its spectrum is in the anomalous-dispersion regime.Otherwise,FCP radiates energy and is broadened in the process of evolution.Then,we study the interaction of two-FCPs and three-FCPs and found the two interaction modes of the two-FCPs and three-FCPs:elastic collisions,inelastic collisions. |
