In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evo...In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized （3＋1）-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material （I^HM） and left-handed material （LHM） is derived. By the commonly used Drude dispersive model for LHM, a （3＋1）-dimensional nonlinear Schrodinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.展开更多
The nonlinear propagation of an intense Laguerre-Gaussian(LG)laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method.The evolution equation of the spot size is derived includ...The nonlinear propagation of an intense Laguerre-Gaussian(LG)laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method.The evolution equation of the spot size is derived including the effects of relativistic self-focusing,preformed channel focusing,and ponderomotive self-channeling.The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size,periodically focusing and defocusing oscillation,catastrophic focusing,and solitary waves are obtained.Compared with the laser pulse with fundamental Gaussian(FG)mode,it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse,while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse.Thus,the matched condition for the intense LG laser pulse with constant spot size is released obviously,while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.展开更多
The nonlinear propagation of positron acoustic periodic （PAP） travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positi...The nonlinear propagation of positron acoustic periodic （PAP） travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positive ions is examined. The reductive perturbation technique is employed to derive a nonlinear Zakharov Kuznetsov equation that governs the essential features of nonlinear PAP travelling waves. Moreover, the bifurcation theory is used to investigate the propagation of nonlinear PAP periodic travelling wave solutions. It is found that kappa distributed hot positrons and electrons provide only the possibility of existence of nonlinear compressive PAP travelling waves. It is observed that the superthermality of hot positrons, the concentrations of superthermal electrons and positrons, the positron cyclotron frequency, the direction cosines of wave vector k along the z-axis, and the concentration of ions play pivotal roles in the nonlinear propagation of PAP travelling waves. Tile present investigation may be used to understand the formation of PAP structures in the space and laboratory plasmas with superthermal hot positrons and electrons.展开更多
We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, th...We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.展开更多
From Maxwell＇s equations and Post＇s formalism, a generalized chiral nonlinear Schr6dinger equation （CNLSE） is obtained for the nonlinear chiral fiber. This equation governs light transmission through a dispersive ...From Maxwell＇s equations and Post＇s formalism, a generalized chiral nonlinear Schr6dinger equation （CNLSE） is obtained for the nonlinear chiral fiber. This equation governs light transmission through a dispersive nonlinear chiral fiber with joint action of chirality in linear and nonlinear ways. The generalized CNLSE shows a modu- lation of chirality to the effect of attenuation and nonlinearity compared with the case for a conventional fiber. Simulations based on the split-step beam propagation method reveal the role of nonlinearity with cooperation to chirality playing in the pulse evolution. By adjusting its strength the role of chirality in forming solitons is demonstrated for a given circularly polarized component. The application of nonlinear optical rotation is also discussed in an all-optical switch.展开更多
The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer. It is found that the initially positive chirp-type bandwidth can ...The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer. It is found that the initially positive chirp-type bandwidth can suppress the nonlinear image, while the negative one can enhance it, and that both effects are inversely proportional to the incident pulse duration. Numerical simulations further demonstrate that the location of nonlinear image is at the conjugate plane of the scatterer and that, for negatively pre-chirped pulsed beam, the nonlinear image peak intensity can be higher than that in the corresponding monochromatic case under certain conditions. Moreover the effect of group velocity dispersion on nonlinear image is found to be similar to that of chirp-type bandwidth.展开更多
We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(R...We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(RK4IP-CQE), and the other is the local error adaptive step-control method(RK4IP-LEM). The methods are developed in the vector form of fourthorder Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.展开更多
Self-compression of femtosecond pulses in noble gases with an input power close to the self-focusing threshold has been investigated experimentally and theoretically. It is demonstrated that either multiphoton ionizat...Self-compression of femtosecond pulses in noble gases with an input power close to the self-focusing threshold has been investigated experimentally and theoretically. It is demonstrated that either multiphoton ionization （MPI） or space-time focusing and self-steepening effects can induce pulse shortening, but they predominate at different beam intensities during the propagation. The latter effects play a key role in the final pulse self-compression. By choosing an appropriate focusing parameter, action distance of the space-time focusing and self-steepening effects can be lengthened, which can promote a shock pulse structure with a duration as short as two optical cycles. It is also found that, for our calculation cases in which an input pulse power is close to the self-focusing threshold, either group velocity dispersion （GVD） or multiphoton absorption （MPA） has a negligible influence on pulse characteristics in the propagation process.展开更多
基金Supported by the National Natural Science Foundation of China （Grant Nos 10576012 and 60538010）, the Program for New Century Excellent Talents in University and the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No 20040532005）.
文摘In this paper a comprehensive framework for treating the nonlinear propagation of ultrashort pulse in metamaterial with dispersive dielectric susceptibility and magnetic permeability is presented. Under the slowly-evolving-wave approximation, a generalized （3＋1）-dimensional wave equation first order in the propagation coordinate and suitable for both right-handed material （I^HM） and left-handed material （LHM） is derived. By the commonly used Drude dispersive model for LHM, a （3＋1）-dimensional nonlinear Schrodinger equation describing ultrashort pulsed beam propagation in LHM is obtained, and its difference from that for conventional RHM is discussed. Particularly, the self-steeping effect of ultrashort pulse is found to be anomalous in LHM.
基金the National Natural Science Foundation of China(Grant Nos.61665006 and 61865011)the Natural Science Foundation of Jiangxi Province of China(Grant Nos.20171ACB21018,20161BAB212041,and 20162BCB23012).
文摘The nonlinear propagation of an intense Laguerre-Gaussian(LG)laser pulse in a parabolic preformed plasma channel is analyzed by means of the variational method.The evolution equation of the spot size is derived including the effects of relativistic self-focusing,preformed channel focusing,and ponderomotive self-channeling.The parametric conditions of the LG laser pulse and plasma channel for propagating with constant spot size,periodically focusing and defocusing oscillation,catastrophic focusing,and solitary waves are obtained.Compared with the laser pulse with fundamental Gaussian(FG)mode,it is found that the effect of vacuum diffraction is reduced by half and the effects of relativistic and wakefield focusing are decreased by a quarter due to the hollow transverse intensity profile of the LG laser pulse,while the effect of channel focusing is the same order of magnitude with that of the FG laser pulse.Thus,the matched condition for the intense LG laser pulse with constant spot size is released obviously,while the parameters of the laser and plasma for the existence of solitary waves nearly coincide with those of the FG laser pulse.
文摘The nonlinear propagation of positron acoustic periodic （PAP） travelling waves in a magnetoplasma composed of dynamic cold positrons, superthermal kappa distributed hot positrons and electrons, and stationary positive ions is examined. The reductive perturbation technique is employed to derive a nonlinear Zakharov Kuznetsov equation that governs the essential features of nonlinear PAP travelling waves. Moreover, the bifurcation theory is used to investigate the propagation of nonlinear PAP periodic travelling wave solutions. It is found that kappa distributed hot positrons and electrons provide only the possibility of existence of nonlinear compressive PAP travelling waves. It is observed that the superthermality of hot positrons, the concentrations of superthermal electrons and positrons, the positron cyclotron frequency, the direction cosines of wave vector k along the z-axis, and the concentration of ions play pivotal roles in the nonlinear propagation of PAP travelling waves. Tile present investigation may be used to understand the formation of PAP structures in the space and laboratory plasmas with superthermal hot positrons and electrons.
基金supported by the National Natural Science Foundation of China (Grant Nos 10674045 and 60538010)the National Natural Science Foundation of Hunan Province,China (Grant No 08jj3001)
文摘We propose and implement a quasi-discrete Hankel transform algorithm based on Dini series expansion （DQDHT） in this paper. By making use of the property that the zero-order Bessel function derivative J0^1（0）=0, the DQDHT can be used to calculate the values on the symmetry axis directly. In addition, except for the truncated treatment of the input function, no other approximation is made, thus the DQDHT satisfies the discrete Parsevat theorem for energy conservation, implying that it has a high numerical accuracy. Further, we have performed several numerical tests. The test results show that the DQDHT has a very high numerical accuracy and keeps energy conservation even after thousands of times of repeating the transform either in a spatial domain or in a frequency domain. Finally, as an example, we have applied the DQDHT to the nonlinear propagation of a Gaussian beam through a Kerr medium system with cylindrical symmetry. The calculated results are found to be in excellent agreement with those based on the conventional 2D-FFT algorithm, while the simulation based on the proposed DQDHT takes much less computing time.
基金Supported by the National Natural Science Foundation of China under Grant No 60977032the Program for Innovation Research of Science of Harbin Institute of Technology(PIRS-HIT)under Grant No T201407
文摘From Maxwell＇s equations and Post＇s formalism, a generalized chiral nonlinear Schr6dinger equation （CNLSE） is obtained for the nonlinear chiral fiber. This equation governs light transmission through a dispersive nonlinear chiral fiber with joint action of chirality in linear and nonlinear ways. The generalized CNLSE shows a modu- lation of chirality to the effect of attenuation and nonlinearity compared with the case for a conventional fiber. Simulations based on the split-step beam propagation method reveal the role of nonlinearity with cooperation to chirality playing in the pulse evolution. By adjusting its strength the role of chirality in forming solitons is demonstrated for a given circularly polarized component. The application of nonlinear optical rotation is also discussed in an all-optical switch.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 60890202 and 10974049)
文摘The bandwidth and the duration of incident pulsed beam are proved to play important roles in modifying the nonlinear image of amplitude-type scatterer. It is found that the initially positive chirp-type bandwidth can suppress the nonlinear image, while the negative one can enhance it, and that both effects are inversely proportional to the incident pulse duration. Numerical simulations further demonstrate that the location of nonlinear image is at the conjugate plane of the scatterer and that, for negatively pre-chirped pulsed beam, the nonlinear image peak intensity can be higher than that in the corresponding monochromatic case under certain conditions. Moreover the effect of group velocity dispersion on nonlinear image is found to be similar to that of chirp-type bandwidth.
基金supported by the National Key Research and Development Program of China (Grant Nos. 2021YFC2201803 and 2020YFC2200104)。
文摘We extend two adaptive step-size methods for solving two-dimensional or multi-dimensional generalized nonlinear Schr ¨odinger equation(GNLSE): one is the conservation quantity error adaptive step-control method(RK4IP-CQE), and the other is the local error adaptive step-control method(RK4IP-LEM). The methods are developed in the vector form of fourthorder Runge–Kutta iterative scheme in the interaction picture by converting a vector equation in frequency domain. By simulating the supercontinuum generated from the high birefringence photonic crystal fiber, the calculation accuracies and the efficiencies of the two adaptive step-size methods are discussed. The simulation results show that the two methods have the same global average error, while RK4IP-LEM spends more time than RK4IP-CQE. The decrease of huge calculation time is due to the differences in the convergences of the relative photon number error and the approximated local error between these two adaptive step-size algorithms.
基金supported by the National Basic Research Program of China (Grant No 2006CB806000)the National Natural Science Foundation of China (Grant Nos 60578049 and 10523003)the Science and Technology Commission of Shanghai Municipality of China (Grant No 07JC14055)
文摘Self-compression of femtosecond pulses in noble gases with an input power close to the self-focusing threshold has been investigated experimentally and theoretically. It is demonstrated that either multiphoton ionization （MPI） or space-time focusing and self-steepening effects can induce pulse shortening, but they predominate at different beam intensities during the propagation. The latter effects play a key role in the final pulse self-compression. By choosing an appropriate focusing parameter, action distance of the space-time focusing and self-steepening effects can be lengthened, which can promote a shock pulse structure with a duration as short as two optical cycles. It is also found that, for our calculation cases in which an input pulse power is close to the self-focusing threshold, either group velocity dispersion （GVD） or multiphoton absorption （MPA） has a negligible influence on pulse characteristics in the propagation process.
