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
The purpose of this work is to study the nonlinear propagation of coupled pulses within birefringent optical fibers.To achieve this,an effective analytical technique using iB-function was applied.With this approach,we...The purpose of this work is to study the nonlinear propagation of coupled pulses within birefringent optical fibers.To achieve this,an effective analytical technique using iB-function was applied.With this approach,we decoupled the nonlinear partial differential equations governing the wave propagation and solved them to obtain prototype solutions likely to propagate in the medium.A Mathlab program was then developed to validate the behavior of the propagated waves and analyze the resulting curves.The results revealed distinct complex phenomena such as stable propagation of coupled dark-bright vector soliton,energy exchange between the components during propagation to severe pulse broadening and conditions leading to group velocity walk-off.These findings provided a deeper insight into light propagation,improving its application for advanced optical communication systems and fiber-based devices.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
Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied. A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solv...Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied. A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation. Because of the nonlinear wave distortion and reflected sound waves at the mouth, broadband time-domain impedance boundary conditions are employed. The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions, which can be calculated by fast and efficient recursive convolution. The numerical results agree very well with experi- mental data in the situations of weak nonlinear wave propagation in an exponential horn, it is shown that the model can describe the broadband characteristics caused by nonlinear distortion. Moreover, finite-amplitude acoustic propagation in types of horns is simulated, including hyperbolic, conical, exponential and sinusoidal horns. It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles, the driving velocity and frequency of the piston. The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.展开更多
Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step t...Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom （SDOF） system, can be applied to a nonlinear multiple degree of freedom （MDOF） system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.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
It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to ...It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.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
The harmonics of plane longitudinal and transverse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonline...The harmonics of plane longitudinal and transverse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic.This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a primary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.展开更多
Although the step degree of nonlinearity has been introduced to conduct basic analysis and error propagation analysis for the pseudodynamic testing of nonlinear systems, it cannot be reliably used to select an appropr...Although the step degree of nonlinearity has been introduced to conduct basic analysis and error propagation analysis for the pseudodynamic testing of nonlinear systems, it cannot be reliably used to select an appropriate time step before performing a pseudodynamic test. Therefore, a novel parameter of instantaneous degree of nonlinearity is introduced to monitor the stiffness change at the end of a time step, and can thus be used to evaluate numerical and error propagation properties for nonlinear systems. Based on these properties, it is possible to select an appropriate time step to conduct a pseudodynamic test in advance. This possibility is very important in pseudodynamic testing, since the use of an arbitrary time step might lead to unreliable results or even destroy the test specimen. In this paper, guidelines are proposed for choosing an appropriate time step for accurate integration of nonlinear systems. These guidelines require estimation of the maximum instantaneous degree of nonlinearity and the solution of the initial natural frequency. The Newmark explicit method is chosen for this study. All the analytical results and the guidelines proposed are thoroughly confirmed with numerical examples.展开更多
Stable propagating waves and wake fields in relativistic electromagnetic plasma are investigated. The incident electromagnetic field has a finite initial constant amplitude meanwhile the longitudinal momentum of elect...Stable propagating waves and wake fields in relativistic electromagnetic plasma are investigated. The incident electromagnetic field has a finite initial constant amplitude meanwhile the longitudinal momentum of electrons is taken into account in the problem. It is found that in the moving frame with transverse wave group velocity the stable propagating transverse electromagnetic waves and longitudinal plasma wake fields can exist in the appropriate regime of plasma.展开更多
A numerical method dealing with anti-sound effect is presented to calculate nonlinear sound propagation in varying cross section area and hard-wall ducts with transonic flow and without acoustic shock waves . The effe...A numerical method dealing with anti-sound effect is presented to calculate nonlinear sound propagation in varying cross section area and hard-wall ducts with transonic flow and without acoustic shock waves . The effects of duct geometry , the flow Mach number at the throat, the sound source intensity at the inlet and the anti- sound intensity on the nonlinear sound propagation are discussed through several examples. It is also shown from the examples that there is an optimal anti-sound intensity at which a remarkable sound attenuation can be obtained at the exit.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.
文摘The purpose of this work is to study the nonlinear propagation of coupled pulses within birefringent optical fibers.To achieve this,an effective analytical technique using iB-function was applied.With this approach,we decoupled the nonlinear partial differential equations governing the wave propagation and solved them to obtain prototype solutions likely to propagate in the medium.A Mathlab program was then developed to validate the behavior of the propagated waves and analyze the resulting curves.The results revealed distinct complex phenomena such as stable propagation of coupled dark-bright vector soliton,energy exchange between the components during propagation to severe pulse broadening and conditions leading to group velocity walk-off.These findings provided a deeper insight into light propagation,improving its application for advanced optical communication systems and fiber-based devices.
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(51076005)
文摘Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied. A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation. Because of the nonlinear wave distortion and reflected sound waves at the mouth, broadband time-domain impedance boundary conditions are employed. The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions, which can be calculated by fast and efficient recursive convolution. The numerical results agree very well with experi- mental data in the situations of weak nonlinear wave propagation in an exponential horn, it is shown that the model can describe the broadband characteristics caused by nonlinear distortion. Moreover, finite-amplitude acoustic propagation in types of horns is simulated, including hyperbolic, conical, exponential and sinusoidal horns. It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles, the driving velocity and frequency of the piston. The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.
基金NSC, Chinese Taipei Under Grant No. NSC-97-2221-E-027-036-MY2
文摘Two important extensions of a technique to perform a nonlinear error propagation analysis for an explicit pseudodynamic algorithm （Chang, 2003） are presented. One extends the stability study from a given time step to a complete step-by-step integration procedure. It is analytically proven that ensuring stability conditions in each time step leads to a stable computation of the entire step-by-step integration procedure. The other extension shows that the nonlinear error propagation results, which are derived for a nonlinear single degree of freedom （SDOF） system, can be applied to a nonlinear multiple degree of freedom （MDOF） system. This application is dependent upon the determination of the natural frequencies of the system in each time step, since all the numerical properties and error propagation properties in the time step are closely related to these frequencies. The results are derived from the step degree of nonlinearity. An instantaneous degree of nonlinearity is introduced to replace the step degree of nonlinearity and is shown to be easier to use in practice. The extensions can be also applied to the results derived from a SDOF system based on the instantaneous degree of nonlinearity, and hence a time step might be appropriately chosen to perform a pseudodynamic test prior to testing.
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National Science Council. Chinese Taipei, Under Grant No. NSC-92-2211-E-027-015
文摘It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.
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.
基金supported by the National Natural Science Foundation of China (Grants 11621062 and 11532001)the China Scholarship Council (CSC)
文摘The harmonics of plane longitudinal and transverse waves in nonlinear elastic solids with up to cubic nonlinearity in a one-dimensional setting are investigated in this paper. It is shown that due to quadratic nonlinearity, a transverse wave generates a second longitudinal harmonic.This propagates with the velocity of transverse waves, as well as resonant transverse first and third harmonics due to the cubic and quadratic nonlinearities. A longitudinal wave generates a resonant longitudinal second harmonic, as well as first and third harmonics with amplitudes that increase linearly and quadratically with distance propagated. In a second investigation, incidence from the linear side of a primary wave on an interface between a linear and a nonlinear elastic solid is considered. The incident wave crosses the interface and generates a harmonic with interface conditions that are equilibrated by compensatory waves propagating in two directions away from the interface. The back-propagated compensatory wave provides information on the nonlinear elastic constants of the material behind the interface. It is shown that the amplitudes of the compensatory waves can be increased by mixing two incident longitudinal waves of appropriate frequencies.
基金supported by the NSC,Chinese Taipei,Under Grant No.NSC-95-2221-E-027-099
文摘Although the step degree of nonlinearity has been introduced to conduct basic analysis and error propagation analysis for the pseudodynamic testing of nonlinear systems, it cannot be reliably used to select an appropriate time step before performing a pseudodynamic test. Therefore, a novel parameter of instantaneous degree of nonlinearity is introduced to monitor the stiffness change at the end of a time step, and can thus be used to evaluate numerical and error propagation properties for nonlinear systems. Based on these properties, it is possible to select an appropriate time step to conduct a pseudodynamic test in advance. This possibility is very important in pseudodynamic testing, since the use of an arbitrary time step might lead to unreliable results or even destroy the test specimen. In this paper, guidelines are proposed for choosing an appropriate time step for accurate integration of nonlinear systems. These guidelines require estimation of the maximum instantaneous degree of nonlinearity and the solution of the initial natural frequency. The Newmark explicit method is chosen for this study. All the analytical results and the guidelines proposed are thoroughly confirmed with numerical examples.
基金supported by National Natural Science Foundation of China under Grant No.10475009partly by the New Century Excellent Talents in University of China
文摘Stable propagating waves and wake fields in relativistic electromagnetic plasma are investigated. The incident electromagnetic field has a finite initial constant amplitude meanwhile the longitudinal momentum of electrons is taken into account in the problem. It is found that in the moving frame with transverse wave group velocity the stable propagating transverse electromagnetic waves and longitudinal plasma wake fields can exist in the appropriate regime of plasma.
基金Supported by National Natural Science Foundation of ChinaNational Education Commission Foundation of China
文摘A numerical method dealing with anti-sound effect is presented to calculate nonlinear sound propagation in varying cross section area and hard-wall ducts with transonic flow and without acoustic shock waves . The effects of duct geometry , the flow Mach number at the throat, the sound source intensity at the inlet and the anti- sound intensity on the nonlinear sound propagation are discussed through several examples. It is also shown from the examples that there is an optimal anti-sound intensity at which a remarkable sound attenuation can be obtained at the exit.
