A series of experiments on the instability of steeP water wave trains in water with finite water depths and infinite water depths in a wide wave basin were performed. It was found that under the coupled development of...A series of experiments on the instability of steeP water wave trains in water with finite water depths and infinite water depths in a wide wave basin were performed. It was found that under the coupled development of modulational instability and class-Ⅱ instability, the initial two-dimensional steep wave trains evolved into three＇dimensional crescent waves, followed by the occurrence of disordered water surfaces, and that the wave energy transferred to sidebands in the amplitude spectrum of the water surface elevation. The results also show that water depth has a significant effect on the growth of modulational instability and the evolutiin of crescent waves. The larger the water depth, the more quickly the modulational instability suppresses class-II instability.展开更多
Perturbation analysis and scale expansion are used to derive the(2+1)-dimensional coupled nonlinear Schr¨odinger(CNLS)equations that can describe interactions of two Rossby waves propagating in stratified fluids....Perturbation analysis and scale expansion are used to derive the(2+1)-dimensional coupled nonlinear Schr¨odinger(CNLS)equations that can describe interactions of two Rossby waves propagating in stratified fluids.The(2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately.The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method,and the influence factors of modulational instability are analyzed.The results suggest that,when two Rossby waves with slightly different wave numbers propagate in the stratified fluids,the intensity of bright soliton decreases with the increases of dark soliton coefficients.In addition,the size of modulational instable area is related to the amplitude and wave number in y direction.展开更多
The modulational instability of two incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity is investigated analytically and numerically. Our results show that as a precursor t...The modulational instability of two incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity is investigated analytically and numerically. Our results show that as a precursor to spatial optical soliton formation, modulational instability can be adjusted and controlled by the wavelength combinations of the signal and background beams. We also discuss the dependences of strength of modulational instability on intensities of two signal beams and background beam. These findings make it possible to predict the formation of incoherently coupled soliton pairs in azobenzene-containing polymer.展开更多
By performing modulational instability analysis of the the nonlinear coupled dimensionless equations between a fast magnetosonic wave(FMSW)propagating obliquely with the magneticfield and a low-frequency slow Alfv...By performing modulational instability analysis of the the nonlinear coupled dimensionless equations between a fast magnetosonic wave(FMSW)propagating obliquely with the magneticfield and a low-frequency slow Alfvén wave(SAW),we obtain the dispersion relation of the perturbation wave.The growth rate of the perturbation wave is obtained.It is found that the growth rate increases as background magnetic field increases,which is in agreement with that reported by Tiwary et al(2016 Phys.Plasmas 23122307).A critical perturbation wave number is found.When the perturbation wave number is greater than or equal to the critical value,the growth rate is positive and it increases as the perturbation wave number increases,while the wave is stable.The maximum growth rate is reached when the frequency of the FMSW is half of the ion cyclotron frequency.The minimum growth rate is reached when the propagation direction of the perturbation wave is the same as that of the FMSW.展开更多
The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting of warm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schr?dinger ...The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting of warm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schr?dinger equation including one additional term that comes from the effect of relativistic electron beam is derived. It is found that the inclusion of a relativistic electron beam would modify the modulational instability of the wave packet and could not admit any stationary soliton waves.展开更多
By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold ...By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10^(23) m^(-3) and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.展开更多
The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a...The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a linear stability analysis, we analytically study the discrete modulational instability and analyze the effect of the frustration strength on the discrete modulational instability region. Using the results from the discrete modulational instability analysis, the presence conditions of those stationary bright type localized solutions are presented. On the other hand, we obtain the analytical expressions for the stationary bright localized solutions and analyze the effect of the frustration on their emergence conditions. By taking advantage of these bright type single-magnon bound wave functions obtained, quantum breather states in the present frustrated ferromagnetic zig-zag lattice are constructed. What is more, the analytical forms for quantum two-breather states are also obtained. In particular, the energy level formulas of quantum breathers and two-breathers are derived.展开更多
We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demo...We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our resuRs reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.展开更多
By means of the multiple-scale expansion method, the coupled nonlinear Schrgdinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensa...By means of the multiple-scale expansion method, the coupled nonlinear Schrgdinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.展开更多
The nonlinear propagation of quantum ion acoustic wave（QIAW） is investigated in a four-component plasma composed of warm classical positive ions and negative ions,as well as inertialess relativistically degenerate e...The nonlinear propagation of quantum ion acoustic wave（QIAW） is investigated in a four-component plasma composed of warm classical positive ions and negative ions,as well as inertialess relativistically degenerate electrons and positrons.A nonlinear Schrodinger equation is derived by using the reductive perturbation method,which governs the dynamics of QIAW packets.The modulation instability analysis of QIAWs is considered based on the typical parameters of the white dwarf.The results exhibit that both in the weakly relativistic limit and in the ultrarelativistic limit,the modulational instability regions are sensitively dependent on the ratios of temperature and number density of negative ions to those of positive ions respectively,and on the relativistically degenerate effect as well.展开更多
We study modulational instability of a resonantly polariton condensate in a discrete lattice.Employing a discrete gain-saturation model,we derive the dispersion relation for the modulational instability by means of th...We study modulational instability of a resonantly polariton condensate in a discrete lattice.Employing a discrete gain-saturation model,we derive the dispersion relation for the modulational instability by means of the linear-stability analysis.Effects of the pumping strength,the nonlinearity,the strength of the detuning,and the coupling strength on the modulation instability are investigated.It is found that the interplay between these parameters will dramatically change the modulational instability condition.We believe that the predicted results in this work can be useful for future possible experiment of exciton-polariton condensate in lattices.展开更多
Propagation of light beams in turbid media such as underwater environments,fog,clouds,or biological tissues finds increasingly important applications in science and technology,including bio-imaging,underwater communic...Propagation of light beams in turbid media such as underwater environments,fog,clouds,or biological tissues finds increasingly important applications in science and technology,including bio-imaging,underwater communication,and free-space communication technologies.While many of these applications traditionally relied on conventional,linearly polarized Gaussian beams,light possesses many degrees of freedom that are still largely unexplored,such as spin angular momentum(SAM)and orbital angular momentum(OAM).Here,we present nonlinear light-matter interactions of such complex light beams with"rotational"degrees of freedom in engineered nonlinear colloidal media.By making use of both variational and perturbative approach,we consider non-cylindrical optical vortices,elliptical optical vortices,and higher-order Bessel beams integrated in time(HOBBIT)to predict the dynamics and stability of the evolution of these beams.These results may find applications in many scenarios involving light transmission in strongly scattering environments.展开更多
We present a theoretical study of the one-dimensional modulational instability of a broad optical beam propagating in a biased photorefractive crystal with both linear and quadratic electro-optic effects(Kerr effect)u...We present a theoretical study of the one-dimensional modulational instability of a broad optical beam propagating in a biased photorefractive crystal with both linear and quadratic electro-optic effects(Kerr effect)under steadystate conditions.One-dimensional modulational instability growth rates are obtained by treating the space-charge field equation globally and locally.Both theoretical reasoning and numerical simulation show that both the global and local modulational instability gains are governed simultaneously by the strength and the polarity of external bias field and by the ratio of the intensity of the broad beam to that of the dark irradiance.Under a strong bias field,the results obtained using these two methods are in good agreement in the low spatial frequency regime.Moreover,the instability growth rate increases with the bias field,and the maximum instability growth occurs when ratio of light intensity to dark irradiance is 0.88.展开更多
We study the nonlinear stage of modulation instability(MI)in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically.Using the three-mode trunca...We study the nonlinear stage of modulation instability(MI)in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically.Using the three-mode truncation,we reveal the complex recurrence of parametric resonance(PR)breathers,where each recurrence is associated with two oscillation periods(PR period and internal oscillation period).The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.展开更多
This study investigates the dromion structure within the context of(2+1)-dimensional modulated positron-acoustic waves in a magnetoplasma consisting of inertial cold positrons and inertialess nonthermal hot electrons ...This study investigates the dromion structure within the context of(2+1)-dimensional modulated positron-acoustic waves in a magnetoplasma consisting of inertial cold positrons and inertialess nonthermal hot electrons and positrons as well as stationary positive ions.The reductive perturbation approach reduces the fluid governing equations to the plasma model to a Davey–Stewartson system.This study provides a detailed analysis of the influence of many related plasma parameters,including the density ratio of hot and cold positrons,the external magnetic field strength,the nonthermal parameter and the density ratio of electrons and cold positrons,on the growing rate of instability.Using the Hirota Bilinear method,it is found that the system supports some exact solutions,such as one-and two-dromion solutions.The change of plasma parameters significantly enhances the characteristics of dromion solutions.The elastic and inelastic collisions between two dromions are discussed at different times.The relevance of this study can help us to understand the various types of collision between energetic particles in confined plasma during the production of energy by thermonuclear fusion.展开更多
Modeling of instability and collision of nonlinear dust-acoustic（NDA） envelope solitons in strongly coupled dusty plasmas（SCDPs） is theoretically investigated. The SCDPs consists of strongly correlated negatively ...Modeling of instability and collision of nonlinear dust-acoustic（NDA） envelope solitons in strongly coupled dusty plasmas（SCDPs） is theoretically investigated. The SCDPs consists of strongly correlated negatively variable-charged dust grains and weakly correlated Boltzmann electrons and ions. Using the derivative expansion perturbation technique, a nonlinear Schr dinger-type（NLST） equation for describing the propagation of NDA envelope solitons is derived. Moreover,the extended Poincar′e–Lighthill–Kuo（EPLK） method is employed to deduce the analytical phase shifts and the trajectories after the collision of NDA envelope solitons. In detail, the results show that both modulation instability and phase shift after collision of NDA envelope solitons will modify with the increase in the effects of the viscosity, the relaxation time, and the dust charge fluctuation. Crucially, the modeling of dust-acoustic envelope solitons collision, as reported here, is helpful for understanding the propagation of NDA envelope solitons in strongly coupled dusty plasmas.展开更多
Passive Kerr fiber-loop resonators driven by coherent lasers exhibit a variety of nonlinear states,including modulation instability(MI),localized dissipative structures(solitons),and chaos.Although these transitions h...Passive Kerr fiber-loop resonators driven by coherent lasers exhibit a variety of nonlinear states,including modulation instability(MI),localized dissipative structures(solitons),and chaos.Although these transitions have been predicted theoretically,experimental real-time observations are rare in coherently driven Kerr fiber-loop resonators.In this study,we observed real-time transitions between the predicted nonlinear states by sweeping detuning both positively and negatively.We discovered the transition path between nonlinear states depending on the direction of detuning,providing new insights into the nonlinear dynamics.Our findings directly validate theoretical predictions and offer potential implications for future nonlinear optical applications.展开更多
Modulational instability is an important area of research with important practical and theoretical significance in fluid mechanics,optics,plasma physics,and military and communication engineering.In this paper,using m...Modulational instability is an important area of research with important practical and theoretical significance in fluid mechanics,optics,plasma physics,and military and communication engineering.In this paper,using multiscale analysis and a perturbation expansion method,starting from the quasi-geostrophic potential vortex equation,a new(2+1)-dimensional highorder nonlinear Schrodinger equation describing Rossby waves in stratified fluids is obtained.Based on this equation,conditions for the occurrence of modulational instability of Rossby waves are analyzed.Moreover,the effects of factors such as the dimension and order of the equation and the latitude at which Rossby waves occur on modulational instability are discussed.It is found that the(2+1)-dimensional equation provides a good description of the modulational instability of Rossby waves on a plane.The high-order terms affect the modulational instability,and it is found that instability is more likely to occur at high latitudes.展开更多
Four-wave mixing induced by modulation instability in a single-mode fiber is analyzed from the phase-matching point of view. For the two-channel transmission, a method is proposed to select the four-wave-mixing-induce...Four-wave mixing induced by modulation instability in a single-mode fiber is analyzed from the phase-matching point of view. For the two-channel transmission, a method is proposed to select the four-wave-mixing-induced sidebands, which is based on the proper use of a continuous-wave and a pulse as light sources. We find that a mass of sidebands are generated in the modulation instability resonance region, and the power of the sideband increases with not only the peak power of the pump pulse but also the continuous-wave power which acts as a seed. The research will provide guidance for fiber communication and sensing systems using wavelength division multiplexing technology.展开更多
This paper investigates the effects of walk-off among optical pulses on cross-phase modulation induced modulation instability in the normal dispersion region of an optical fibre with high-order dispersion. The results...This paper investigates the effects of walk-off among optical pulses on cross-phase modulation induced modulation instability in the normal dispersion region of an optical fibre with high-order dispersion. The results indicate that, in the case of high-order dispersion, the walk-off effect takes on new characteristics and will influence considerably the shape, position and especially the number of the spectral regions of the gain spectra of modulation instability. Not only the group-velocity mismatch, but also the difference of the third-order dispersion of two optical waves will alter the gain spectra of modulation instability but in different ways. Depending on the values of the walk-off parameters, the number of the spectral regions may increase from two to at most four, and the spectral shape and position may change too.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.51079024)the National Foundation for Creative Research Groups(Grant No.50921001)
文摘A series of experiments on the instability of steeP water wave trains in water with finite water depths and infinite water depths in a wide wave basin were performed. It was found that under the coupled development of modulational instability and class-Ⅱ instability, the initial two-dimensional steep wave trains evolved into three＇dimensional crescent waves, followed by the occurrence of disordered water surfaces, and that the wave energy transferred to sidebands in the amplitude spectrum of the water surface elevation. The results also show that water depth has a significant effect on the growth of modulational instability and the evolutiin of crescent waves. The larger the water depth, the more quickly the modulational instability suppresses class-II instability.
基金the National Natural Science Foundation of China(Grant No.11805114)the Shandong University of Science and Technology Research Fund(Grant No.2018TDJH101)。
文摘Perturbation analysis and scale expansion are used to derive the(2+1)-dimensional coupled nonlinear Schr¨odinger(CNLS)equations that can describe interactions of two Rossby waves propagating in stratified fluids.The(2+1)-dimensional equations can reflect and describe the wave propagation more intuitively and accurately.The properties of the two waves in the process of propagation can be analyzed by the solution obtained from the equations using the Hirota bilinear method,and the influence factors of modulational instability are analyzed.The results suggest that,when two Rossby waves with slightly different wave numbers propagate in the stratified fluids,the intensity of bright soliton decreases with the increases of dark soliton coefficients.In addition,the size of modulational instable area is related to the amplitude and wave number in y direction.
基金Project supported by the National Natural Science Foundation of China (Grant No 10574167)
文摘The modulational instability of two incoherently coupled beams in azobenzene-containing polymer with photoisomerization nonlinearity is investigated analytically and numerically. Our results show that as a precursor to spatial optical soliton formation, modulational instability can be adjusted and controlled by the wavelength combinations of the signal and background beams. We also discuss the dependences of strength of modulational instability on intensities of two signal beams and background beam. These findings make it possible to predict the formation of incoherently coupled soliton pairs in azobenzene-containing polymer.
基金supported by National Natural Science Foundation of China(No.11965019)
文摘By performing modulational instability analysis of the the nonlinear coupled dimensionless equations between a fast magnetosonic wave(FMSW)propagating obliquely with the magneticfield and a low-frequency slow Alfvén wave(SAW),we obtain the dispersion relation of the perturbation wave.The growth rate of the perturbation wave is obtained.It is found that the growth rate increases as background magnetic field increases,which is in agreement with that reported by Tiwary et al(2016 Phys.Plasmas 23122307).A critical perturbation wave number is found.When the perturbation wave number is greater than or equal to the critical value,the growth rate is positive and it increases as the perturbation wave number increases,while the wave is stable.The maximum growth rate is reached when the frequency of the FMSW is half of the ion cyclotron frequency.The minimum growth rate is reached when the propagation direction of the perturbation wave is the same as that of the FMSW.
文摘The modulational instability of ion-acoustic wave in a collisionless, unmagnetized plasma consisting of warm ions, hot isothermal electrons, and relativistic electron beam is studied. A modified nonlinear Schr?dinger equation including one additional term that comes from the effect of relativistic electron beam is derived. It is found that the inclusion of a relativistic electron beam would modify the modulational instability of the wave packet and could not admit any stationary soliton waves.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11765017,11865014,11847304,and 11764039)the Scientific Research Project of Gansu Higher Education,China(Grant No.2019B-034)the Science and Technology Project of Guizhou Province,China(Grant No.QiankeheLH-20177008)。
文摘By one-dimensional particle-in-cell(PIC) simulations, the propagation and stability of relativistic electromagnetic(EM) solitary waves as well as modulational instability of plane EM waves are studied in uniform cold electron-ion plasmas.The investigation not only confirms the solitary wave motion characteristics and modulational instability theory, but more importantly, gives the following findings. For a simulation with the plasma density 10^(23) m^(-3) and the dimensionless vector potential amplitude 0.18, it is found that the EM solitary wave can stably propagate when the carrier wave frequency is smaller than 3.83 times of the plasma frequency. While for the carrier wave frequency larger than that, it can excite a very weak Langmuir oscillation, which is an order of magnitude smaller than the transverse electron momentum and may in turn modulate the EM solitary wave and cause the modulational instability, so that the solitary wave begins to deform after a long enough distance propagation. The stable propagation distance before an obvious observation of instability increases(decreases) with the increase of the carrier wave frequency(vector potential amplitude). The study on the plane EM wave shows that a modulational instability may occur and its wavenumber is approximately equal to the modulational wavenumber by Langmuir oscillation and is independent of the carrier wave frequency and the vector potential amplitude.This reveals the role of the Langmuir oscillation excitation in the inducement of modulational instability and also proves the modulational instability of EM solitary wave.
基金Project supported by the National Natural Science Foundation of China(Grant No.11604121)the Scientific Research Fund of Hunan Provincial Education Department,China(Grant Nos.16B210 and 16A170)the Natural Science Fund Project of Jishou University,China(Grant No.jdx17036)
文摘The modulational instability, quantum breathers and two-breathers in a frustrated easy-axis ferromagnetic zig-zag chain under an external magnetic field are investigated within the Hartree approximation. By means of a linear stability analysis, we analytically study the discrete modulational instability and analyze the effect of the frustration strength on the discrete modulational instability region. Using the results from the discrete modulational instability analysis, the presence conditions of those stationary bright type localized solutions are presented. On the other hand, we obtain the analytical expressions for the stationary bright localized solutions and analyze the effect of the frustration on their emergence conditions. By taking advantage of these bright type single-magnon bound wave functions obtained, quantum breather states in the present frustrated ferromagnetic zig-zag lattice are constructed. What is more, the analytical forms for quantum two-breather states are also obtained. In particular, the energy level formulas of quantum breathers and two-breathers are derived.
基金Supported by the National Natural Science Foundation of China under Grant No.11274095the Program of USTITSPHP under Grant No.13IRTSTHN016
文摘We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our resuRs reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.
基金Project supported by the National Natural Science Foundation of China (Grant No 10875098)the Science Foundation of the Northwest Normal University (Grant Nos NWNU-KJCXGC-03-17 and NWNU-KJCXGC-03-48)
文摘By means of the multiple-scale expansion method, the coupled nonlinear Schrgdinger equations without an explicit external potential are obtained in two-dimensional geometry for a self-attractive Bose-Einstein condensate composed of different hyperfine states. The modulational instability of two-component condensate is investigated by using a simple technique. Based on the discussion about two typical cases, the explicit expression of the growth rate for a purely growing modulational instability and the optimum stable conditions are given and analysed analytically. The results show that the modulational instability of this two-dimensional system is quite different from that in a one-dimensional system.
基金supported by the National Natural Science Foundation of China(Grant No.11104012)the Fundamental Research Funds for the Central Universities(Grant Nos.FRF-TP-09-019A and FRF-BR-11-031B)
文摘The nonlinear propagation of quantum ion acoustic wave（QIAW） is investigated in a four-component plasma composed of warm classical positive ions and negative ions,as well as inertialess relativistically degenerate electrons and positrons.A nonlinear Schrodinger equation is derived by using the reductive perturbation method,which governs the dynamics of QIAW packets.The modulation instability analysis of QIAWs is considered based on the typical parameters of the white dwarf.The results exhibit that both in the weakly relativistic limit and in the ultrarelativistic limit,the modulational instability regions are sensitively dependent on the ratios of temperature and number density of negative ions to those of positive ions respectively,and on the relativistically degenerate effect as well.
基金the National Natural Science Foundation of China(Grant No.11805116)the Natural Science Basic Research Plan in Shaanxi Province,China(Grant No.2023-JC-YB-037).
文摘We study modulational instability of a resonantly polariton condensate in a discrete lattice.Employing a discrete gain-saturation model,we derive the dispersion relation for the modulational instability by means of the linear-stability analysis.Effects of the pumping strength,the nonlinearity,the strength of the detuning,and the coupling strength on the modulation instability are investigated.It is found that the interplay between these parameters will dramatically change the modulational instability condition.We believe that the predicted results in this work can be useful for future possible experiment of exciton-polariton condensate in lattices.
基金support from the Office of Naval Research MURI(N00014-20-1-2550)。
文摘Propagation of light beams in turbid media such as underwater environments,fog,clouds,or biological tissues finds increasingly important applications in science and technology,including bio-imaging,underwater communication,and free-space communication technologies.While many of these applications traditionally relied on conventional,linearly polarized Gaussian beams,light possesses many degrees of freedom that are still largely unexplored,such as spin angular momentum(SAM)and orbital angular momentum(OAM).Here,we present nonlinear light-matter interactions of such complex light beams with"rotational"degrees of freedom in engineered nonlinear colloidal media.By making use of both variational and perturbative approach,we consider non-cylindrical optical vortices,elliptical optical vortices,and higher-order Bessel beams integrated in time(HOBBIT)to predict the dynamics and stability of the evolution of these beams.These results may find applications in many scenarios involving light transmission in strongly scattering environments.
文摘We present a theoretical study of the one-dimensional modulational instability of a broad optical beam propagating in a biased photorefractive crystal with both linear and quadratic electro-optic effects(Kerr effect)under steadystate conditions.One-dimensional modulational instability growth rates are obtained by treating the space-charge field equation globally and locally.Both theoretical reasoning and numerical simulation show that both the global and local modulational instability gains are governed simultaneously by the strength and the polarity of external bias field and by the ratio of the intensity of the broad beam to that of the dark irradiance.Under a strong bias field,the results obtained using these two methods are in good agreement in the low spatial frequency regime.Moreover,the instability growth rate increases with the bias field,and the maximum instability growth occurs when ratio of light intensity to dark irradiance is 0.88.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12175178 and 12247103)the Natural Science Basic Research Program of Shaanxi Province,China(Grant No.2022KJXX-71)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSY016).
文摘We study the nonlinear stage of modulation instability(MI)in the non-intergrable pure-quartic nonlinear Schrödinger equation where the fourth-order dispersion is modulated periodically.Using the three-mode truncation,we reveal the complex recurrence of parametric resonance(PR)breathers,where each recurrence is associated with two oscillation periods(PR period and internal oscillation period).The nonlinear stage of parametric instability admits the maximum energy exchange between the spectrum sidebands and central mode occurring outside the MI gain band.
基金The authors extend their appreciation to the Deanship of Scientific Research and Libraries in Princess Nourah bint Abdulrahman University for funding this research work through the Research Group project under Grant No.(RG-1445-0005).
文摘This study investigates the dromion structure within the context of(2+1)-dimensional modulated positron-acoustic waves in a magnetoplasma consisting of inertial cold positrons and inertialess nonthermal hot electrons and positrons as well as stationary positive ions.The reductive perturbation approach reduces the fluid governing equations to the plasma model to a Davey–Stewartson system.This study provides a detailed analysis of the influence of many related plasma parameters,including the density ratio of hot and cold positrons,the external magnetic field strength,the nonthermal parameter and the density ratio of electrons and cold positrons,on the growing rate of instability.Using the Hirota Bilinear method,it is found that the system supports some exact solutions,such as one-and two-dromion solutions.The change of plasma parameters significantly enhances the characteristics of dromion solutions.The elastic and inelastic collisions between two dromions are discussed at different times.The relevance of this study can help us to understand the various types of collision between energetic particles in confined plasma during the production of energy by thermonuclear fusion.
文摘Modeling of instability and collision of nonlinear dust-acoustic（NDA） envelope solitons in strongly coupled dusty plasmas（SCDPs） is theoretically investigated. The SCDPs consists of strongly correlated negatively variable-charged dust grains and weakly correlated Boltzmann electrons and ions. Using the derivative expansion perturbation technique, a nonlinear Schr dinger-type（NLST） equation for describing the propagation of NDA envelope solitons is derived. Moreover,the extended Poincar′e–Lighthill–Kuo（EPLK） method is employed to deduce the analytical phase shifts and the trajectories after the collision of NDA envelope solitons. In detail, the results show that both modulation instability and phase shift after collision of NDA envelope solitons will modify with the increase in the effects of the viscosity, the relaxation time, and the dust charge fluctuation. Crucially, the modeling of dust-acoustic envelope solitons collision, as reported here, is helpful for understanding the propagation of NDA envelope solitons in strongly coupled dusty plasmas.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12475006 and 12004309)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSQ036)。
文摘Passive Kerr fiber-loop resonators driven by coherent lasers exhibit a variety of nonlinear states,including modulation instability(MI),localized dissipative structures(solitons),and chaos.Although these transitions have been predicted theoretically,experimental real-time observations are rare in coherently driven Kerr fiber-loop resonators.In this study,we observed real-time transitions between the predicted nonlinear states by sweeping detuning both positively and negatively.We discovered the transition path between nonlinear states depending on the direction of detuning,providing new insights into the nonlinear dynamics.Our findings directly validate theoretical predictions and offer potential implications for future nonlinear optical applications.
基金supported by the National Natural Science Foundation of China(No.11975143)。
文摘Modulational instability is an important area of research with important practical and theoretical significance in fluid mechanics,optics,plasma physics,and military and communication engineering.In this paper,using multiscale analysis and a perturbation expansion method,starting from the quasi-geostrophic potential vortex equation,a new(2+1)-dimensional highorder nonlinear Schrodinger equation describing Rossby waves in stratified fluids is obtained.Based on this equation,conditions for the occurrence of modulational instability of Rossby waves are analyzed.Moreover,the effects of factors such as the dimension and order of the equation and the latitude at which Rossby waves occur on modulational instability are discussed.It is found that the(2+1)-dimensional equation provides a good description of the modulational instability of Rossby waves on a plane.The high-order terms affect the modulational instability,and it is found that instability is more likely to occur at high latitudes.
基金Project supported by the National Natural Science Foundation of China (Grant No. 61177073)the Specialized Research Fundfor the Doctoral Program of Higher Education of China (Grant No.20104307110020)+1 种基金the Fund of Innovation of Graduate School of National University of Defense Technology, China (Grant No.B110703)the Hunan Provincial Innovation Foundation for Postgraduate, China (Grant No. CX2011B033)
文摘Four-wave mixing induced by modulation instability in a single-mode fiber is analyzed from the phase-matching point of view. For the two-channel transmission, a method is proposed to select the four-wave-mixing-induced sidebands, which is based on the proper use of a continuous-wave and a pulse as light sources. We find that a mass of sidebands are generated in the modulation instability resonance region, and the power of the sideband increases with not only the peak power of the pump pulse but also the continuous-wave power which acts as a seed. The research will provide guidance for fiber communication and sensing systems using wavelength division multiplexing technology.
基金Project supported by the Fundamental Application Research Project of the Department of Science ＆ Technology of Sichuan Province （Grant Nos 05JY029-084 and 04JY029-103）, the Key Program of Natural Science Foundation of Educational Commission of Sichuan Province （Grant No 2006A124）, and the Foundation of Science ＆ Technology Development of Chengdu University of Information Technology （Grant No KYTZ20060604）.
文摘This paper investigates the effects of walk-off among optical pulses on cross-phase modulation induced modulation instability in the normal dispersion region of an optical fibre with high-order dispersion. The results indicate that, in the case of high-order dispersion, the walk-off effect takes on new characteristics and will influence considerably the shape, position and especially the number of the spectral regions of the gain spectra of modulation instability. Not only the group-velocity mismatch, but also the difference of the third-order dispersion of two optical waves will alter the gain spectra of modulation instability but in different ways. Depending on the values of the walk-off parameters, the number of the spectral regions may increase from two to at most four, and the spectral shape and position may change too.
