We show that the nonlinear stage of the dual-wavelength pumped modulation instability(MI)in nonlinear Schrödinger equation(NLSE)can be effectively analyzed by mode truncation methods.The resulting complicated het...We show that the nonlinear stage of the dual-wavelength pumped modulation instability(MI)in nonlinear Schrödinger equation(NLSE)can be effectively analyzed by mode truncation methods.The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves.Significantly,the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories run along the Hamiltonian contours of the heteroclinic structure.It is demonstrated that there has much richer dynamic behavior,in contrast to the nonlinear waves reported before.This novel nonlinear wave promises to inject new vitality into the study of MI.展开更多
We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on t...We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on the frequency-wavenumber plane.Conventional single-frequency modulation instability leads to simultaneous excitation of three ABs with two of them being non-degenerate.展开更多
The utilization of the dispersive Fourier transformation approach has enabled comprehensive observation of the birth process of dissipative solitons in fiber lasers.However,there is still a dearth of deep understandin...The utilization of the dispersive Fourier transformation approach has enabled comprehensive observation of the birth process of dissipative solitons in fiber lasers.However,there is still a dearth of deep understanding regarding the extinction process of dissipative solitons.In this study,we have utilized a combination of experimental and numerical techniques to thoroughly examine the breathing dynamics of dissipative solitons during the extinction process in an Er-doped mode-locked fiber laser.The results demonstrate that the transient breathing dynamics have a substantial impact on the extinction stage of both steady-state and breathing-state dissipative solitons.The duration of transient breathing exhibits a high degree of sensitivity to variations in pump power.Numerical simulations are utilized to produce analogous breathing dynamics within the framework of a model that integrates equations characterizing the population inversion in a mode-locked laser.These results corroborate the role of Q-switching instability in the onset of breathing oscillations.Furthermore,these findings offer new possibilities for the advancement of various operational frameworks for ultrafast lasers.展开更多
We investigate the properties of spatial solitons in the fractional Schr?dinger equation(FSE) with parity-time(PT)-symmetric lattice potential supported by the focusing of Kerr nonlinearity. Both one-and two-dimension...We investigate the properties of spatial solitons in the fractional Schr?dinger equation(FSE) with parity-time(PT)-symmetric lattice potential supported by the focusing of Kerr nonlinearity. Both one-and two-dimensional solitons can stably propagate in PT-symmetric lattices under noise perturbations. The domains of stability for both one-and two-dimensional solitons strongly depend on the gain/loss strength of the lattice. In the spatial domain, the solitons are rigidly modulated by the lattice potential for the weak diffraction in FSE systems. In the inverse space, due to the periodicity of lattices, the spectra of solitons experience sharp peaks when the values of wavenumbers are even. The transverse power flows induced by the imaginary part of the lattice are also investigated, which can preserve the internal energy balances within the solitons.展开更多
基金Project supported by the National Natural Science Foundation of China(NSFC)(Grant No.12004309)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSQ036)the Scientific Research Program funded by Shaanxi Provincial Education Department(Grant No.20JK0947).
文摘We show that the nonlinear stage of the dual-wavelength pumped modulation instability(MI)in nonlinear Schrödinger equation(NLSE)can be effectively analyzed by mode truncation methods.The resulting complicated heteroclinic structure of instability unveils all possible dynamic trajectories of nonlinear waves.Significantly,the latticed-Fermi-Pasta-Ulam recurrences on the modulated-wave background in NLSE are also investigated and their dynamic trajectories run along the Hamiltonian contours of the heteroclinic structure.It is demonstrated that there has much richer dynamic behavior,in contrast to the nonlinear waves reported before.This novel nonlinear wave promises to inject new vitality into the study of MI.
基金supported by the National Natural Science Foundation of China(Grant Nos.12175178,12047502,and 12004309)the Major Basic Research Program of Natural Science of Shaanxi Province(Grant No.2017KCT-12)the Natural Science basic Research Program of Shaanxi Province(Grant No.2022KJXX-71)。
文摘We reveal a special subset of non-degenerate Akhmediev breather(AB)solutions of Manakov equations that only exist in the focusing case.Based on exact solutions,we present the existence diagram of such excitations on the frequency-wavenumber plane.Conventional single-frequency modulation instability leads to simultaneous excitation of three ABs with two of them being non-degenerate.
基金supported by the National Natural Science Foundation of China(Grant Nos.62305299 and 62205296)the Zhejiang Provincial Natural Science Foundation of China(Nos.LQ22F050007 and LQ23F050004)+1 种基金the Open Project Program of Wuhan National Laboratory for Optoelectronics(No.2020WNLOKF008)the“Pioneer”and“Leading Goose”R&D Program of Zhejiang(No.2022C03084).
文摘The utilization of the dispersive Fourier transformation approach has enabled comprehensive observation of the birth process of dissipative solitons in fiber lasers.However,there is still a dearth of deep understanding regarding the extinction process of dissipative solitons.In this study,we have utilized a combination of experimental and numerical techniques to thoroughly examine the breathing dynamics of dissipative solitons during the extinction process in an Er-doped mode-locked fiber laser.The results demonstrate that the transient breathing dynamics have a substantial impact on the extinction stage of both steady-state and breathing-state dissipative solitons.The duration of transient breathing exhibits a high degree of sensitivity to variations in pump power.Numerical simulations are utilized to produce analogous breathing dynamics within the framework of a model that integrates equations characterizing the population inversion in a mode-locked laser.These results corroborate the role of Q-switching instability in the onset of breathing oscillations.Furthermore,these findings offer new possibilities for the advancement of various operational frameworks for ultrafast lasers.
基金National Natural Science Foundation of China(NSFC)(61525505,11774310)Natural Science Foundation of Shaanxi Province(2015KCT-06)
文摘We investigate the properties of spatial solitons in the fractional Schr?dinger equation(FSE) with parity-time(PT)-symmetric lattice potential supported by the focusing of Kerr nonlinearity. Both one-and two-dimensional solitons can stably propagate in PT-symmetric lattices under noise perturbations. The domains of stability for both one-and two-dimensional solitons strongly depend on the gain/loss strength of the lattice. In the spatial domain, the solitons are rigidly modulated by the lattice potential for the weak diffraction in FSE systems. In the inverse space, due to the periodicity of lattices, the spectra of solitons experience sharp peaks when the values of wavenumbers are even. The transverse power flows induced by the imaginary part of the lattice are also investigated, which can preserve the internal energy balances within the solitons.