A theory is presented to investigate the existence and propagation stability of gap solitons in a parity-time （PT） com- plex superlattice with dual periods. In this superlattice, the real and imaginary parts are bot...A theory is presented to investigate the existence and propagation stability of gap solitons in a parity-time （PT） com- plex superlattice with dual periods. In this superlattice, the real and imaginary parts are both in the form of superlattices with dual periods. In the self-focusing nonlinearity, PT solitons can exist in the semi-infinite gap. However, only those gap solitons with low powers can propagate stably, whereas the high-power solitons present periodic oscillation and simultane- ously suffer energy decay. In the self-defocusing nonlinearity, PT solitons only exist in the first gap and all these solitons are stable.展开更多
We comprehensively investigate the nontrivial states of an interacting Bose system in a cosine potential under the open boundary condition. Our results show that there exists a kind of stable localized state： edge ga...We comprehensively investigate the nontrivial states of an interacting Bose system in a cosine potential under the open boundary condition. Our results show that there exists a kind of stable localized state： edge gap solitons. We argue that the states originate from the eigenstates of independent edge parabolas. In particular, the edge gap solitons exhibit a nonzero topological-invariant behavior. The topological nature is due to the connection of the present model to the quantized adiabatic particle transport problem. In addition, the composition relations between the gap solitons and the extended states are also discussed.展开更多
We systematically investigate the motion of slowly moving matter wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we ...We systematically investigate the motion of slowly moving matter wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Cross-Pitaevskii equation.展开更多
We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedde...We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedded in the two-dimensional optical lattice gives rise to some unique properties. It is interestingly found that for the negative defect, stable surface defect gap solitons can exist both in the semi-infinite gap and in the first gap. The deeper the negative defect, the narrower the stable region in the semi-infinite gap will be. For a positive defect, the surface defect gap solitons exist only in the semi-infinite gap and the stable region localizes in a low power region.展开更多
We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice.Honeycomb lattices possess a unique band structure,the first an...We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice.Honeycomb lattices possess a unique band structure,the first and second bands intersect at a set of so-called Dirac points.Deformation can result in the merging and disappearance of the Dirac points,and support the gap solitons.We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons.These multipoles can have their bright solitary structures being in-phase or out-of-phase.We also investigate the linear stabilities and nonlinear stabilities of these gap solitons.These results have applications of the localized structures in nonlinear optics,and may helpful for exploiting topological properties of a deformed lattice.展开更多
We numerically investigate the gap solitons in Bose–Einstein condensates(BECs)with spin–orbit coupling(SOC)in the parity–time(PT)-symmetric periodic potential.We find that the depths and periods of the imaginary la...We numerically investigate the gap solitons in Bose–Einstein condensates(BECs)with spin–orbit coupling(SOC)in the parity–time(PT)-symmetric periodic potential.We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap.The dynamics of these gap solitons are checked by the split-time-step Crank–Nicolson method.It is proved that the depths of the imaginary part of the PT-symmetric periodic potential gradually increase,and the gap solitons become unstable.But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.展开更多
We study the surface defect gap solitons in an interface between a defect of one-dimensional dual-frequency lattices and the uniform media. Some unique properties are revealed that such lattices can broaden the region...We study the surface defect gap solitons in an interface between a defect of one-dimensional dual-frequency lattices and the uniform media. Some unique properties are revealed that such lattices can broaden the region of semi-finite gap, and the semi-finite gap exists not only in the positive and zero defects but also in the negative defect; unlike in the regular lattices, the semi-finite gap exists in the positive and zero defects but does not exist in the negative defect. In particular, stable solitons exist almost in the whole semi-finite gap for the positive and zero defects. These properties are different from other lattices with defects. In addition, it is found that the existence of surface dual-frequency lattice solitons does not need a threshold power.展开更多
We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons （IBSs） and gap soliton trains （GSTs）, in optically induced two-dimensional photonic lattices with self-defocusing nonl...We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons （IBSs） and gap soliton trains （GSTs）, in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity. It is revealed that the π-staggered phase structures of the lattice soliton trains will lead to anomalous interactions. Solely by changing their initial separations, the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained. The ‘negative refraction＇ effect of the soliton trains on the interaction is also discussed. Moreover, two interacting IBSs can merge into one GST when attraction or energy transfer happens.展开更多
Vortex solitons with a ring vortex core residing in a single lattice site in the semi-infinite gap of square optical lattices are reported. These solitons are no longer bound states of the Bloch-wave unit （Bloch-wave...Vortex solitons with a ring vortex core residing in a single lattice site in the semi-infinite gap of square optical lattices are reported. These solitons are no longer bound states of the Bloch-wave unit （Bloch-wave distribution in one lattice site） at the band edge of the periodic lattice, and consequently they do not bifurcate from the corresponding band edge. For saturable nonlinearity, one family of such solitons is found, and its existing curve forms a closed loop, which is very surprising. For Kerr nonlinearity, two families of such vortex solitons are found.展开更多
A brief historical narrative of the study of grating solitons in fiber Bragg grating is presented from the late 1970’s up to now. The formation of photogeneration gratings in optical fiber by sustained exposure of th...A brief historical narrative of the study of grating solitons in fiber Bragg grating is presented from the late 1970’s up to now. The formation of photogeneration gratings in optical fiber by sustained exposure of the core to the interference pattern produced by oppositely propagating modes of argon-ion laser radiation was first reported in 1978. One important nonlinear application of fiber Bragg grating is grating solitons, including gap soliton and Bragg soliton. This paper summarily introduces the numerous theoretical and experimental results on this field, each indicating the potential these solitons have in all-optical switching, pulse compression, limiting, and logic operations, and especially important for the optical communication systems.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61308019)the Foundation for Distinguished Young Talents in Higher Education of Guangdong Province,China(Grant No.Yq2013157)
文摘A theory is presented to investigate the existence and propagation stability of gap solitons in a parity-time （PT） com- plex superlattice with dual periods. In this superlattice, the real and imaginary parts are both in the form of superlattices with dual periods. In the self-focusing nonlinearity, PT solitons can exist in the semi-infinite gap. However, only those gap solitons with low powers can propagate stably, whereas the high-power solitons present periodic oscillation and simultane- ously suffer energy decay. In the self-defocusing nonlinearity, PT solitons only exist in the first gap and all these solitons are stable.
基金supported by the Natural Science Foundation of Hebei Province,China(Grant Nos.A2012203174 and A2015203387)the National Natural Science Foundation of China(Grant Nos.10974169 and 11304270)
文摘We comprehensively investigate the nontrivial states of an interacting Bose system in a cosine potential under the open boundary condition. Our results show that there exists a kind of stable localized state： edge gap solitons. We argue that the states originate from the eigenstates of independent edge parabolas. In particular, the edge gap solitons exhibit a nonzero topological-invariant behavior. The topological nature is due to the connection of the present model to the quantized adiabatic particle transport problem. In addition, the composition relations between the gap solitons and the extended states are also discussed.
基金Project supported by the National Basic Research Program of China (Grant No 2006CB921701-6)Pujiang Talent Project (Grant No PJ2005(00593))the Hundred Tarent Project of the Chinese Academy of Sciences, China
文摘We systematically investigate the motion of slowly moving matter wave gap solitons in a nonlinear potential, produced by the weak random spatial variation of the atomic scattering length. With the weak randomness, we construct an effective-particle theory to study the motion of gap solitons. Based on the effective-particle theory, the effect of the randomness on gap solitons is obtained, and the motion of gap solitons is finally solved. Moreover, the analytic results for the general behaviours of gap soliton motion, such as the ensemble-average speed and the reflection probability depending on the weak randomness are obtained. We find that with the increase of the random strength the ensemble-average speed of gap solitons decreases slowly where the reduction is proportional to the variance of the weak randomness, and the reflection probability becomes larger. The theoretical results are in good agreement with the numerical simulations based on the Cross-Pitaevskii equation.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11174147)the Natural Science Foundation of Jiangsu Province, China (Grant No. BK2009366)
文摘We investigate the existence and stability of surface defect gap solitons at an interface between a defect in a two-dimensional optical lattice and a uniform saturable Kerr nonlinear medium. The surface defect embedded in the two-dimensional optical lattice gives rise to some unique properties. It is interestingly found that for the negative defect, stable surface defect gap solitons can exist both in the semi-infinite gap and in the first gap. The deeper the negative defect, the narrower the stable region in the semi-infinite gap will be. For a positive defect, the surface defect gap solitons exist only in the semi-infinite gap and the stable region localizes in a low power region.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12065022,12005173,11747018,and 11565021)the Natural Science Foundation of Gansu Province of China(Grant No.20JR10RA082)+1 种基金the China Postdoctoral Science Foundation(Grant No.2020M680318)the Scientific Research Foundation of NWNU(Grant No.NWNU-LKQN-16-3)。
文摘We investigate the existence and dynamical stability of multipole gap solitons in Bose-Einstein condensate loaded in a deformed honeycomb optical lattice.Honeycomb lattices possess a unique band structure,the first and second bands intersect at a set of so-called Dirac points.Deformation can result in the merging and disappearance of the Dirac points,and support the gap solitons.We find that the two-dimensional honeycomb optical lattices admit multipole gap solitons.These multipoles can have their bright solitary structures being in-phase or out-of-phase.We also investigate the linear stabilities and nonlinear stabilities of these gap solitons.These results have applications of the localized structures in nonlinear optics,and may helpful for exploiting topological properties of a deformed lattice.
基金Science and Technology Project of Hebei Education Department,China(Grant No.ZD2020200)。
文摘We numerically investigate the gap solitons in Bose–Einstein condensates(BECs)with spin–orbit coupling(SOC)in the parity–time(PT)-symmetric periodic potential.We find that the depths and periods of the imaginary lattice have an important influence on the shape and stability of these single-peak gap solitons and double-peak gap solitons in the first band gap.The dynamics of these gap solitons are checked by the split-time-step Crank–Nicolson method.It is proved that the depths of the imaginary part of the PT-symmetric periodic potential gradually increase,and the gap solitons become unstable.But the different periods of imaginary part hardly affect the stability of the gap solitons in the corresponding parameter interval.
基金Project supported by the National Natural Science Foundation of China (Grant No 10774031)Natural Science Foundation of Guangdong Province of China (Grant No 07001790)
文摘We study the surface defect gap solitons in an interface between a defect of one-dimensional dual-frequency lattices and the uniform media. Some unique properties are revealed that such lattices can broaden the region of semi-finite gap, and the semi-finite gap exists not only in the positive and zero defects but also in the negative defect; unlike in the regular lattices, the semi-finite gap exists in the positive and zero defects but does not exist in the negative defect. In particular, stable solitons exist almost in the whole semi-finite gap for the positive and zero defects. These properties are different from other lattices with defects. In addition, it is found that the existence of surface dual-frequency lattice solitons does not need a threshold power.
基金Project supported by the Northwestern Polytechnical University (NPU) Foundation for Fundamental Research and the Doctorate Foundation of NPU (Grant No.CX200914)
文摘We demonstrate the coherent interactions of lattice soliton trains, including in-band solitons （IBSs） and gap soliton trains （GSTs）, in optically induced two-dimensional photonic lattices with self-defocusing nonlinearity. It is revealed that the π-staggered phase structures of the lattice soliton trains will lead to anomalous interactions. Solely by changing their initial separations, the transition between attractive and repulsive interaction forces or reversion of the energy transfer can be obtained. The ‘negative refraction＇ effect of the soliton trains on the interaction is also discussed. Moreover, two interacting IBSs can merge into one GST when attraction or energy transfer happens.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10904009)the Fundamental Research Funds for the Central Universities(Grant Nos. ZYGX2011J039 and ZYGX2011J047)
文摘Vortex solitons with a ring vortex core residing in a single lattice site in the semi-infinite gap of square optical lattices are reported. These solitons are no longer bound states of the Bloch-wave unit （Bloch-wave distribution in one lattice site） at the band edge of the periodic lattice, and consequently they do not bifurcate from the corresponding band edge. For saturable nonlinearity, one family of such solitons is found, and its existing curve forms a closed loop, which is very surprising. For Kerr nonlinearity, two families of such vortex solitons are found.
文摘A brief historical narrative of the study of grating solitons in fiber Bragg grating is presented from the late 1970’s up to now. The formation of photogeneration gratings in optical fiber by sustained exposure of the core to the interference pattern produced by oppositely propagating modes of argon-ion laser radiation was first reported in 1978. One important nonlinear application of fiber Bragg grating is grating solitons, including gap soliton and Bragg soliton. This paper summarily introduces the numerous theoretical and experimental results on this field, each indicating the potential these solitons have in all-optical switching, pulse compression, limiting, and logic operations, and especially important for the optical communication systems.
