从非线性Schr d inger方程出发,应用数学解析的方法,详细讨论了在饱和非线性介质中(2+1)维空间光学孤子存在满足物理意义的自洽解的条件,给出数值计算所需要的边界条件。通过数值计算,给出了基模和一阶模在某一组参数下的部分模式的光...从非线性Schr d inger方程出发,应用数学解析的方法,详细讨论了在饱和非线性介质中(2+1)维空间光学孤子存在满足物理意义的自洽解的条件,给出数值计算所需要的边界条件。通过数值计算,给出了基模和一阶模在某一组参数下的部分模式的光场慢变包络、光强度的二维和三维分布的直观图形,以及相应能量(无量纲)。结果表明,孤子的存在不是任意的,而是依赖于一定的能量。当光脉冲能量不足以支持孤子的存在时,其解呈振荡形式,说明不存在孤子解。同时还给出介质的饱和参数、孤子在传播方向上的波矢k对孤子模式的影响等有意义的结论。展开更多
We study fundamental modes trapped in a rotating ring with a saturated nonlinear double-well potential. This model, which is based on the nonlinear Schrodinger equation, can be constructed in a twisted waveguide pipe ...We study fundamental modes trapped in a rotating ring with a saturated nonlinear double-well potential. This model, which is based on the nonlinear Schrodinger equation, can be constructed in a twisted waveguide pipe in terms of light propagation, or in a Bose-Einstein condensate （BEC） loaded into a toroidal trap under a combination of a rotating π-out-of-phase linear potential and nonlinear pseudopotential induced by means of a rotating optical field and the Feshbach resonance. Three types of fundamental modes are identified in this model, one symmetric and the other two asymmetric. The shape and stability of the modes and the transitions between different modes are investigated in the first rotational Brillouin zone. A similar model used a Kerr medium to build its nonlinear potential, but we replace it with a saturated nonlinear medium. The model exhibits not only symmetry breaking, but also symmetry recovery. A specific type of unstable asymmetric mode is also found, and the evolution of the unstable asymmetric mode features Josephson oscillation between two linear wells. By considering the model as a configuration of a BEC system, the ground state mode is identified among these three types, which characterize a specific distribution of the BEC atoms around the trap.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
文摘从非线性Schr d inger方程出发,应用数学解析的方法,详细讨论了在饱和非线性介质中(2+1)维空间光学孤子存在满足物理意义的自洽解的条件,给出数值计算所需要的边界条件。通过数值计算,给出了基模和一阶模在某一组参数下的部分模式的光场慢变包络、光强度的二维和三维分布的直观图形,以及相应能量(无量纲)。结果表明,孤子的存在不是任意的,而是依赖于一定的能量。当光脉冲能量不足以支持孤子的存在时,其解呈振荡形式,说明不存在孤子解。同时还给出介质的饱和参数、孤子在传播方向上的波矢k对孤子模式的影响等有意义的结论。
基金Acknowledgements G. Chen appreciates the useful discussions with Yongyao Li （SCAU Univ.）. This work was supported by the National Natural Science Foundation of China （Grant No. 61308019）, Guangdong Natural Science Foundation （Grant No. 2015A030313650）, and the Foundation for Distin- guished Young Talents in Higher Education of Guangdong （Grant No. Yq2013157）.
文摘We study fundamental modes trapped in a rotating ring with a saturated nonlinear double-well potential. This model, which is based on the nonlinear Schrodinger equation, can be constructed in a twisted waveguide pipe in terms of light propagation, or in a Bose-Einstein condensate （BEC） loaded into a toroidal trap under a combination of a rotating π-out-of-phase linear potential and nonlinear pseudopotential induced by means of a rotating optical field and the Feshbach resonance. Three types of fundamental modes are identified in this model, one symmetric and the other two asymmetric. The shape and stability of the modes and the transitions between different modes are investigated in the first rotational Brillouin zone. A similar model used a Kerr medium to build its nonlinear potential, but we replace it with a saturated nonlinear medium. The model exhibits not only symmetry breaking, but also symmetry recovery. A specific type of unstable asymmetric mode is also found, and the evolution of the unstable asymmetric mode features Josephson oscillation between two linear wells. By considering the model as a configuration of a BEC system, the ground state mode is identified among these three types, which characterize a specific distribution of the BEC atoms around the trap.
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.
