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One- and two-dimensional gap solitons and dynamics in the PT-symmetric lattice potential and spatially-periodic momentum modulation

机译:PT对称晶格势和空间周期动量调制中的一维和二维间隙孤子和动力学

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Highlights In the linear regime, the momentum modulation can alter the first and second PT thresholds of the classical lattice, periodically or regularly change the shapes of the band structure, rotate and split the diffraction patterns of beams leading to multiple refraction and emissions. A large family of fundamental solitons within the semi-infinite gap can be found to be stable, even beyond the second PT threshold; In the nonlinear regime, the momentum modulation can shrink the existing range of fundamental solitons and not change their stability. The momentum modulation can also utterly change the direction of the transverse power flow and control the energy exchange among gain or loss regions. Abstract The influence of spatially-periodic momentum modulation on beam dynamics in parity-time ( PT ) symmetric optical lattice is systematically investigated in the one- and two-dimensional nonlinear Schrödinger equations. In the linear regime, we demonstrate that the momentum modulation can alter the first and second PT thresholds of the classical lattice, periodically or regularly change the shapes of the band structure, rotate and split the diffraction patterns of beams leading to multiple refraction and emissions. In the Kerr-nonlinear regime for one-dimension (1D) case, a large family of fundamental solitons within the semi-infinite gap can be found to be stable, even beyond the second PT threshold; it is shown that the momentum modulation can shrink the existing range of fundamental solitons and not change their stability. For two-dimension (2D) case, most solitons with higher intensities are relatively unstable in their existing regions which are narrower than those in 1D case, but we also find stable fundamental solitons corroborated by linear stability analysis and direct beam propagation. More importantly, the momentum modulation can also utterly change the direction of the transverse power flow and control the energy exchange among gain or loss regions.
机译: 突出显示 在线性状态下,动量调制可以更改经典晶格的第一和第二PT阈值,定期或定期更改能带结构的形状,旋转并分裂光束的衍射图样,从而导致多次折射和发射。 A l即使在第二个PT阈值之上,半无限间隙内的基本孤子的Arge系列也可以保持稳定; 在非线性状态下,动量调制可以缩小基本孤子的现有范围,而不会改变其稳定性。 动量调制还可以完全改变横向功率流的方向,并控制增益或损耗区域之间的能量交换。 摘要 空间周期动量调制的影响奇偶校验时间内的射束动力学( PT )在一维和二维非线性Schrödinger方程中被系统研究。在线性状态下,我们证明了动量调制可以改变第一和第二 PT 阈值,定期或有规律地改变能带结构的形状,旋转并分裂光束的衍射图样,从而导致多次折射和发射。在用于一维(1D)的Kerr非线性系统中,即使在第二个 PT 阈值;结果表明,动量调制可以缩小基本孤子的现有范围,而不会改变其稳定性。对于二维(2D)情况,大多数强度较高的孤子在其现有区域中都相对不稳定,比一维情况更窄,但是我们还发现,通过线性稳定性分析和直接光束传播可以证实稳定的基本孤子。更重要的是,动量调制还可以完全改变横向功率流的方向,并控制增益或损耗区域之间的能量交换。

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