四极孤子在自聚焦光诱导四方晶格中的动态演化

Evolution of Quadrupole Solitons in Self-Focusing Photoinduction Tetragonal Photonic Lattices

运用交替隐式光束传输法研究了异相和同相四极光束在自聚焦光诱导的四方晶格中的传输特性。给出了异相和同相四极光束在连续均匀介质、自聚焦介质和自聚焦光诱导的光子晶格中的动态演化。在均匀介质中传输时,异相四极光束发生线性衍射,峰值强度逐渐变小,光束间相互排斥,峰值间距变大;而同相四极光束先各自衍射,而后聚合为单束光,峰值幅度先减小后增加,继续向前传输,光束衍射,峰值递减。引入自聚焦光折变介质后,异相四极光束发生自聚焦现象,且相互分离现象更加明显;而同相四极光束相互吸引融合为单束光,能量几乎全部汇聚到晶格中心点。引入自聚焦光诱导光子晶格后,异相四极光束一定条件下能形成稳定传输的异相四极孤子,其对角波峰相位相同,相邻波峰相位差为π;而同相四极光束在一定的条件下能形成局域的同相四极孤子,其波峰相位均相同。

Out-of-phase （OOP） and in-phase （IP） quadrupole beams propagation in self-focusing photoinduction tetragonal photonie lattices is investigated by alternative direction implicit-beam propagation method （ADI-BPM）. The evolution of OOP and IP quadrupole beams in continuous homogeneous medium, self-focusing medium and self- focusing photoinduction photonic lattices is presented respectively. In the continuous homogeneous medium, it is shown that OOP quadrupole beams are linearly diffracted, with the peak intensity decreasing gradually. Besides, the beams repel each other and the peak spacing becomes larger. IP quadrupole beams are diffracted originally, and then fused into the single beam. The peak is decreased in the beginning and then increased. As the beam is transmitted forward and diffracted, the peak intensity declines. In the self-focusing nonlinear medium, the OOP quadrupole beams could self-focus and the separation becomes more obvious, while the IP quadrupole beams could attract each other and merge into a single beam. In the self-focusing light photoinduction lattices, under appropriate conditions, the OOP quadrupole beams could form the stable OOP quadrupole solitons whose diagonal humps have the same phase but the adjacent humps have π-phase difference, while the IP quadrupole beams could form the localized IP quadrupole solitons whose four humps have the same phase.