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结合均匀光子晶格的衍射关系和晶格中正负缺陷的布里渊区谱特性,探讨了光诱导二维光子晶格中线性缺陷模式的形成条件,对布里渊区中各点的缺陷模式进行了模拟分析,并得到了光子带隙结构中“嵌入点”X1点的正、负缺陷模式.结果表明:对于二维缺陷,只有当衍射关系曲面中沿两个正交的横向波矢方向同时为正常(反常)衍射的区域才能存在正(负)缺陷模式;而对于一维缺陷,只要在一个横向波矢方向上存在正常(反常)衍射的区域就可以支持正(负)缺陷模式,因此在某些特殊点处,正和负的缺陷模式可以同时存在.X1点正缺陷模式的存在预示着自聚焦非线性同样可以支持带内孤子.研究结果有助于对光子晶格中晶格孤子(特别是带内孤子)的理解和进一步研究.
Combining with the diffraction relationship of uniform photonic lattice and the Brillouin spectral characteristics of positive and negative defects in the lattice, the formation conditions of the linear defect mode in the two-dimensional photonic lattice induced by light are discussed, and the defects of each point in the Brillouin zone Mode was simulated and the positive and negative defect modes of “embedding point ” X1 point in the photonic band gap structure were obtained.The results show that for the two-dimensional defect only when the diffraction relation surface is along two orthogonal transverse directions For the one-dimensional defect, the normal (anomalous) diffraction region can support the positive (negative) region as long as there is a normal (anomalous) diffraction region in a transverse wave-vector direction, Defect mode, so at certain special points, positive and negative defect modes can coexist.X1 point positive defect mode indicates that self-focusing nonlinearity can also support in-band solitons.The results of the study contribute to the photonic crystal lattice The understanding and further study of lattice solitons (especially in-band solitons).