Two-dimensional defect modes in optically induced photonic lattices

Abstract

In this article, localized linear defect modes due to bandgap guidance in two-dimensional photonic lattices with localized or non-localized defects are investigated theoretically. First, when the defect is localized and weak, eigenvalues of defect modes bifurcated from edges of Bloch bands are derived analytically. It is shown that in an attractive (repulsive) defect, defect modes bifurcate out from Bloch-band edges with normal (anomalous) diffraction coefficients. Furthermore, distances between defect-mode eigenvalues and Bloch-band edges are exponentially small functions of the defect strength, which is very different from the one-dimensional case where such distances are quadratically small with the defect strength. It is also found that some defect-mode branches bifurcate not from Bloch-band edges, but from quasi-edge points within Bloch bands, which is very unusual. Second, when the defect is localized but strong, defect modes are determined numerically. It is shown that both the repulsive and attractive defects can support various types of defect modes such as fundamental, dipole, quadrupole, and vortex modes. These modes reside in various bandgaps of the photonic lattice. As the defect strength increases, defect modes move from lower bandgaps to higher ones when the defect is repulsive, but remain within each bandgap when the defect is attractive, similar to the one-dimensional case. The same phenomena are observed when the defect is held fixed while the applied dc field (which controls the lattice potential) increases. Lastly, if the defect is non-localized (i.e. it persists at large distances in the lattice), it is shown that defect modes can be embedded inside the continuous spectrum, and they can bifurcate out from edges of the continuous spectrum algebraically rather than exponentially.

17 pages, 10 figures, to appear in Phys. Rev. A

References in corpus (11)

• Observation of discrete vortex solitons in optically-induced photonic lattices
• Fundamental and vortex solitons in a two-dimensional optical lattice
• Spatial Solitons in Optically-Induced Gratings
• Discrete solitons and soliton-induced dislocations in partially-coherent photonic lattices
• Rotary solitons in Bessel photonic lattices
• Bifurcations and stability of gap solitons in periodic potentials
• Nonlinear localized waves in a periodic medium
• Defect modes in one-dimensional photonic lattices
• Observation of 2nd band vortex solitons in 2D photonic lattices
• Reduced-symmetry two-dimensional solitons in photonic lattices
• Solitary Waves Bifurcated from Bloch Band Edges in Two-dimensional Periodic Media

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• Soliton shape and mobility control in optical lattices
• Defect solitons in defective PT potentials with real part of dual-frequency lattices