Self-trapping of optical vortices in waveguide lattices with a self-defocusing nonlinearity

Geometric stabilization of extendedS=2vortices in two-dimensional photonic lattices: Theoretical analysis, numerical computation, and experimental results

“…8(a)] is different from that in Fig. 7(a) in order to have the extended 8-site excitation, now that the waveguides are located at the intensity minima (rather than maxima) of the lattice-inducing beam under self-defocusing nonlinearity [29]. In comparison with very recent study of S=2 discrete vortex solitons in hexagonal photonic lattices [33,34], we found that the S=2 vortex can remain self-trapped [ Fig.…”

“…8(d)] also under the self-defocusing nonlinearity. In addition, differently from the more localized 4-site excitation of the S=2 vortex which evolves into a self-trapped quadrupole-like structure [29], here the vortex phase structure remains. Furthermore, the Fourier-space spectrum [ Fig.…”

Experiments on Linear and Nonlinear Localization of Optical Vortices in Optically Induced Photonic Lattices

“…These results suggest that although the m = 1 vortex can evolve into a gap vortex soliton, it does not bifurcate from the edge of the first Bloch band, quite different from all previously observed fundamental, dipole, or quadrupole-like gap soliton in selfdefocusing lattices [28,29]. On the other hand, the m = 2 vortex can evolve into a quadrupole-like localized state, which does seem to bifurcate from the edge of the first Bloch bands as confirmed by numerical analysis [26,30].…”

“…For the limited propagation distance of our crystal length (10 mm), it appears that the vortex singularity (manifested by the central forks in the interferograms) persists after the nonlinear propagation through the crystal, although it seems that charge-flipping (reversal of forks) is associated with the DCV at crystal output. However, from numerical simulations to longer propagation distances, the singularity can maintain only for the m = 1 but not for the m = 2 vortices [26]. In fact, our theoretical analysis shows that a "true" doubly charged gap vortex soliton does not exist under this excitation condition, and a quadrupole-like soliton structure is found instead for the m = 2 vortex [26].…”

“…However, from numerical simulations to longer propagation distances, the singularity can maintain only for the m = 1 but not for the m = 2 vortices [26]. In fact, our theoretical analysis shows that a "true" doubly charged gap vortex soliton does not exist under this excitation condition, and a quadrupole-like soliton structure is found instead for the m = 2 vortex [26]. The other technique is to send a coaxial broad Gaussian beam as an interference beam.…”