Propagation dynamics of multipole solitons and influence of fractional diffraction effect on solitons in II-type Dirac photonic lattices

By changing the depth of the waveguide and adjusting the band structure to make the bandgap appear, the influence of the integer- and fractional-order diffractions on two-dimensional spatial localized modes in the IItype Dirac photonic lattices are investigated. Under the nonlinear action, the linear topological mode is transformed into a set of topological gap solitons, which form stable integer-order fundamental and dipole solions, and unstable quadrupole solion. Stable fractional-order fundamental and dipole solions and metastable quadrupole solion are obtained by decreasing the Levy index, and the propagation dynamics of these solitons are discussed. By comparing the integer-order with the fractional-order solitons, it is proved that the propagation constant as well as the Levy index play a crucial role in the stability of soliton. The findings enable insightful studies of highly localized gap modes in linear nonlocality (fractional) physical systems.