The evolution of the out-of-phase dipole beams in the repulsive defect photonic moire lattice with saturable self-focusing nonlinearity media

We demonstrate in a numerical manner the intriguing transmission of the out-of-phase (OOP) dipole beams in the repulsive defect photonic moir & eacute; lattice with rotation angle theta = arctan (3/4) and defect depth epsilon = -0.5 under saturable self-focusing nonlinearity. Photonic moir & eacute; lattices, that are created by two mutually rotated square patterns with a relative rotation angle theta. We introduce a single-site repulsive defect in periodic photonic moir & eacute; lattices, and excite this site with the OOP dipole beams. We reveal that the OOP dipole beams undergoes two evolution stages during propagation, for the first time to our knowledge. It is shown that the OOP dipole beams maintain stable propagation over a certain distance in the first stage, which depends on the defect depth. Then the energy of the OOP dipole beams flows between its two spots, exhibiting periodic-like oscillation in the second stage, along with discussion about the effect of defect depth on the stable propagation distance of the OOP dipole beams, one finds that the stable propagation distance decreases linearly with increasing defect depth |epsilon|. At the same time, we perform a polynomial fit between the oscillation period of the OOP dipole beams and the defect depth |epsilon|. These two fitting curves fully demonstrate that the repulsive defect can profoundly affect the propagation behavior of the OOP dipole beams. Our results may provide novel insights into the localization and oscillation of beams in defect structures.