The Propagation Of Multipole Beam In The Lieb Like Photonic Lattice

Since the optical localization in photonic Lieb lattices was observed experimentally in 2015,Lieb lattice has attracted ever-increasing attention because of its flat dispersion band.The flat band photonic lattice is a kind of photonic lattice with flat energy band(zero bandwidth)under tight-binding approximation.Its special topological structure produces geometric frustration,which can suppress the discrete diffraction effect of the beam.Therefore,flat band photonic lattices have been used in local states and non-diffraction.Generally,Lieb lattice or Kagome lattice is the research object of flat band lattice.In this paper,based on the novel Lieb like photonic lattice,we study the propagation characteristics of multipolar beams in it by Split Step Fourier Method,and observe some novel phenomena.The conclusion of this paper provides valuable research results for the realization of light control with photonic lattice and undistorted image transmission with flat band.It can also be applied in optical coupling and beam splitting.The main contents and achieveents are as follows:1.The influence of relative lattice intensity and lattice constant on the propagation of octupole beam in Lieb-5 photonic lattice is studied.The results show that the relative position of the flat band of Lieb-5 photonic lattice in the Bloch band structure and the transmission localization of the out of phase octupole beam can be controlled by adjusting the ratio of the relative lattice intensity.At the same time,the dynamic periodic coupling of the energy in each incident lattice is observed.Similar to other lattices,the lattice constant also affects the coupling between adjacent lattice points of Lieb-5 photonic lattice,thus affecting the beam localization.2.The effects of absolute lattice intensity,incident light intensity and incident light phase distribution on the propagation of octupole beams in Lieb-5 photonic lattice are studied.In a certain range,increasing the absolute lattice intensity or decreasing the incident light intensity will lead to the change of the oscillation characteristics during the evolution of the peak intensity of the beam: the amplitude of the oscillation will be weakened and the period of the oscillation will be longer,that is,the degree of energy coupling between adjacent lattice points will be weakened.Finally,it is verified that thephase out of phase of the incident multipole beam is the necessary condition to keep the beam localized.3.The transmission characteristics of multipolar light beam in Lieb-7 photonic lattice are studied.Compared with Lieb-5 photonic lattice,the structure of Lieb-7photonic lattice is relatively complex,so the transmission of multipolar light beam in Lieb-7 lattice will have different phenomena.The simulation results show that there is a threshold between the incident light intensity and the absolute lattice intensity when the phase distribution of the incident light beam meets the conditions.If the corresponding threshold conditions are met,the shape of the incident multipolar light beam will have different conversion in the transmission process,and its peak intensity evolution diagram has "size peak",and the incident light beam will be in the quadrupole beam,the octupole beam and the twelve pole beam periodic transformation between beams.