Study Of Band Gap Solitons In Photorefractive Crystals

Light propagation in the periodic media has become a considerate topic in nonlinear optics.In such optical periodic structure,the propagation of linear optical waves can produce Bloch wave band and forbidden band gap structure.For the propagation of nonlinear optical waves in the optical periodic structure,gap solitons are generated when the nonlinear effects of the optical wave are balanced with the discrete diffraction.Gap solitons have high research value in the fabrication of optical waveguides,harmonic generation,optical communication and optical information processing.In this paper,the existence and stability of surface gap soliton,multiple gap soliton and twisted soliton in the photorefractive crystal are studied by the numerical method.For surface gap solitons at the interface between a metal and self-defocusing periodic medium,it exists only in the limited band gap with the critical value beyond the lattice depth.And there exist stable and unstable regions in the first and second band gap.In the first gap,for a given lattice depth,when the propagation constant increases,the energy flow of the gap solitons is smaller and the oscillation trailing is shorter.It is also found that the unstable surface gap soliton tends to self-bend toward the positive direction of the transverse axis during propagation,and the self-bend angle gradually decreases with the increase of the lattice depth.In the second gap,there are more trailing oscillations on the surface gap solitons,and the unstable region decreases gradually with the increase of the propagation constant.For self-focusing centrosymmetric photorefractive crystals,the gap solitons exist in the first band gap.The existence range of gap solitons increases with the increase of lattice depth,and have the form of one to six orders.The energy flow of gap soliton increases with the increase of the propagation constant.When the propagation constant is small,the intensity of the lobe of the high-order gap solitons are the same.When the propagation constant is close to the first gap edge,the central lobe of the gap soliton is weaker than the side lobe.In the self-defocusing centrosymmetric photorefractive crystal,the intensity of each lobe of the gap soliton is the same.Moreover,the gap soliton has more amplitude oscillations when the propagation constant is small.As the propagation constant increases,the amplitude oscillation decreases.In addition,twisted solitons have also been found in centrosymmetric photorefractive crystals.In the self-focusing centrosymmetric photorefractive crystal,the twisted soliton exists in the semi-infinite band gap and the first band gap,and only have stable region in the first gap.The existence region of the twisted soliton increases with the increase of the lattice depth.The higher order of twisted solitons occupies more lattices,and the energy flow value is higher too.In the self-defocusing centrosymmetric photorefractive crystals,all the order of twisted solitons is unstable.