Finite Energy Airy Beam Propagation In Logatithmic Nonlinear Media

Based on the theory of quantum mechanics,Berry et al.deduced that the Schr?dinger equation has a non-diffusion property and follows the wave packet solution of the Airy function.Since then,the research on the non-diffractive beam has become one of the important research topics in the field of optics.The non-diffractive Airy beam theoretically carries infinite energy,which cannot be realized and applied in reality.Until 2007,it was found that the finite energy Airy beam solution can be obtained by the method of truncated,and the finite energy Airy beam is obtained in the experiment.In recent years,Airy beams have received great attention because of their non-diffractive,self-healing,and lateral self-accelerating properties.And the research on the propagation characteristics of Airy beam in various nonlinear media has become a research hotspot.In this paper,the transmission characteristics of the finite energy Airy beam in logarithmic nonlinear media are studied by the method of step-by-step Fourier numerical simulation.The main research contents and results are as follows:1.Starting from the basic theory and characteristics of Airy beam and the transmission theory of light beam in logarithmic nonlinear medium,the propagation characteristics of Airy beam in logarithmic nonlinear medium are investigated.According to the results of numerical simulations,the logarithmic media like Kerr does not generate soliton beams at low initial input power,but forms solitons in the logarithmic saturation nonlinearity and is less affected by the initial input.Under the same conditions,the self-focusing effect caused by the nonlinear interaction in the logarithmic medium is weaker than that in the Kerr medium,and the dispersion effect leads to the widening of the soliton beam.In the logarithmically saturated nonlinear medium,the soliton beam retains the self-acceleration characteristics of the partial Airy beam,and the soliton shifts toward the acceleration direction.In addition,the logarithmic nonlinear medium is less affected by the attenuation coefficient,and the energy loss of the Airy beam after propagation in this medium is huge.In contrast,in the logarithmically saturated nonlinear medium,the Airy beam retains part of its acceleration characteristics.When the initial input beam sidelobe energy is transferred to the forming soliton,it is worth our attention that the energy loss during the transmission in the logarithmically saturated nonlinear medium is small.attention.2.The interactions of the in-phase input and the out-of-phase input of the two Airy beams are investigated.The propagation in the Kerr nonlinear medium,the logarithmic nonlinear medium and the saturated nonlinear medium is compared and analyzed by numerical simulation.Single soliton and soliton pairs can be generated in the interaction in a logarithmic nonlinear medium,and the resulting soliton pairs do not accelerate.The effect of soliton and soliton on the initial spacing and nonlinear intensity shows the attraction of the in-phase input,the repulsion of the opposite input phase,and the oscillation under energy saturation.Compared to Kerr medium,the logarithmically nonlinear medium is less affected by the initial amplitude than in the logarithmic nonlinear medium.The stability is better,and the interaction hardly appears at high nonlinear strength.Disturbance or strong oscillations.The resulting peak period also exhibits some regularity.