Controllable Transmission Of Airy Solitons In Dissipative Systems

In the past decade,considerable progress has been made in the field of accelerated wave not only in basic principles and experimental proof,but also in its wide application.Starting with the presentation and prediction of typical Airy beams,new accelerating waves are found in the time and space parallels and non-parallels,and different methods are used to control their trajectories,amplitudes and beam widths at will.Accelerated waves exhibit a number of compelling properties,moving along curved or accelerated paths,while selfhealing and non-diffracting perturbations.Because of its unique and novel characteristics,it has been widely used in beam focusing,particle manipulation,biomedical imaging,plasma exciton and material processing.In recent years,the regulation effect of fractional order effect on Airy beam and soliton transmission has attracted the attention of scholars.The interaction of Airy beam under fractional order effect can not only form spatial and soliton pairs,but also serrated transmission mode.In this paper,the interaction of Airy beams in fractional order systems with controllable diffraction,the influence of cubic-quintic nonlinear effects and fractional effects on the propagation characteristics of Airy beams and the propagation management of beams in fractional order systems with self-focusing nonlinearity are studied.The specific work is summarized as follows:(1)The interaction characteristics of double Airy beams propagating in the variable coefficient fractional Schr(?)dinger equation are numerically simulated The results show that the evolution of in-phase and out-phase double airy beams exhibits periodic oscillation when the initial input double airy beams do not contain chirp due to longitudinal periodic modulation.As the initial interval increases,the number of intensity peaks due to the sidevalve interaction increases,resulting in an increase in the number of stripes between the two main valves.When the initial chirp is not zero,the chirp causes the oscillation period of the double-airy beam to increase to twice that of the chirp less beam.(2)The propagation characteristics of double Airy beams with initial chirped in the fractional cubic-quintic nonlinear Schr(?)dinger equation are studied numerically.The results show that respiratory or mutually exclusive pairs of solitons are formed under the combined action of fractional order diffraction effect and initial chirp.Airy beams attract each other to produce quasi-stable transmission of respiratory solitons and repel each other to form pairs of solitons with larger transverse spacing.When the initial interval is not zero,the larger the absolute value of the initial chirp,the stronger the repulsion force between the double Airy beams,and the larger the beam evolution deflection angle.The diffraction effect enlarges the beam width.When the initial double airy beams are inverted,they all exhibit repulsion as a whole,and the larger the initial chirp,the stronger the repulsion between the double airy beams.(3)The beam propagation management in a fractional order system with self-focusing nonlinearity is studied numerically.The results show that the periodic lattice potential makes the beam evolution exhibit periodic oscillation behavior,and the larger the Lévy index,the smaller the beam oscillation period and the larger the beam width.When the gradient longitudinal modulation function is applied,the Gaussian beam evolves into respiratory solitons with stable propagation,and the longitudinal modulation function can precisely adjust the propagation direction of solitons.The random noise added to the initial input amplitude affects the oscillation amplitude and destroys the stable transmission structure of the soliton.The noise will not affect the existence of the longitudinally modulated lattice.Controlling the beam propagation path provides an excellent idea for various applications,including optical switch and signal transmission.