Investigation Of Propagation Properties And Interactions Of Airy Beams And Their Derived Beams

Since it was firstly reported in 2007,the Airy beam has become a research hotspot in optics for its fascinating properties of self-acceleration,self-healing and non-diffraction which endow it with potential utility in diverse applications such as physics,biomedicine and military when compared with traditional Gaussian beam.However,the theoretical research of Airy beam is still lacked among reported works and some practical issues such as the propagation properties and interaction rules of Airy beam in various media,as far as we know,have not been systematically studied.Given these issues,the propagation properties and interaction rules of Airy beam and its derived beams have been studied deeply by utilizing the method of theoretical analysis and experimental verification in this dissertation.1.The exact analytical solution to Airy beam's one dimensional paraxial diffraction equation,which describes the propagation behavior of Airy beam in free space,is derived completely by utilizing the classic Fourier analysis and the unique property of Airy function.A combined phase mask is utilized to increase the spatial distances among generated Airy beams with different orders of diffraction.The self-acceleration,self-healing and non-diffraction properties of Airy beam are studied by utilizing the generated beams.The experimental results show that the decay factor of Airy beam can be altered by controlling the orders of the cubic phase mask loaded into the liquid cystal spatial light modulator(LC-SLM).2.The traditional Twyman-Green interference method,which is used to measure the phase modulation characteristics of a LC-SLM,has some obvious disadvantages in practice such as unavailability of adjusting the optical path difference subtly and dynamically,which makes it hard to acquire interference fringes with high intensity and ideal shapes.In this work,an improved strategy is proposed to overcome these shortcomings.An extra lens which can be adjusted subtly in two dimensions is added in the original system.Meanwhile,an automatically data processing system has been designed to process interference fringes and measure the shift distances and cycles.What's more,in order to compensate and correct the nonlinear characteristics of LC-SLM when it works on the non-operating wavelength,three universal inverse interpolation methods are utilized.The experimental results show that the shape-preserving subsection cubic interpolation method can achieve the best performance as well as the highest computation efficiency.3.The quasi-Airy beam is introduced and the propagation properties of the beam in free space are studied by utilizing the split-step Fourier method.The corresponding experiments are also carried out by utilizing the LC-SLM.The numerical simulation results show that the quasi-Airy beam will evolve into two separated parts during propagation and the propagation directions of both parts are decided by the beam's initial light field distributions.And the separation behavior results from the asymmetrical spatial distribution of the quasi-Airy beam.Moreover,it is found the propagation trajectories of quasi-Airy beam can be controlled arbitrarily through adjusting the included angle of the outermost sidelobes,but is at the expense of sacrificing the non-diffraction property of the beam to some degree.Afterwards,the propagation properties of quasi-Airy beam with a spiral phase are investigated numerically and experimentally.The corresponding results indicate that the influence of spiral phase on the propagation dynamics of quasi-Airy beam is also decided by the initial light field distribution.The calculation results on the first-moment radius and second-moment radius of quasi-Airy beam show that the optical vortex can accelerate the beam center drift and the accelerating effect will be enhanced by increasing the topological charges while the beam spreading behavior of quasi-Airy beam is almost unaffected during propagation.4.The propagation properties of Airy beam in linear medium are studied in this work.The simulation results indicate that the propagation trajectories of Airy beam can be arbitrarily controlled through tuning medium's graded refractive index.Besides,the propagation properties of Airy beam in nonlinear Kerr medium and nonlinear nonlocal medium are investigated systematically.The simulation results show that the Airy beam can be evolved into non-spreading spatial solitons which result from the balance between linear effect and nonlinear effect when it propagates in nonlinear media.And the propagation states and trajectories of the formed solitons can be controlled arbitrarily by properly choosing the initial parameters.Lastly,the propagation dynamics of Airy beam in atmosphere turbulence are investigated by utilizing the phase mask method.The results indicate that scintillation effect of Airy beam in atmosphere turbulence will be enhanced when the transverse scale of the beam is increased.Moreover,the beam center drift of Airy beam is weaker than that of Guassian beam when they propagate in atmosphere turbulence.Therefore,it can be deduced that the Airy beam can acquire better anti-disturbance performance than Gaussian beam especially under complex transmission environment.5.The interaction dynamics of Airy beams and Airy-Gaussian beams in nonlinear Kerr medium are investigated firstly in this part.The results show that the breathing spatial solitons,bound states of solitons,etc.can be formed through the interactions among beams.And these soliton states can be modulated by adjusting the initial parameters of the beams and medium.It should be noted that the energy threshold of the Airy-Gussian beams to form the soliton states is much larger than that of Airy beam.Moreover,under some specific conditions such as “Same Phase Different Amplitude” and “Reversed Phase Same Amplitude” among incident beams,the breathing solitons can also be produced but hard to achieve the bound states.Besides,some types of specific soliton state such as breathing solitons with sinusoidal propagation trajectory or oscillating solitons with triangular propagation trajectory,etc.can be formed through interactions among beams in nonlinear nonlocal medium.Meanwhile,it is found that a new non-overlapping bound states of solitons can be formed when the beam amplitudes are the same and with inverse phases in nonlocal media.This newly proposed bound states of solitons have a novel spatial structure that differs from the common ones.