Research On The Propagation Dynamics Of The Special Beams In Different Media

Special beams have become a focus in the optics domain due to their unique properties and different applications in many fields.The dynamic behavior of special beams in different media and systems has been particularly concerned by researchers.This paper mainly studies the propagation dynamics and control methods of special beams in different media or systems.In Chapter 3,based on the fractional Schr(?)dinger equation with a variable coefficient(VFSE),we analytically and numerically investigate the propagation dynamics of the Gaussian beam.In the absence of the beam's chirp,for smaller Lévy index,the Gaussian beam splits into two beams;however,under the action of the longitudinal periodic modulation,they exhibit a periodically oscillating behaviour.In the presence of the beam's chirp,one of the splitting beams is gradually suppressed with the increasing of the chirp,while another beam in the opposite direction becomes stronger and exhibits a periodically oscillating behaviour.The results show that the oscillating amplitude is dependent on the modulation frequency,the Lévy index and the beam's chirp.Thus,by controlling the system parameters and the chirp parameter the evolution of the Gaussian beam can be well manipulated to achieve the beam management in the framework of the VFSE.In addition,the dynamic behavior of Airy beam in the fractional system is also studied,and is compared with that of Gaussian beam.In Chapter 4,based on a reduction of the nonlocal nonlinear Schr(?)dinger equation in strongly nonlocal regime — the linear Schr(?)dinger equation with parabolic potential,analytical results describing the evolution of dual Airy beam are presented.The results show that the dual Airy beam in a strongly nonlocal medium exhibits a periodic focusing and defocusing behavior and forms the interference fringes between the focusing and defocusing positions.By numerically solving the nonlocal nonlinear Schr(?)dinger equation under strongly nonlocal regime,we find that theoretically obtained analytical results are valid in actual physical systems.Furthermore,the characteristics of the interference fringes induced by the dual Airy beam are also investigated in detail and can be used for the measurement of the system parameters.Finally,we propose a method of generating dual Airy beam in strongly nonlocal medium.In Chapter 5,based on potential-free linear Schr(?)dinger equation,we investigate the dynamics of one-dimensional and two-dimensional finite energy Pearcey beam in free space,respectively.For 1D case,the results show that the one-dimensional Pearcey beam splits into two Airy-like beams that accelerate along the opposite direction,which results in Dual self-accelerating behavior of the Pearcey beam.For 2D case,the results show that the two-dimensional Pearcey beam first focuses toward the center,then begins to diffuse around.During the diffusion,the intensity on the outermost ring is always dominant,and finally forms a cone pattern,which is completely different from the free diffusion of Gaussian beams.The results in this paper are helpful to better understand the dynamics of the special beams,and provide theoretical guidance for beam manipulation.It is expected that part of the results of this paper can be used for system parameter measurement and beam generation.