Numerical experiments on self-imaging effects generated by vortex Gaussian beams
[Objective]Due to the extensive application of self-imaging effects in different fields such as precise measurements,structured light illumination,high-resolution imaging,image processing,and other fields,studies on self-imaging effects,also known as the Talbot effects,have gradually expanded to various physical systems.In the field of optics,it has been theoretically predicted and experimentally demonstrated that self-imaging effects can be realized by using different types of structural beams.Meanwhile,optical beams carrying orbital angular momentum have significant applications in optical manipulation,optical imaging,quantum key distribution,and quantum entanglement.Propagation dynamics of vortex beams are a hotspot in optics research.Focusing on the formation of well-ordered spatial arrays of optical vortices,the effect of different optical vortices on the dynamic behavior of periodic beam evolution would offer novel ideas and ways to systematically understand the evolution dynamic behaviors of vortex beams and the realization of novel structural beams.[Methods]Herein,theoretical and numerical investigations on the propagation dynamics of three different types of vortex Gaussian beams are performed.Classical optical vortex beams,asymmetric power-law optical vortices,beams and symmetric power-law optical vortices beams are considered.Both the intensity distribution and self-imaging distance of transverse periodic Gaussian beams are determined based on the Fresnel diffraction integral theorem.Afterward,the above three types of vortex phases imposed on the initial transverse periodic Gaussian beams are considered,which are chosen as the input beams to directly solve the two-dimensional paraxial wave equation numerically by using the beam propagation method.The dynamic behavior of beam energy evolution is obtained.In addition,the light field distribution is examined in detail,and its self-imaging distance is determined.Comparison of the theoretical and numerical results is performed.[Results]The focus is on the dynamics of three types of optical vortex Gaussian beams modeled by the two-dimensional paraxial wave equation.The simulation results reveal that:1)All three types of optical vortex Gaussian beams can produce integer and fractional self-imaging effects,where the optical field is periodically self-imaged along a straight trajectory during propagation,and the field pattern of the fractional self-imaging effects shows a half-period shift along the transverse direction.2)The self-imaging distance of the three kinds of optical vortex Gaussian beam is measured by the reproducing distance of the self-imaging phenomenon generated by the transverse periodic Gaussian beam.3)The vortex phases for the three optical vortex Gaussian beams are still basically unchanged during the propagation.[Conclusions]The light field structure on the self-imaging plane is composed of well-ordered two-dimensional annular beamlet arrays with ring-shaped fields for all the Talbot planes.The intensity distribution on the self-imaging planes is closely associated with the topological charge and power exponent order of the vortex phase and suffers from some distortions resulting from the weak intensity at the center of the incident beam.For the three types of optical vortex Gaussian beams,the array beam demonstrates various field strength distributions of circular,spiral,and petal shapes.However,the vortex phases for all optical vortex Gaussian beams can remain constant during long propagation distances.According to this principle and method,further research is warranted on the self-imaging effects produced by other structure beams,such as power exponent fractional order optical vortices beams and non-Gaussian periodic beams.
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