Study On The Diffraction Characteristics Of Vortex Beam

The vortex beam is a kind of beam with a spiral phase factor exp(ilθ),where l is the topological charge,which can take any integer value.Due to the special phase structure,a vortex beam with l≠0 has a hollow intensity distribution and a well-defined orbital angular momentum equal to lh per photon.Theoretically,vortex beams can carry any mode of orbital angular momentum(OAM),and OAM modes of different topological charges are orthogonal to each other.Until now,owing to these exotic properties,vortex beams have been applied in various applications ranging from laser communication,laser remote sensing,microscopy and biological manipulation.In many applications,diffraction usually occurs when a vortex beam passes through optical elements such as apertures and lenses.And there is scattering of a vortex beam by particles as it travels through the atmospheric channel.In this thesis,we systematically investigate the diffraction and scattering properties of vortex beams by considering Laguerre-Gaussian(LG)modes,which are typical vortex beams.In this thesis,based on the Fresnel diffraction integral,the expression of the diffraction field distribution of a LG beam by shaped apertures is derived.We analyze the result theoretically and show that the topological charge of a vortex beam diffracted by a circular aperture remains invariant.The diffraction patterns of LG beams through several shaped apertures,including square aperture,triangular aperture,circular aperture and circular screen,are systematically studied.The relationship between the number of spots in the square and triangular diffraction patterns and the topological charge is summarized.It is found that the intensity distribution of the diffracted LG beam through a circular screen is characterized by concentric rings around a dark center.With the increasing topological charge,the radius of the central bright ring increases,but the number of bright rings remains the same,the external ring becomes darker,and eventually,the central ring covers the external one.We also demonstrate the OAM dispersion of the diffracted LG beam by the spiral spectrum.It is shown that polygonal apertures can break the spiral phase structure of LG beams to varying degrees,leading to the OAM dispersion of diffracted light,while rotationally symmetric apertures,such as circular aperture and circular screen,do not affect the singularity and stability of the OAM carried by vortex beams.Such results provide a theoretical basis for the rational selection of optical elements in the design and construction of laser communication systems with vortex beams.In this thesis,we also investigate the scattering of an on-axis incident LG beam by a homogenous spherical particle based on the generalized Lorenz-Mie theory.The expressions of the beam shape coefficients for LG beams in spherical coordinates are derived by using the finite series method,which has high accuracy and computational efficiency.The effects of the topological charge of the incident LG beams,the radius and refractive index of the particles on the differential scattering cross section and scattering intensity are systematically analyzed.And the transverse amplitude distribution,phase distribution and OAM dispersion of the scattered far field are studied.The obtained results indicate that the hollow amplitude distribution of a scattered LG beam diverges in the diagonal direction,while a new phase singularity is generated at the same position.The OAM carried by the LG beam is dispersed.Such results provide theoretical support for the rational selection of vortex beams with different topological charges in laser communication.