Generation And Characteristics Of Vector Ince-Gaussian Beam

The inseparability of space and polarization degrees of freedom is one of the important characteristics of the complex vector light field.The non-uniformity of the lateral polarization distribution and the infinite dimensions of the space degrees of freedom can be used in particle manipulation,multi-free metric storage,and quantum Key distribution coding and other fields have a wide range of potential applications.However,in the application research of traditional vector light field,the cylindrical symmetrical vector beam is usually adopted.This single-level research limits the dimension of light field in a certain extent,and increases the research cost.For the generation of complex vector light fields,spatial light modulators that are only sensitive to laterally polarized light are often used as modulating devices,and the resulting vector beams are unstable and easily jittered.In view of the above problems,this paper proposes the use of the eigen-solution of the wave equation in the elliptical coordinate system,that is,the Ince-Gaussian(IG)beam,to construct an elliptical vector beam.By adjusting the characteristic parameters of the ellipse,the flexible switching of different dimensions among the cylindrical coordinate system,the elliptical coordinate system and the rectangular coordinate system can be realized.Based on the Digital Micromirror Device(DMD)with no polarization selectivity,a high-quality vector IG beam is generated.With the help of the Poincaré sphere,the polarization properties of the vector IG beam are explored and characterized.First,the solutions of the paraxial wave equation in cylindrical,elliptic and Cartesian coordinates are introduced,namely Laguerre-Gaussian(LG),IG and Hermite-Gaussian(HG)beam theoretical model,designed to provide theoretical support for the following research content;according to the characteristics of DMD '0'and '1' modulation,a binary amplitude digital hologram was prepared.Secondly,a vector characterization model with odd and even mode IG modes as the base vector is constructed,and a vector IG beam is generated based on the DMD;the polarization state distribution characteristics on the Poincaré sphere are explored,observe the change of the intensity and polarization of the vector IG beam as the ellipse characteristic parameter ? increases,the root-mean-square error of the polarization direction and saturation between the generated vector IG beam and the theoretical results is quantitatively analyzed,and the entanglement parameter C between the vector base vectors is calculated,and the indivisibility of the vector is studied.The accuracy of vector beam generated based on DMD is verified.Finally,we propose a new method of the generation of vector IG beams based on the coefficient synthesis method,realizing the direct generation of vector IG beams from LG or HG beams.It reveals more potential applications of physics research.Based on the coefficient synthesis method,a vector HIG beam with vortex characteristics is generated.