The Ray Model Of Structured Gaussian Beam And Its Application

Because of rich phase information and light intensity distribution,structured Gaussian beams are widely used in micro imaging,information transfer,particle manipulation and other fields.At present,the structured Gaussian beams which have been confirmed by experiments include Hermite-Gaussian beams,Laguerre-Gaussian beams,Hermite-Laguerre-Gaussian beams and Ince-Gaussian beams.Hermite-Gaussian beam and Laguerre-Gaussian beam are well-known structured Gaussian beams in laser science.Their light field distribution can be separated in rectangular coordinate and cylindrical coordinate respectively.Hermite-Laguerre-Gaussian beam is a kind of Gaussian mode between Hermite-Gaussian beam and Laguerre-Gaussian beam.In the experiment,the Hermite-Laguerre-Gaussian beam is obtained by transforming Hermite-Gaussian beam or Laguerre-Gaussian beam using pairs of cylindrical lenses.Ince-Gaussian beam is also a kind of Gaussian mode between Hermite-Gaussian beam and Laguerre Gaussian beam,which is different from Hermit-Laguerre-Gaussian beam in that its light field distribution can be separated in elliptic coordinate system.The above-mentioned structured Gaussian beams have been studied a lot.Therefore,the structured Gaussian beams outside these beam categories have aroused our interest.In 2017,M.A.Alonso and M.R.Dennis et al.proposed ray-optical Poincare sphere for structured Gaussian beams.The model reproduces Hermite-Gaussian beam and Laguerre-Gaussian beam successfully,and gives the ray characterization of these beams,the transmission mode of light field along the rays and the reconstruction method of light field.In addition,the model reveals the geometric relationship between the Poincare equatorial disks path and the caustics(the outer envelope of the light field distribution)of the structured Gaussian beam,which provides a novel visualization method for studying the designing and transmission of the structured Gaussian beam.In a word,the ray model not only describes the structure Gaussian beam such as Hermite-Gaussian beam and Laguerre-Gaussian beam successfully,but also opens the door to design new structured Gaussian beam.Based on the ray model proposed by M.A.Alonso and M.R.Dennis,new polygonal structured Gaussian beams,including octagonal structure and hexagonal structure,are constructed in this paper.The influence of relevant parameters on the field distribution of the two beams is studied,and their phase singularity characteristics are discussed.The innovation points and main work of this paper are as follows:1.The PED path of octagonal structured Gaussian beam is solved.Based on the geometric relationship between the PED path and the caustics,the PED path of the octagonal Gaussian beam is obtained by the combination of caustics.This method is not only useful for the octagonal structured Gaussian beam,but also suitable for other polygonal structured Gaussian beam.2.The problem of ill-definition of Maslov phase is solved when constructing hexagonal structured Gaussian beam.In the process of constructing hexagonal structured Gaussian beam by analogy with octagonal Gaussian beam,the problem of ill-definition of Maslov phase is encountered,which hinders the construction of hexagonal structured Gaussian beam.By making the rectangular PED path of octagonal structured Gaussian beam approach to the triangular PED path of hexagonal structured Gaussian beam,the Maslov phase is redefined,and the hexagonal structured Gaussian beam is successfully simulated.This method is also applicable to other other polygon with 4N+2 edges that may lead to this problem.3.The octagonal and hexagonal structured Gaussian beams are successfully constructed,and the simulation results are analyzed.The transverse field distribution,phase distribution and phase singular distribution under different parameters,such as propagation distance z,quantum numbers N,?,are simulated respectively,and the effects of these parameters on the distribution are discussed.Because octagonal structured Gaussian beam and hexagonal structured Gaussian beam is constructed using Laguerre-Gaussian expansion,and the Laguerre-Gaussian mode is the stable transmission mode in optical fiber,which promises potential realization in fiber.