Generation And Optical Properties Of Diffraction Free Helical Mathieu Beams

Diffraction is the transmission nature of light that makes the beam to diffuse on propagation.In practical science and technology,a beam that can keep its shape stable in the process of free space propagation is necessary.The concept of non-diffractive beam provides guidance for the stable transmission of beams.The essence of non-diffracted beam is a particular solution of wave equation.By solving the wave equation in different coordinate system,such as Cartesian coordinate system,polar coordinate system,elliptic coordinate system,and parabolic coordinate system,four kinds of non-diffracted beams are obtained accordingly,namely harmonic beam,Bessel beam,Mathieu beam,and parabolic beam respectively.With different orders,the light field distribution of non-diffracting beams is also different,and Bessel beams and Mathieu beams can be divided into zero-order Bessel beams,higher-order Bessel beams,zero-order Mathieu beams,and higher-order Mathieu beams.Non-diffraction beams are widely used in laser drilling,laser precision collimation,optical precision control,optical micro-control,optical communication,plasma steering,optical bullet generation,optical communication,self-focusing beam synthesis,and nonlinear optics.High-order Mathieu beam is also called helical Mathieu(HM)beams because of its helical wavefront.HM beams can be described as a non-diffracting solution of the Helmholtz equation in elliptical cylindrical coordinates and carrying orbital angular momentum(OAM).It is one of the main research directions in the field of beam propagation to control the distribution shape of light field by changing the order and ellipticity.In this thesis,a new method to generate HM beams experimentally through theoretical analysis.In addition,by using the Fourier transform property of HM beam to generate a perfect helical Mathieu vortex(PHMV)beam that with radius independent of topological charge value.The paper mainly consists of four parts:(1)Based on the stationary phase method,a new method to generate HM beam is proposed through theoretical analytical,By using the complex amplitude modulation method,HM beams of different order and ellipticity are generated experimentally.The new method has high light energy utilization efficiency and high beam quality.The experimental results agree well with the theoretical results,which is proves the effectiveness of the new method.(2)The OAM and orthogonality of HM beams are theoretically researched.The research results show that the OAM of HM beams is fractional order continuously adjustable,hence the HM beams will have wider applications than classical Bessel beams since their OAM can be flexibly adjusted.Moreover,for any two HM beams have great orthogonality when their topological charge value or scale factors are not equal.(3)By using the generation mechanism of perfect vortex beam,the Fourier transform property of HM is used to generate the PHMV beam,and the predicted experimental results are obtained.Different from the traditional perfect vortex(PV)beam,the PHMV beams has a fixed circle radius with different charge and the light field distribution is also controlled by changing the order and the ellipticity as well as the HM.