Experimentally Generation And Measurement Of Vortex Beams With Orbital Angular Momentums

The vortex beam is a special light field with a phase structuref(r,j)=exp(ilj),in which j is the azimuth angle and l is called the topological number.The optical amplitude is zero in the central region of the beam,and the wavefront is spiral.It is an important research branch of modern singularity optics.The beam structure of the vortex beam has a series of special physical properties,such as a circular distribution of intensity,a small central dark spot size,no heating effect,no diffraction effect,etc.One of the most important features is that during the forward propagation of the beam,each photon around the optical axis carries a photon orbital angular momentum(OAM)quantum number associated with the helical phase structure.Compared with the traditional Gaussian beam,the vortex beam has a wide application due to its spatial field distribution has one more dimension,so it has a wide range of applications in laser optics,photo-photography,optical communication,optical imaging,atomic,molecular,and cold atomic systems.This paper studies the generation and a series of characteristics of vortex beams with OAM.The main research contents are as follows.(1)A novel interference method for vortex beam OAM detection: Although OAM beams have a helical phase structure,we can only observe a ring structure on intensity profiles.Therefore,OAM detection of vortex beams has become an important and necessary technology.From these,we propose a new method to detect the OAM of vortex beams using interferometry,the basic principle is due to the incomplete modulation of the reflective phase-type spatial light modulator(SLM).It has been experimentally found that when a spatial light modulator is used to generate a vortex beam,coaxial interference can occur directly only by the modulated vortex beam and the incident Gaussian beam which is not fully modulated,thereby producing perfect petal-like interference pattern.The number of interfering petals coincides with the value of the orbital angular momentum carried by the modulated vortex beam,and thus a separate reference beam are not required when detecting the orbital angular momentum of the vortex beams produced by the spatial light modulator.We experimentally analyzed the interference pattern of Bessel-Gaussian beam,Laguerre-Gaussian beam with integer orbital angular momentum,and the interference pattern of vortex beam with fractional OAM.The interference pattern structure not only reflects the size and sign of the OAM of the vortex beam,but also reflects the radial factor of the LaguerreGaussian beam and the evolution of the helical phase structure of the fractional OAM beam.The light path is simple,the interference mode is clear and stable,and the symmetry is high.(2)Experimental generation and research of focused vortex beam:This letter reports the generation of a focusing vortex beam(FVB)by using the hybrid hologram with a spire phase and a lens phase imprinting on a SLM.We study the intensity distributions of the FVB in free propagation space,as well as the relationship between the waist w0 of the incident Gaussian beam(or the focal length f of the lens)and the dark sport size(DSS)at the focal point.The OAM of the FVB is then measured based on the above interferometric method.We studied the characteristics of interference patterns,including intensity distribution,phase structure,and phase plate structure.In addition,the relationship between the DSS of the FVB and the OAM quantum number at different propagation distances is also analyzed.Such a laser beam can be used to guide and focus the molecular beam and form a molecular lens.Based on the above research,we propose a scheme for constructing a crossed focusing vortex beam by vertically propagating two focused vortex beams and converge them at a focal plane.This beam we produce not only has a very small local hollow confinement volume,but also has OAM,and the confinement volume can be adjusted by changing the quantum number of the OAM.Such a strongly focused optical potential well can be used for dipole trapping of cold atoms(molecules),and has important application prospects even in further optical potential evaporative cooling or further narrowing the size of the well to achieve the trapping of a single molecule.The above is the main research of this paper,including experimental and theoretical research on the generation,detection and focusing of vortex beams.