Research On Diffraction Of Laser Vortex Beams And Partially Coherent Light Based On The Method Of Orbital Angular Momentum Eigenmode Decomposition

Over the last two decades,vortex beams,which carry an orbital angular momentum(OAM),have attracted great interest due to their characteristic properties and far-ranging applications.In this paper,based on the method of OAM eigenmode decomposition,we theoreticaly and experimentally study the diffraction of laser vortex beams with a triangular aperture and angular diffraction of partially coherent light.First,from the angle of modal decomposition,our method provides an intuitive physical picture to understand the diffraction of laser vortex beams,where the constituent Laguerre-Gaussian(LG)modes propagate independently from the initial-field plane and contribute cooperatively to form diffraction patterns at any desired plane.In experiment,a phase-only spatial light modulator(SLM)is used to display a holographic grating for generating vortex beams and a diffraction aperture.Without loss of generality,we take a triangular aperture as an example to study the diffraction behavior of a vortex beam with l?3 from the near-field to far-field regions.We observe the gradual formation of triangular optical lattices arrays as the light beams propagate,and demonstrate the relationship between optical lattices in the far-field diffraction patterns and topological charges of laser vortex beams.Although we only investigate the cases of a specific LG mode as the incident light diffracted by an aperture of specific shape,in principle,our method can be applied to the situations,where any incident light beams of arbitrary intensity or phase profiles are diffracted by apertures of arbitrary shape.Moreover,under the condition of a known input twisted beam,the method may also be used to estimate the propagation distance and the rotational symmetry of the aperture for a given diffraction pattern,which may be very useful in OAM-based optical remote sensing.Angular position and angular momentum,a pair of conjugate variables,are linked by a Fourier transformation The OAM sidebands,which is enveloped by a sinc2 function,are generated on the transmitted light owing to the restriction of the angular range within a light beam profile.In the second work of this paper,we investigate the influence of light's coherence on OAM spectrum of angular diffraction According to modal decomposition and Mercer's theorem,we represent cross-spectral density of partially coherent light by OAM eigen states exp(il?),leading to obtain the OAM spectrum.In experiment,we use digital micro-mirror device(DMD)to manipulate spatial coherence widths of light to study the effect of spatial coherence on modulation mechanism and rules for angular diffraction.And a SLM is used to display angular masks with single and multiple slits.We experimentally obtain different kinds of OAM spectra,which are generated by angular diffraction of partially coherent light.Numerical and experimental results show that the OAM spectrum becomes more flat and the contrast decreases as the spatial coherence width of light decreases.Our approach may provide a new perspective to study the Fourier relation and uncertainty principle for angular position and angular momentum with partially coherent light beams.