Fractional vortex light has fractional topology charge

unique radial gap

and relatively many control parameters

which has attracted much attention recently.Based on the diffraction integral theory

the light field expression of fractional order vortex light is derived in the paper.In addition

simulation is conducted on the light intensity distribution and phase distribution with MATLAB.The simulation results show that the radial gap size is related to the decimal part of topological charge value.To be specific

when the decimal part of topological charge value is closer to half integer

the radial gap is more obvious.Moreover

with the increase of the integer part of topological charge

the light spot radius increases.In this paper

a variety of vortex light with topological charge being half integer is produced through reflective type of liquid crystal spatial light modulator.The transmission light spot collected by CCD is consistent with the simulation results of the paper.