A theoretical study of the Fresnel diffraction of Laguerre-Bessel-Gaussian beam by a helical axicon

Based on the Fresnel diffraction integral formula, the diffraction of Laguerre-Bessel-Gaussian (LBG) beam by a helical axicon is investigated. The expressions of the amplitude and the intensity distributions of the diffracted wave field are derived analytically by using the stationary phase method. Numerical examples are given to illustrate the variation of the intensity in radial and longitudinal directions versus the parameters of the incident LBG beam and the topological charge of the helical axicon. The results provide more general characteristics and diffraction by a helical axicon of Laguerre-Gaussian beam, Bessel-Gaussian beam and fundamental Gaussian beam are deduced as particular cases of this study.