Propagation characteristics of non-diffracting Lommel beams in a gradient-index medium

Abstract

We investigate the propagation of the Lommel beams in a gradient-index medium. Based on the ABCD transfer matrix and Collins diffraction integral formula, the analytical expressions of the complex amplitude of the Lommel beams through the gradient-index medium are derived. The intensity distribution and the Poynting vector of the Lommel beams are studied analytically and numerically. The results show that the Lommel beam is focused at the singularities and the corresponding periodic beam profile is induced by the symmetrical refractive index pattern during the beam propagating in the gradient-index medium. The effects of the asymmetry factor and the topological charge on the propagation characteristics of the Lommel beams in the gradient-index medium are discussed in detail. Especially, the propagation trajectories of the Lommel beams become visible as the topological charge increases and the symmetry of the Lommel beam’s transverse intensity pattern can be controlled by varying the asymmetry factor. It is expected that the results obtained in this paper may be useful for potential applications of optical control and trapping.