Propagation of a Bessel-Gaussian beam in a gradient-index medium.

Based on the ABCD matrix method and Collins diffraction integral formula, analytical expression for Bessel-Gaussian beam propagation in a gradient-index medium is derived. The propagation trajectory, intensity, and phase distributions of the zeroth-order, second-order, and superposition cases are numerically investigated. The effect of beam waist radius w on the properties of beam propagation in a gradient-index medium is discussed in detail. The result shows that the beam is focused at z/L=N/2 (N=0,1,2,…) and propagates periodically in the medium. Evolution of the vortical structure of the superposed Bessel-Gaussian beam is investigated, showing that the superposed beam forms new singularities, and the rotation of the beam occurs mainly near the singularities.