Abstract
Based on the 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 on the properties of beam propagation in a gradient-index medium is discussed in detail. The result shows that the beam is focused at () 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.
© 2019 Optical Society of America
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