The transition of the vortex structure of fractional elegant Laguerre-Gaussian beams is discussed in detail as the angular mode index of the beam is continuously varied between integer values. Under this kind of variation, the vortices can be classified into five groups. Contrary to the behavior of the vortices of the nondiffracting Bessel beams of fractional order, the nodal lines of the vortices in the case of the fractional eLG beams exhibit intricate shapes.
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