Optical vortices evolving from helicoidal integer and fractional phase steps

The evolution of a wave starting at z = 0a s exp(iαφ) (0 φ 0as trength n optical vortex, whose neighbourhood is described in detail. Far from the axis, the wave is the sum of exp{i(αφ + kz)} and a diffracted wave from r = 0. The paraxial wave and the wave far from the vortex are incorporated into a uniform approximation that describes the wave with high accuracy, even well into the evanescent zone. For fractional α ,n o fractional-strength vortices can propagate; instead, the interferenc eb etween an additional diffracted wave, from the phase step discontinuity, with exp{i(αφ + kz)} and the wave scattered from r = 0, generates a pattern of strength-1 vortex lines, whose total (signed) strength Sα is the…

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