Shaping optical beams with non-integer orbital-angular momentum: a generalized differential operator approach.

We introduce an analytical procedure to construct an optical beam with an arbitrary value of orbital-angular momentum (OAM) by keeping the flexibility of shaping its transverse intensity distribution without changing its OAM. We apply the general theory of fractional differential operators in Fourier domain to derive general expressions for the OAM content in the beam and find the relevant parameters that determine its OAM value and those that can be freely modified without affecting it.

Vortex structure of elegant Laguerre-Gaussian beams of fractional order.

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.