Intrinsic orbital angular momentum of paraxial beams with off-axis imprinted vortices

Abstract

We investigate the orbital angular momentum (OAM) of paraxial beams containing off-axis phase dislocations and put forward a simple method to calculate the intrinsic orbital angular momentum of an arbitrary paraxial beam. Using this approach we find that the intrinsic OAM of a fundamental Gaussian beam with a vortex imprinted off axis has a Gaussian dependence on the vortex displacement, implying that the expectation value of the intrinsic OAM of a photon can take on a continuous range of values (i.e., integer and noninteger values in units of h). Finally, we investigate, both numerically and experimentally, the far-field profiles of beams carrying half-integer OAM per photon, these beams having been created by the method of imprinting off-axis vortices.

Nonclassicality of vortex Airy beams in the Wigner representation

“…The shapes of the WDFs are different from that of an on-axial vortex superimposed on a Gaussian beam [12,17]. This suggests that a vortex located at the origin of an Airy beam is not purely in a single angular momentum state, but a superposition of many various vortex states [16,30,31]. At other positions of the beam, the WDFs become asymmetric due to the superposition of the Airy beam with the vortex.…”

Phase contrast enhancement in microscopy using spiral phase filtering

“…This leads to a shadow effect similar to the one obtained with the above method. There is a phase factor in the non-vortex term whose value depends on the position of the singularity of the SPP [17,18]. By shifting the spiral phase filter one can change the phase difference between the two interference terms and therefore the position of the vortex core, which determines the degree and orientation of the shadow appearance in the output.…”

Orbital angular momentum in noncollinear second-harmonic generation by off-axis vortex beams

“…The output momentum thus results smaller, following the Gaussian law presented in ref. [21] Q*exp(-2 r v 2 /w 0 2 ), where Q is the topological charge impressed by the device, r v is the displacement and w 0 the spot size of the incident beam. In this way the OAM can be tuned to a well defined value.…”