Observation of the vortex structure of a non-integer vortex beam

TLDR

An optical beam with an \(e^{i\ell\phi}\) phase structure carries \(\ell\hbar\) of orbital angular momentum per photon; for integer \(\ell\) the phase fronts form perfect helices with a single vortex on the axis, whereas Berry predicts that non‑integer \(\ell\) produces a complex phase containing multiple vortices across the beam. We generate \(e^{i\ell\phi}\) beams with a spatial light modulator for various \(\ell\) values and analyze their phase structure after propagation using an interference‑based phase‑measurement technique. For half‑integer \(\ell\), we observe a line of alternating‑charge vortices near the radial dislocation, confirming Berry’s prediction.

Abstract

An optical beam with an eilϕ phase structure carries an orbital angular momentum of lℏ per photon. For integer l values, the phase fronts of such beams form perfect helices with a single screw-phase dislocation, or vortex, on the beam axis. For non-integer l values, Berry (2004 J. Opt. A: Pure Appl. Opt. 6 259) predicts a complex-phase structure comprising many vortices at differing positions within the beam cross-section. Using a spatial light modulator we produce eilϕ beams with varying l. We examine the phase structure of such beams after propagation through an interference-based phase-measurement technique. As predicted, we observe that for half-integer l values, a line of alternating charge vortices is formed near the radial dislocation.