Abstract
The study and application of optical vortices have gained significant prominence over the last two decades. An interesting challenge remains the determination of the azimuthal index (topological charge) ℓ of an optical vortex beam for a range of applications. We explore the diffraction of such beams from a triangular aperture and observe that the form of the resultant diffraction pattern is dependent upon both the magnitude and sign of the azimuthal index and this is valid for both monochromatic and broadband light fields. For the first time we demonstrate that this behavior is related not only to the azimuthal index but crucially the Gouy phase component of the incident beam. In particular, we explore the far field diffraction pattern for incident fields incident upon a triangular aperture possessing non-integer values of the azimuthal index ℓ. Such fields have a complex vortex structure. We are able to infer the birth of a vortex which occurs at half-integer values of ℓ and explore its evolution by observations of the diffraction pattern. These results demonstrate the extended versatility of a triangular aperture for the study of optical vortices.
Highlights
In 1992 Allen et al [1] recognized that certain optical fields may carry an angular momentum in addition to that associated with photon spin
The triangular aperture is even more flexible in that it can reveal both the magnitude and sign of the azimuthal index using the orientation of the intensity pattern [10]. This begs the question of the physical origin of the 180◦ rotation of the intensity pattern upon reversing the sign of the azimuthal index, and here we provide an answer to this question by demonstrating that the 180◦ rotation may be traced to the Gouy phase-shift
This is the main result of this analysis, and it explains the fact that diffraction of a optical vortex core from a polygonal aperture in general depends upon the sign of the azimuthal index, and exposes that this dependence stems from the Gouy phase-shift, giving new physical insight into this problem, compared to previous studies [10]
Summary
In 1992 Allen et al [1] recognized that certain optical fields may carry an angular momentum in addition to that associated with photon spin. Such light fields have been the subject of intense study and potential ground-breaking applications over the last fifteen years In particular they have found significant application in the fields of optical micromanipulation [3, 4, 5] where they may set microscopic particles into rotation, trapped low refractive index particles and created micropumps. A key issue is the simple, direct measurement of the orbital angular momentum content of the light field. As an example this has been achieved using two slit interferometry. Experimental studies have been performed using interference [14, 15], observation of the diffraction pattern from our triangular aperture offers a very simple route for exploration of this topic and we can deduce the birth and evolution of a vortex within the light field incident upon the triangular aperture
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