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Optics Letters

Information content of optical vortex fields

Ashok Kumar, Shashi Prabhakar, Pravin Vaity, Ravindra Pratap Singh

Published Mar 25, 2011• 28 citations
Publisher

Abstract

We study, experimentally as well as theoretically, the spatial coherence function and the Wigner distribution function for one-dimensional projections of optical vortices of different orders. The information entropy derived from the spatial coherence functions has been used to quantify the information content of the vortices and compared with those obtained for the Gaussian beam. The experimental results verify the theoretical findings of Agarwal and Banerji [Opt. Lett. 27, 800 (2002)].

DOI
10.1364/ol.36.001161

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We study, experimentally as well as theoretically, the spatial coherence function and the Wigner distribution function for one-dimensional projections of optical vortices of different orders. The information entropy derived from the spatial coherence functions has been used to quantify the information content of the vortices and compared with those obtained for the Gaussian beam. The experimental results verify the theoretical findings of Agarwal and Banerji [Opt. Lett. 27, 800 (2002)].
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Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for parameter estimation and sensing. Here we introduce Fisher information as an operational metric to assess the metrological content of structured optical fields. By treating the measured intensity distribution as a statistical object, we define Fisher information with respect to physically relevant parameters, such as transverse displacement. We demonstrate that optical modes with comparable Shannon entropy can exhibit markedly different Fisher information, revealing sensitivity features associated with nodal structure and local curvature. Using Hermite--Gaussian modes as minimal test cases, we show that increasing modal order systematically enhances Fisher information. We then extend the analysis to two widely used families in structured light: Laguerre--Gaussian vortex beams and finite-energy Bessel--Gauss beams. Across these representative families, Fisher information provides a unified and experimentally accessible criterion for comparing structured optical fields in sensing applications.
Optical vortices became a hot topic since almost two decades ago, when it was recognized that Laguerre-Gaussian laser modes carry orbital angular momentum [Allen et al. Phys Rev A 45, 8185 (1992)] related with a screw phase dislocation, and different from the spin angular momentum associated to circular polarization. In 1995, this dynamical quantity was transferred to matter in an optical micromanipulation system for the first time [H. He, et al., Phys. Rev. Lett. 75, 826 (1995)], and since then, a number of studies on angular momentum of light have unveiled different interesting aspects on the subject. However, there are still open questions, which have arisen together with the generation of novel light beams, such as vector vortices, for instance. In contrast with scalar vortices, with usual polarization states (linear, circular, elliptical), the orientation and magnitude of the electric field of vector vortices (solutions of the vector wave equation) is a function of space and time. In this work, we present an experimental study of the local angular momentum density of a Bessel vector vortex of first order by means of an optical trap. For this purpose, we used different probe particles in order to sense the local contribution to the optical angular momentum in each region of the beam. But optical fields are not the only wave fields that may exhibit phase dislocations or singularities. There are close analogies between light and sound fields that can be exploited in order to get a better understanding of common phenomena and study new aspects in both branches of physics. Here we also present the first experimental demonstration and theoretical analysis of acoustical vortices in free field, with similar properties to those of the optical vortices, including the angular momentum that can be transferred to matter. The corresponding analogies and differences with the optical case turn out to be very enlightening for the understanding of the phenomenon of angular momentum in wave fields.