The orbital angular momentum of light represents a fundamentally new optical degree of freedom. Unlike linear momentum, or spin angular momentum, which is associated with the polarization of light, orbital angular momentum arises as a subtler and more complex consequence of the spatial distribution of the intensity and phase of an optical field — even down to the single photon limit. Consequently, researchers have only begun to appreciate its implications for our understanding of the many ways in which light and matter can interact, or its practical potential for quantum information applications. This article reviews some of the landmark advances in the study and use of the orbital angular momentum of photons, and in particular its potential for realizing high-dimensional quantum spaces.Peer ReviewedPostprint (published version

We put forward schemes to prepare photons in multi-dimensional vector states of orbital angular momentum. We show realizable light distributions that yield prescribed states with finite or infinite normal modes. In particular, we show that suitable light vortex-pancakes allow the add-drop of specific vector projections. We suggest that such photons might allow the generation of engineered quNits in multi-dimensional quantum information systems.

In this Letter, we show that the electromagnetic duality symmetry, broken in the microscopic Maxwell's equations by the presence of charges, can be restored for the macroscopic Maxwell's equations. The restoration of this symmetry is shown to be independent of the geometry of the problem. These results provide a tool for the study of light-matter interactions within the framework of symmetries and conservation laws. We illustrate its use by determining the helicity content of the natural modes of structures possessing spatial inversion symmetries and by elucidating the root causes for some surprising effects in the scattering off magnetic spheres.

Kerr black holes are among the most intriguing predictions of Einstein's general relativity theory 1,2 . These rotating massive astrophysical objects drag and intermix their surrounding space and time, deflecting and phase-modifying light emitted near them. We have found that this leads to a new relativistic effect that imprints orbital angular momentum on such light. Numerical experiments, based on the integration of the null geodesic equations of light from orbiting point-like sources in the Kerr black hole equatorial plane to an asymptotic observer 3 , indeed identify the phase change and wavefront warping and predict the associated light-beam orbital angular momentum spectra 4 . Setting up the best existing telescopes properly, it should be possible to detect and measure this twisted light, thus allowing a direct observational demonstration of the existence of rotating black holes. As non-rotating objects are more an exception than a rule in the Universe, our findings are of fundamental importance.In curved spacetime geometries, the direction of a vector is generally not preserved when parallel-transported from one event to another, and light beams are deflected because of gravitational lensing. If the source of the gravitational field also rotates, it drags spacetime with it, causing linearly polarized electromagnetic radiation to undergo polarization rotation similar to the Faraday rotation of light in a magnetized medium. This is known as the gravitational Faraday effect 5 . As a result of the rotation of the central mass, each photon of a light beam propagating along a null geodesic will experience a well-defined phase variation. As a result, the beam will be transformed into a superposition of photon eigenstates, each with a well-defined value sh of spin angular momentum and h of orbital angular momentum 6 . Patterns drawn by such beams experience an anamorphosis 7 with polarization rotation due to the gravitational Faraday effect, accompanied by image deformation and rotation due to the gravitational Berry phase effect 8,9 . Hence, light propagating near rotating black holes experiences behaviour analogous to light propagating in an inhomogeneous, anisotropic medium in which spin-to-orbital angular momentum conversion occurs 10 .Whereas the linear momentum of light is connected with radiation pressure and force action, the total angular momentum J = S + L is connected with torque action. The spin-like form S, also known as spin angular momentum (SAM), is associated with photon helicity and hence with the polarization of light. The second form, L, is associated with the orbital phase profile of the beam, measured in the direction orthogonal to the propagation axis, and is also known as orbital angular momentum (OAM). This physical observable, which is present in natural light, finds practical applications in nanotechnology 11 , communication technology 12 and many other fields. In observational astronomy, OAM of light [13][14][15] can improve the resolving power of diffraction-limited optical instrument...

A general protocol in quantum information and communication relies in the ability of producing, transmitting, and reconstructing, in general, qunits. In this Letter we show for the first time the experimental implementation of these three basic steps on a pure state in a three-dimensional space, by means of the orbital angular momentum of the photons. The reconstruction of the qutrit is performed with tomographic techniques and a maximum-likelihood estimation method. For the tomographic reconstruction we used more than 2400 different projections. In this way we also demonstrate that we can perform any transformation in the three-dimensional space.

We propose a new theoretical and practical framework for the study of light-matter interactions and the angular momentum of light. Our proposal is based on helicity, total angular momentum, and the use of symmetries. We compare the new framework to the current treatment, which is based on separately considering spin angular momentum and orbital angular momentum and using the transfer between the two in physical explanations. In our proposal, the fundamental problem of spin and orbital angular momentum separability is avoided, predictions are made based on the symmetries of the systems, and the practical application of the concepts is straightforward. Finally, the framework is used to show that the concept of spin to orbit transfer applied to focusing and scattering is masking two completely different physical phenomena related to the breaking of different fundamental symmetries: transverse translational symmetry in focusing and electromagnetic duality symmetry in scattering.

In this Letter we present the first implementation of a quantum coin-tossing protocol. This protocol belongs to a class of "two-party" cryptographic problems, where the communication partners distrust each other. As with a number of such two-party protocols, the best implementation of the quantum coin tossing requires qutrits, resulting in a higher security than using qubits. In this way, we have also performed the first complete quantum communication protocol with qutrits. In our experiment the two partners succeeded to remotely toss a row of coins using photons entangled in the orbital angular momentum. We also show the experimental bounds of a possible cheater and the ways of detecting him.

We unveil the relationship between two anomalous scattering processes known as Kerker conditions and the duality symmetry of Maxwell equations. We generalize these conditions and show that they can be applied to any particle with cylindrical symmetry, not only to spherical particles as the original Kerker conditions were derived for. We also explain the role of the optical helicity in these scattering processes. Our results find applications in the field of metamaterials, where new materials with directional scattering are being explored.