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

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

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.

We put forward the concept of quantum spiral bandwidth of the spatial mode function of the two-photon entangled state generated in spontaneous parametric down-conversion. We obtain the bandwidth using the eigenstates of the orbital angular momentum of the biphoton states, and reveal its dependence with the length of the down-converting crystals and waist of the pump beam.The connection between the quantum spiral bandwidth and the entropy of entanglement of the quantum state is discussed.

A major application of optics is imaging all types of structural, physical, chemical and biological features of matter. Techniques based on most known properties of light have been developed over the years to remotely acquire information about such features. They include the spin angular momentum, encoded in the polarization, but not yet the orbital angular momentum encoded in its spiral spectrum. Here we put forward the potential of such spiral spectra. In particular, we use several canonical examples to show how the orbital angular momentum spectra of a light beam can be used to image a variety of intrinsic and extrinsic properties encoded, e.g., in phase and amplitude gradients, dislocations or delays.

We introduce spatiotemporal spinning solitons (vortex tori) of the three-dimensional nonlinear Schrödinger equation with focusing cubic and defocusing quintic nonlinearities. The first ever found completely stable spatiotemporal vortex solitons are demonstrated. A general conclusion is that stable spinning solitons are possible as a result of competition between focusing and defocusing nonlinearities.Optical solitons (spatial, temporal, or spatiotemporal) are self-trapped light beams or pulses that are supported by a balance between diffraction and/or dispersion and various nonlinearities. They are ubiquitous objects in optical media [1] [3,7], quadratically nonlinear (χ (2) ) [2,8], and graded-index Kerr media [9]. While a fully localized STS in three dimensions (3D) has not yet been found in an experiment, 2D ones were observed in a bulk χ (2) medium [10]. The interplay of spatio-temporal coupling and nonlinearity may also play an important role in self-defocusing media [11].Spinning (vortex) solitons are also possible in optical media. Starting with the works [12], both delocalized ("dark") and localized ("bright") optical vortices in 2D were investigated [13,14,15]. In the 3D case they take the shape of a torus ("doughnut") [16,17]. However, the only previously known physical model which could support stable 3D vortex solitons is the Skyrme model [18], which has recently found a new important application to Bose-Einstein condensates (BEC) [19]. Our objective in this paper is to identify fundamental models of the nonlinear-Schrödinger (NLS) type in 3D that give rise to stable spinning solitons, as NLS models are much simpler and closer to more experimental situations, having applications to optics, BEC, plasmas, etc. (see below).For bright vortex solitons stability is a major issue as, unlike their zero-spin counterparts, the spinning solitons are prone to destabilization by azimuthal perturbations. In 2D models with χ (2) and saturable nonlinearities an azimuthal instability was revealed by simulations [14] and observed experimentally [15]. As a result, a soliton with spin 1 splits into two or three fragments, each being a moving zero-spin soliton. Simulations of the 3D spinning STS in the χ (2) model also demonstrates its instability-induced splitting into separating zero-spin solitons [17]. Nevertheless, the χ (2) nonlinearity acting in combination with the self-defocusing Kerr (χ (3) ) nonlinearity, gives rise to the first examples of stable spinning (ring-shaped) 2D solitons with spin s = 1 and 2 [20]. It should be stressed that all the 2D spinning solitons actually represent static spatial beams; on the contrary, 3D solitons are moving spatiotemporal ones, which are localized not only in the transverse plane, but also in the propagation coordinate, see below.A model which may support stable spinning solitons in 3D is the one with a cubic-quintic (CQ) nonlinearity, which (in terms of optics) assumes a nonlinear correction to the medium's refractive index in the form δn = n 2 I − n 4 I 2 , I being the lig...

Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.

We generate ultrabroadband biphotons via the process of spontaneous parametric down-conversion (SPDC) in quasi-phase-matched nonlinear gratings that have a linearly chirped wave vector. By using these ultrabroadband biphotons (300-nm bandwidth), we measure the narrowest Hong-Ou-Mandel dip to date, having a full width at half maximum of 7.1 fs. This enables the generation of a high flux of nonoverlapping biphotons with ultrabroad bandwidth, thereby promoting the use of SPDC light in many nonclassical applications.