Monstar polarization singularities with elliptically-symmetric q-plates.

Space-variant polarization patterns present in the transverse mode of optical beams highlight disclination patterns of polarization about a singularity, often a C-point. These patterns are important for understanding rotational dislocations and for characterizing complex polarization patterns. Liquid-crystal devices known as q-plates have been used to produce two of the three types of disclination patterns in optical beams: lemons and stars. Here we report the production of the third type of disclination, which is asymmetric, known as the monstar. We do so with elliptically-symmetric q-plates. We present theory and measurements, and find excellent agreement between the two.

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons.

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems.

Topological structures in vector speckle fields.

We here demonstrate on both theoretical and experimental bases a method to recover the topological structure of a monochromatic optical field that has suffered diffuse transmission. This method consists of two steps: first, a linearly polarized sample beam is mixed with a coaxial Gaussian beam in orthogonal polarization states resulting in a Poincaré beam; second, a polarization-related spatial correlation function is considered and measured for the overall speckle field arising by optical diffusion. The singularities of the sample beam turn out to be imaged into the correlation function of the vector speckle field.

Topological features of vector vortex beams perturbed with uniformly polarized light.

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell's equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions.

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid.

Vortices are archetypal objects that recur in the universe across the scale of complexity, from subatomic particles to galaxies and black holes. Their appearance is connected with spontaneous symmetry breaking and phase transitions. In Bose-Einstein condensates and superfluids, vortices are both point-like and quantized quasiparticles. We use a two-dimensional (2D) fluid of polaritons, bosonic particles constituted by hybrid photonic and electronic oscillations, to study quantum vortex dynamics. Polaritons benefit from easiness of wave function phase detection, a spinor nature sustaining half-integer vorticity, strong nonlinearity, and tuning of the background disorder. We can directly generate by resonant pulsed excitations a polariton condensate carrying either a full or half-integer vortex as initial condition and follow their coherent evolution using ultrafast imaging on the picosecond scale. The observations highlight a rich phenomenology, such as the spiraling of the half-vortex and the joint path of the twin charges of a full vortex, until the moment of their splitting. Furthermore, we observe the ordered branching into newly generated secondary couples, associated with the breaking of radial and azimuthal symmetries. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the vortex dynamics. In addition, our observations suggest that phase singularities may be seen as fundamental particles whose quantized events span from pair creation and recombination to 2D+t topological vortex strings.

Directly measuring mean and variance of infinite-spectrum observables such as the photon orbital angular momentum.

The standard method for experimentally determining the probability distribution of an observable in quantum mechanics is the measurement of the observable spectrum. However, for infinite-dimensional degrees of freedom, this approach would require ideally infinite or, more realistically, a very large number of measurements. Here we consider an alternative method which can yield the mean and variance of an observable of an infinite-dimensional system by measuring only a two-dimensional pointer weakly coupled with the system. In our demonstrative implementation, we determine both the mean and the variance of the orbital angular momentum of a light beam without acquiring the entire spectrum, but measuring the Stokes parameters of the optical polarization (acting as pointer), after the beam has suffered a suitable spin-orbit weak interaction. This example can provide a paradigm for a new class of useful weak quantum measurements.

Efficient generation and control of different-order orbital angular momentum states for communication links.

We present an optical scheme to encode and decode 2 bits of information into different orbital angular momentum (OAM) states of a paraxial optical beam. Our device generates the four light angular momentum states of order ±2 and ±4 by spin-to-orbital angular momentum conversion in a triangular optical loop arrangement. The switching among the four OAM states is obtained by changing the polarization state of the circulating beam by two quarter-wave plates, and the 2 bit information is transferred to the beam OAM exploiting a single q plate. The polarization of the exit beam is left free for an additional 1 bit of information. The switching among the different OAM states can be as fast as a few nanoseconds, if suitable electro-optical cells are used. This may be particularly useful in communication systems based on light OAM.

Quantum information transfer from spin to orbital angular momentum of photons.

The optical "spin-orbit" coupling occurring in a suitably patterned nonuniform birefringent plate known as a "q plate" allows entangling the polarization of a single photon with its orbital angular momentum (OAM). This process, in turn, can be exploited for building a bidirectional "spin-OAM interface," capable of transposing the quantum information from the spin to the OAM degree of freedom of photons and vice versa. Here, we experimentally demonstrate this process by single-photon quantum tomographic analysis. Moreover, we show that two-photon quantum correlations such as those resulting from coalescence interference can be successfully transferred into the OAM degree of freedom.

Light propagation in a birefringent plate with topological charge.

We calculated the Fresnel paraxial propagator in a birefringent plate having topological charge q at its center, named "q-plate." We studied the change of the beam transverse profile when it traverses the plate. An analytical closed form of the beam profile propagating in the q-plate can be found for many important specific input beam profiles. We paid particular attention to the plate having a topological unit charge and found that if small losses due to reflection, absorption, and scattering are neglected, the plate can convert the photon spin into orbital angular momentum with up to 100% efficiency provided the thickness of the plate is less than the Rayleigh range of the incident beam.

Improved focusing with hypergeometric-gaussian type-II optical modes.

We present a novel family of paraxial optical beams having a confluent hypergeometric transverse profile, which we name hypergeometric Gauss modes of type-II (HyGG-II). These modes are eigenmodes of the photon orbital angular momentum and they have the lowest beam divergence in the waist of HyGG-II among all known finite power paraxial modes families. We propose to exploit this feature of HyGG-II modes for generating, after suitable focusing, a "light needle" having record properties in terms of size and aspect ratio, possibly useful for near-field optics applications.

Three-dimensional model for light-induced chaotic rotations in liquid crystals under spin and orbital angular momentum transfer processes.

Liquid crystals interacting with light represent a unique class of soft-matter systems that exhibit various generic nonlinear behaviors, including chaotic rotational dynamics. Despite several experimental observations, complex nematic liquid crystal director rotations in presence of spin and orbital angular momentum transfer processes were left unexplained. We present a self-consistent three-dimensional model able to describe the previous experimental observations, accounting for the dependence on the incident beam intensity, polarization, finite size and shape. More generally, our model is able to describe quantitatively the dynamics of, and beyond, the optical Fréedericksz transition under realistic experimental conditions almost three decades after its experimental discovery.

Two-dimensional photonic quasicrystals by single beam computer-generated holography.

Recently important efforts have been dedicated to the realization of a new kind of photonic crystals, known as photonic quasicrystals, in which the lack of the translational symmetry is compensated by rotational symmetries not achievable by the conventional periodic crystals. Here we show a novel approach to their fabrication based on the use of a programmable Spatial Light Modulator encoding Computer-Generated Holograms. Using this single beam technique we fabricated Penrose-tiled structures possessing rotational symmetry up to 23-fold, and a two-dimensional Thue-Morse structure, which is an aperiodic structure not achievable by multiple beam holography.

Hypergeometric-Gaussian modes.

We studied a novel family of paraxial laser beams forming an overcomplete yet nonorthogonal set of modes. These modes have a singular phase profile and are eigenfunctions of the photon orbital angular momentum. The intensity profile is characterized by a single brilliant ring with the singularity at its center, where the field amplitude vanishes. The complex amplitude is proportional to the degenerate (confluent) hypergeometric function, and therefore we term such beams hypergeometric-Gaussian (HyGG) modes. Unlike the recently introduced hypergeometric modes [Opt. Lett. 32, 742 (2007)], the HyGG modes carry a finite power and have been generated in this work with a liquid-crystal spatial light modulator. We briefly consider some subfamilies of the HyGG modes as the modified Bessel Gaussian modes, the modified exponential Gaussian modes, and the modified Laguerre-Gaussian modes.

Light angular momentum flux and forces in birefringent inhomogeneous media.

The angular momentum carried by a monochromatic optical field is separated into an orbital and a spin part beyond the paraxial approximation. These quantities have been distinguished on the grounds of the different mechanical effects they produce in transparent and birefringent media endowed with internal degrees of freedom. The orbital and the spin angular momentum flux densities exhibited are shown to be divergence free in homogeneous and isotropic media and to give back the correct expressions in the paraxial limit.

Optical Fréedericksz transition in liquid crystals and transfer of the orbital angular momentum of light.

Multistability, out-of-polarization-plane reorientation, and persistent oscillations have been observed in the optical Fréedericks transition in a homeotropically aligned nematic film using a normally incident linearly polarized laser beam with elliptical rather than circular cross section. These features could be ascribed to the presence of an additional optical torque connected with a transfer of the orbital angular momentum of light to the liquid crystal film. A model based on Ritz's variational method confirms this picture.

Optical angular momentum transfer to transparent isotropic particles using laser beam carrying zero average angular momentum.

The torque exerted by an astigmatic optical beam on small transparent isotropic particles was dynamically measured observing the angular motion of the particles under a microscope. The data confirmed that torque was originated by the transfer of orbital angular momentum associated with the spatial changes in the phase of the optical field induced by the moving particle. This mechanism for angular momentum transfer works also with incident light beams with no net angular momentum.