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We present a device based on liquid crystal and via Pancharatnam-Berry phase to generate Poincare beams by the coherent collinear superposition of two Free-Form Dark Hollow (FFDH) beams. We generate beams with spatially-variable polarization encoded on their cross section showing disclinations in the azimuth orientation and mappings of the Poincare sphere onto the transverse mode. We report generated beams characterized by nonuniform rotation rate of the local polarization azimuth in different polarization configurations, radial and azimuthal, lemon and star disclinations, and other richer and complex higher-order disclinations, by using tailored space-varying-axis plates based on liquid crystals.

We demonstrate the possibility to create optical beams with phase singularities engraved into exotic intensity landscapes imitating the shapes of a large variety of diverse plane curves. To achieve this aim, we have developed a method for directly encoding the geometric properties of some selected curve into a single azimuthal phase factor without passing through indirect encryption methods based on lengthy numerical procedures. The outcome is utilized to mould the optic axis distribution of a liquid-crystal-based inhomogeneous waveplate. The latter is finally used to sculpt the wavefront of an input optical gaussian beam via Pancharatnam-Berry phase., Comment: 11 pages, 6 figures, Published on 21 April 2020 Front. Phys

We present a novel mechanism for performing common-path shearing interferometry using geometric phase, enabling almost any directional derivative while securing compactness and robustness. Important applications in freeform optics testing may result.

We mimic one dimensional forced quantum walks by using the photonic implementation obtained by means of a sequence of liquid-crystal devices (”g-plates”), which apply polarization-dependent transverse kicks to the photons in the beam. We observed refocusing phenomena for localized initial states.

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.

The working principle of ordinary refractive lenses can be explained in terms of the space-variant optical phase retardations they introduce, which reshape the optical wavefront curvature and hence affect the subsequent light propagation. These phases, in turn, are due to the varying optical path length seen by light at different transverse positions relative to the lens centre. A similar lensing behavior can however be obtained when the optical phases are introduced by an entirely different mechanism. Here, we consider the "geometric phases" that arise from the polarization transformations occurring in anisotropic optical media, named after Pancharatnam and Berry. The medium anisotropy axis is taken to be space-variant in the transverse plane and the resulting varying geometric phases give rise to the wavefront reshaping and lensing effect, which however depends also on the input polarization. We describe the realization and characterization of a cylindrical geometric-phase lens that is converging for a given input circular polarization state and diverging for the orthogonal one, which provides one of the simplest possible examples of optical element based on geometric phases. The demonstrated lens is flat and only few microns thick (not including the supporting substrates); moreover, its working wavelength can be tuned and the lensing can be switched on and off by the action of an external control electric field. Other kinds of lenses or more general phase elements inducing different wavefront distortions can be obtained by a similar approach. Besides their potential for optoelectronic technology, these devices offer good opportunities for introducing college-level students to an advanced topic of modern physics, such as the Berry phase, with the help of interesting optical demonstrations., Comment: 15 pages, 8 figures

Light beams carrying orbital angular momentum are key resources in modern photonics. In many applications, the ability of measuring the complex spectrum of structured light beams in terms of these fundamental modes is crucial. Here we propose and experimentally validate a simple method that achieves this goal by digital analysis of the interference pattern formed by the light beam and a reference field. Our approach allows one to characterize the beam radial distribution also, hence retrieving the entire information contained in the optical field. Setup simplicity and reduced number of measurements could make this approach practical and convenient for the characterization of structured light fields., 8 pages (including Methods and References), 6 figures

Known methods for transverse confinement and guidance of light can be grouped into a few basic mechanisms, the most common being metallic reflection, total internal reflection and photonic-bandgap (or Bragg) reflection. All of them essentially rely on changes of the refractive index, that is on scalar properties of light. Recently, processes based on "geometric Berry phases", such as manipulation of polarization states or deflection of spinning-light rays, have attracted considerable interest in the contexts of singular optics and structured light. Here, we disclose a new approach to light waveguiding, using geometric Berry phases and exploiting polarization states and their handling. This can be realized in structured three-dimensional anisotropic media, in which the optic axis lies orthogonal to the propagation direction and is modulated along it and across the transverse plane, so that the refractive index remains constant but a phase distortion can be imposed on a beam. In addition to a complete theoretical analysis with numerical simulations, we present a proof-of-principle experimental demonstration of this effect in a discrete element implementation of a geometric phase waveguide. The mechanism we introduce shows that spin-orbit optical interactions can play an important role in integrated optics and paves the way to an entire new class of photonic systems that exploit the vectorial nature of light., Comment: Publication supported by European Union (EU) within Horizon 2020 - ERC-Advanced Grant PHOSPhOR, grant no. 694683. This is the final peer-reviewed manuscript as accepted for publication (including methods and supplementary information)

We demonstrate light guiding in a locally twisted anisotropic medium in the absence of a refractive index gradient. The transverse phase modulation required to compensate diffraction is provided by the Pancharatnam-Berry phase.

The angular momentum state of light can be described by positions on a higher-order Poincar\'e (HOP) sphere, where superpositions of spin and orbital angular momentum states give rise to laser beams that have found many applications, including optical communication, quantum information processing, microscopy, optical trapping and tweezing and materials processing. Many techniques exist to create such beams but none to date allow their creation at the source. Here we report on a new class of laser that is able to generate all states on the HOP sphere. We exploit geometric phase control with a non-homogenous polarization optic and a wave-plate inside a laser cavity to map spin angular momentum (SAM) to orbital angular momentum (OAM). Rotation of these two elements provides the necessary degrees of freedom to traverse the entire HOP sphere. As a result, we are able to demonstrate that the OAM degeneracy of a standard laser cavity may be broken, producing pure OAM modes as the output, and that generalized vector vortex beams may be created from the same laser, for example, radially and azimuthally polarized laser beams. It is noteworthy that all other aspects of the laser cavity follow a standard design, facilitating easy implementation.

In this paper the role played by the angular momentum of light in the optical reorientation of a nematic liquid crystal was studied in the case of a normal incident elliptically shaped laser beam with circular polarization. Above the threshold power for the OFT, the molecular director suffered a stationary reorientation due to the balance between the orbital and spin angular momentum of light transferred to the sample. The director started to rotate only above a second threshold power. The experimental results qualitatively matched theoretical predictions.

In this work we studied experimentally the optical effects produced by the orbital angular momentum of light on the Optical Freedericksz Transition (OFT) in a nematic liquid crystal film. The measurements were carried out using a linearly polarized astigmatic laser beam with elliptical cross-section. The laser-induced reorientation was found to be strongly dependent on the angle between the polarization and the major axis of the beam profile. A threshold increase, out-of-polarization-plane reorientation and persistent oscillations were found to be the newest features observed in our experimental conditions. We ascribed all these features to the presence of an additional torque due to the orbital angular momentum of light.

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.

Standard multiple-beam holography has been largely used to produce gratings in polymer-liquid crystal composites, like POLICRYPS, H-PDLC gratings and POLIPHEM [1]. In this work we present a different approach to liquid crystalpolymeric grating production, based on the Computer-Generated Holography (CGH). The great advantage of using CGH is that interferometer-based schemes are no longer necessary, avoiding problems related to long term stability of the interference pattern and multi-beam complex optical setup. Moreover, the CGH technique allows a wider choice of pattern designs. In this preliminary work, we obtained promising results, as for instance the patterning of a square-wave refractive index modulation of a LCpolymeric composite, a pattern which is not achievable with standard two-beam holography., 6 pages, 3 figures

Multiple-beam holography has been widely used for the realization of photonic quasicrystals with high rotational symmetries not achievable by the conventional periodic crystals. Accurate control of the properties of the interfering beams is necessary to provide photonic band-gap structures. Here we show, by FDTD simulations of the transmission spectra of 8-fold quasiperiodic structures, how the geometric tiling of the structure affects the presence and properties of the photonic band-gap for low refractive index contrasts. Hence, we show an interesting approach to the fabrication of photonic quasicrystals based on the use of a programmable Spatial Light Modulator encoding Computer-Generated Holograms, that permits an accurate control of the writing pattern with almost no limitations in the pattern design. Using this single-beam technique we fabricated quasiperiodic structures with high rotational symmetries and different geometries of the tiling, demonstrating the great versatility of our technique., Comment: 8 pages, 6 figures

A few years ago the possibility of coupling and inter-converting the spin and orbital angular momentum (SAM and OAM) of paraxial light beams in inhomogeneous anisotropic media was demonstrated. An important case is provided by waveplates having a singular transverse pattern of the birefringent optical axis, with a topological singularity of charge q at the plate center, hence named 'q-plates'. The introduction of q-plates has given rise in recent years to a number of new results and to significant progress in the field of orbital angular momentum of light. Particularly promising are the quantum photonic applications, because the polarization control of OAM allows the transfer of quantum information from the SAM qubit space to an OAM subspace of a photon and vice versa. In this paper, we review the development of the q-plate idea and some of the most significant results that have originated from it, and we will briefly touch on many other related findings concerning the interaction of the SAM and OAM of light.

We present a novel optical device to encode and decode two bits of information into different Orbital Angular Momentum (OAM) states of a paraxial optical beam. Our device generates the four angular momentum states of order $\pm 2$ and $\pm4$ by Spin-To-Orbital angular momentum Conversion (STOC) 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 two-bit information is transferred to the beam OAM exploiting a single $q$-plate. The polarization of the exit beam is left free for additional one bit of information. The transmission bandwidth of the device may be as large as several megahertz if electro-optical switches are used to change the beam polarization. This may be particularly useful in communication system based on light OAM., 5 pages, 5 figures, 1 table. Submitted

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 we 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., 3 pages and 3 figures. Optics Letters style

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.

Multistability, out-of-polarization-plane reorientation, and persistent oscillations have been observed in the optical Fre´edericks 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.

Micrometer-sized rod-like non-birefringent transparent particles trapped by an astigmatic laser beam having elliptical intensity profile spontaneously rotate until they become aligned with the major axis of the beam cross-section. The observed rotation confirms a simple picture based on orbital angular momentum transfer from the light beam to the trapped particle. A model which regards the particle as a thin cylindrical lens with effective focal lengths f1 and f2 has allowed to calculate the applied optical torque and, hence, the time law governing the particle alignment. The time evolution of the particle alignment is studied for different rod-like particles by analysing the sequence of frames recorded by a CCD camera. The time evolution of the angle a formed between the main axes of the body and the laser shape results in good agreement with the theory for bodies fully immersed in the spot size of the laser. Discrepancies observed for rod-like particles longer than the minor elliptical axis of the beam cross-section, were removed by developing a more general model taking into account the partial overlapping between the body and the laser profile. 2003 Elsevier B.V. All rights reserved. PACS: 42.50.Vk

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.

International audience; We propose an approach based on geometric phase for performing several types of shearing interfer-ometry through a robust, compact, common-path setup. The key elements are two identical parallel plates with spatially-varying birefringence distributions , which perform the shearing by writing opposite geometric phases on the two circular polarization components of the linearly polarized incident wavefront. This setup allows the independent control of the shearing magnitude and relative phase of the two wavefront replicas. The approach is first illustrated for the simplest case of lateral shearing, and then extended to other ge-ometries where the magnitude and direction of the shear vary smoothly over the wavefront. http://dx.doi.org/10.1364/optica.XX.XXXXXX Introduction-Shearing interferometry is a widespread technique for analyzing optical wavefronts. Its main feature is that of not requiring a known reference; instead, two replicas of the test wavefront are made to interfere after being displaced laterally (lateral shearing), resized differently (radial shearing), or mutually rotated (azimuthal shearing) [1, 2]. The interferogram's interpretation depends not only on the type of shearing but also on its amount-the shear distance (SD)-, and the relative phase difference between the replicas-the shear phase (SP). In typical common-path layouts based on Snell refraction/reflection, such as shear plates or more complex setups [3-5], the SD and SP are coupled and depend on the position or orientation of an optical element. Several mechanisms have been suggested to control SD and SP independently [1, 6-9]. In particular, polarization-based shearing naturally presents this feature because the two replicas are orthogonally polarized. However, polarization-based shearing interferometers often require several optical components and tend to be bulky or expensive [10-14]. More recent propos