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Srinivasa Rao A. Optical skyrmions in the Bessel profile. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2024; 41:1059-1069. [PMID: 38856417 DOI: 10.1364/josaa.522001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Accepted: 04/17/2024] [Indexed: 06/11/2024]
Abstract
Optical skyrmions formed in terms of polarization are topological quasi-particles, and they have garnered much interest in the optical community owing to their unique inhomogeneous polarization structure and simplicity in their experimental realization. These structures belong to the Poincaré beams satisfying the stable topology. We theoretically investigated the non-diffracting and self-healing Poincaré beams based on the superposition of two orthogonal Bessel modes by the longitudinal mode matching technique. These Poincaré beams are topologically protected, and we suggest them as optical skyrmions in the corresponding Stokes vector fields. These optical skyrmions are quasi-skyrmions, and their range of propagation depends on the range of superposed Bessel modes. We have shown longitudinal mode matching of superposed Bessel beams is a necessary condition for the generation of propagation-invariant and non-diffracting skyrmions. The proposed longitudinal mode matching technique facilitates the generation of skyrmions with tunable position and range without any on-axis intensity modulations along the propagation axis. A suitable experimental configuration is suggested to realize variable order skyrmions in Bessel modes. The suggested experimental configuration can produce optical skyrmions even in ultra-short laser pulses with high mode conversion efficacy. This work can provide a new direction for the generation of skyrmions with completely new textures and features with reference to existing skyrmions originating from Laguerre-Gaussian modes.
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Medina-Segura E, Miranda-Culin L, Rodríguez-Fajardo V, Perez-Garcia B, Rosales-Guzmán C. Helico-conical vector beams. OPTICS LETTERS 2023; 48:4897-4900. [PMID: 37707931 DOI: 10.1364/ol.497773] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 08/21/2023] [Indexed: 09/15/2023]
Abstract
In this work, we propose and demonstrate experimentally a new family of vector beams, the helico-conical vector beams (HCVBs), whose spatial degree of freedom is encoded in the helico-conical optical beams. We use Stokes polarimetry to study their properties and find that upon propagation their transverse polarization distribution evolves from nonhomogeneous to quasihomogeneous, such that even though their global degree of nonseparability remains constant, locally it decreases to a minimum value as z → ∞. We corroborated this quantitatively using the Hellinger distance, a novel metric for vectorness that applies to spatially disjoint vector modes. To the best of our knowledge, HCVBs are the second family of vector beams featuring this behavior, paving the way for applications in optical tweezing or information encryption.
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Hu XB, Zhao B, Chen RP, Rosales-Guzmán C. Tunable longitudinal spin-orbit separation of complex vector modes. OPTICS LETTERS 2023; 48:2728-2731. [PMID: 37186751 DOI: 10.1364/ol.486699] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Complex vector modes are opening burgeoning opportunities for a wide variety of applications and therefore the flexible manipulation of their various properties has become a topic of late. As such, in this Letter, we demonstrate a longitudinal spin-orbit separation of complex vector modes propagating in free space. To achieve this, we employed the recently demonstrated circular Airy Gaussian vortex vector (CAGVV) modes, which feature a self-focusing property. More precisely, by properly manipulating the intrinsic parameters of CAGVV modes, the strong coupling between the two constituting orthogonal components can be engineered to undergo a spin-orbit separation along the propagation direction. In other words, while one polarization component focuses at one plane, the other focuses at a different plane. Such spin-orbit separation, which we demonstrated by numerical simulations and corroborated experimentally, can be adjusted on-demand by simply changing the initial parameters of the CAGVV mode. Our findings will be of great relevance in applications such as optical tweezers, to manipulate micro- or nano-particles at two different parallel planes.
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Hu XB, Zhao B, Chen RP, Rosales-Guzmán C. Experimental generation of arbitrary abruptly autofusing Circular Airy Gaussian vortex vector beams. Sci Rep 2022; 12:18274. [PMID: 36316532 PMCID: PMC9622820 DOI: 10.1038/s41598-022-23157-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2022] [Accepted: 10/25/2022] [Indexed: 11/05/2022] Open
Abstract
Complex vector modes represent a general state of light nonseparable in their spatial and polarization degrees of freedom, which have inspired a wide variety of novel applications and phenomena, such as their unexpected propagation behaviour. For example, they can propagate describing periodic polarization transitions, changing from one vector beam to another. Here, we put forward a novel class of vector modes with the capability to experience an abruptly autofocusing behaviour. To achieve such beams, we encode the spatial degree of freedom in the Circular Airy Gaussian vortex (CAGV) beams. We demonstrate the experimental generation of arbitrary CAGV vector beams and evince some of their properties, such as a rotation of intermodal phase. We anticipate that the fascinating properties of theses modes will prompt the development of novel applications associated to their autofocusing behaviour and polarization distribution.
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Affiliation(s)
- Xiao-Bo Hu
- grid.413273.00000 0001 0574 8737Key Laboratory of Optical Field Manipulation of Zhejiang Province, Department of Physics, Zhejiang Sci-Tech University, Hangzhou, 310018 China
| | - Bo Zhao
- grid.411994.00000 0000 8621 1394Wang Da-Heng Collaborative Innovation Center for Quantum Manipulation & Control, Harbin University of Science and Technology, Harbin, 150080 China
| | - Rui-Pin Chen
- grid.413273.00000 0001 0574 8737Key Laboratory of Optical Field Manipulation of Zhejiang Province, Department of Physics, Zhejiang Sci-Tech University, Hangzhou, 310018 China
| | - Carmelo Rosales-Guzmán
- grid.466579.f0000 0004 1776 8315Centro de Investigaciones en Óptica, A.C., Loma del Bosque 115, Colonia Lomas del campestre, C.P. 37150 León, Guanajuato Mexico
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Liu S, Qi S, Li Y, Wei B, Li P, Zhao J. Controllable oscillated spin Hall effect of Bessel beam realized by liquid crystal Pancharatnam-Berry phase elements. LIGHT, SCIENCE & APPLICATIONS 2022; 11:219. [PMID: 35821002 PMCID: PMC9276670 DOI: 10.1038/s41377-022-00888-4] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2022] [Revised: 05/31/2022] [Accepted: 06/10/2022] [Indexed: 06/01/2023]
Abstract
Pancharatnam-Berry (PB) phase has become an effective tool to realize the photonic spin Hall effect (PSHE) in recent years, due to its capacity of enhancing the spin-orbit interaction. Various forms of PSHEs have been proposed by tailoring the PB phase of light, however, the propagation trajectory control of the separated spin states has not been reported. In this paper, we realize the oscillated spin-dependent separation by using the well-designed PB phase optical elements based on the transverse-to-longitudinal mapping of Bessel beams. Two typical oscillated PSHEs, i.e., the spin states are circulated and reversed periodically, are experimentally demonstrated with two PB phase elements fabricated with liquid crystal. The displacements and periods of these oscillations can be controlled by changing the transverse vector of the input Bessel beam. The proposed method offers a new degree of freedom to manipulate the spin-dependent separation, and provides technical supports for the application in spin photonics.
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Affiliation(s)
- Sheng Liu
- Key Laboratory of Light Field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Shuxia Qi
- Key Laboratory of Light Field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Yanke Li
- Key Laboratory of Light Field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an, 710129, China
| | - Bingyan Wei
- Key Laboratory of Light Field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an, 710129, China.
| | - Peng Li
- Key Laboratory of Light Field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an, 710129, China.
| | - Jianlin Zhao
- Key Laboratory of Light Field Manipulation and Information Acquisition, Ministry of Industry and Information Technology, and Shaanxi Key Laboratory of Optical Information Technology, School of Physical Science and Technology, Northwestern Polytechnical University, Xi'an, 710129, China.
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6
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Dorrah AH, Rubin NA, Tamagnone M, Zaidi A, Capasso F. Structuring total angular momentum of light along the propagation direction with polarization-controlled meta-optics. Nat Commun 2021; 12:6249. [PMID: 34716326 PMCID: PMC8556329 DOI: 10.1038/s41467-021-26253-4] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2020] [Accepted: 09/08/2021] [Indexed: 11/28/2022] Open
Abstract
Recent advances in wavefront shaping have enabled complex classes of Structured Light which carry spin and orbital angular momentum, offering new tools for light-matter interaction, communications, and imaging. Controlling both components of angular momentum along the propagation direction can potentially extend such applications to 3D. However, beams of this kind have previously been realized using bench-top setups, requiring multiple interaction with light of a fixed input polarization, thus impeding their widespread applications. Here, we introduce two classes of metasurfaces that lift these constraints, namely: i) polarization-switchable plates that couple any pair of orthogonal polarizations to two vortices in which the magnitude and/or sense of vorticity vary locally with propagation, and ii) versatile plates that can structure both components of angular momentum, spin and orbital, independently, along the optical path while operating on incident light of any polarization. Compact and integrated devices of this type can advance light-matter interaction and imaging and may enable applications that are not accessible via other wavefront shaping tools. Creating complex forms of structured light typically requires bulky optics and multiple interactions with incident light. Here the authors demonstrate versatile control over light’s polarization and orbital angular momentum along the propagation direction with a single metasurface.
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Affiliation(s)
- Ahmed H Dorrah
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.
| | - Noah A Rubin
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Michele Tamagnone
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.,Fondazione Istituto Italiano di Tecnologia, Genova, Italy
| | - Aun Zaidi
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA
| | - Federico Capasso
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA.
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Droop R, Asché E, Otte E, Denz C. Shaping light in 3d space by counter-propagation. Sci Rep 2021; 11:18019. [PMID: 34504187 PMCID: PMC8429748 DOI: 10.1038/s41598-021-97313-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Accepted: 08/06/2021] [Indexed: 11/09/2022] Open
Abstract
We extend the established transverse customization of light, in particular, amplitude, phase, and polarization modulation of the light field, and its analysis by the third, longitudinal spatial dimension, enabling the visualization of longitudinal structures in sub-wavelength (nm) range. To achieve this high-precision and three-dimensional beam shaping and detection, we propose an approach based on precise variation of indices in the superposition of higher-order Laguerre-Gaussian beams and cylindrical vector beams in a counter-propagation scheme. The superposition is analyzed experimentally by digital, holographic counter-propagation leading to stable, reversible and precise scanning of the light volume. Our findings show tailored amplitude, phase and polarization structures, adaptable in 3D space by mode indices, including sub-wavelength structural changes upon propagation, which will be of interest for advanced material machining and optical trapping.
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Affiliation(s)
- Ramon Droop
- Institute of Applied Physics, University of Muenster, Corrensstr. 2/4, 48149, Münster, Germany.
| | - Eric Asché
- Institute of Applied Physics, University of Muenster, Corrensstr. 2/4, 48149, Münster, Germany
| | - Eileen Otte
- Institute of Applied Physics, University of Muenster, Corrensstr. 2/4, 48149, Münster, Germany
| | - Cornelia Denz
- Institute of Applied Physics, University of Muenster, Corrensstr. 2/4, 48149, Münster, Germany
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Singh K, Buono WT, Chavez-Cerda S, Forbes A. Demonstrating Arago-Fresnel laws with Bessel beams from vectorial axicons. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2021; 38:1248-1254. [PMID: 34613130 DOI: 10.1364/josaa.431186] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/13/2021] [Accepted: 07/14/2021] [Indexed: 06/13/2023]
Abstract
Two-dimensional Bessel beams, both vectorial and scalar, have been extensively studied to date, finding many applications. Here we mimic a vectorial axicon to create one-dimensional scalar Bessel beams embedded in a two-dimensional vectorial field. We use a digital micro-mirror device to interfere orthogonal conical waves from a holographic axicon, and study the boundary of scalar and vectorial states in the context of structured light using the Arago-Fresnel laws. We show that the entire field resembles a vectorial combination of parabolic beams, exhibiting dependence on solutions to the inhomogeneous Bessel equation and asymmetry due to the orbital angular momentum associated rotational diffraction. Our work reveals the rich optical processes involved at the interplay between scalar and vectorial interference, opening intriguing questions on the duality, complementarity, and non-separability of vectorial light fields.
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Nguyen HD, Sedao X, Mauclair C, Bidron G, Faure N, Moreno E, Colombier JP, Stoian R. Non-Diffractive Bessel Beams for Ultrafast Laser Scanning Platform and Proof-Of-Concept Side-Wall Polishing of Additively Manufactured Parts. MICROMACHINES 2020; 11:E974. [PMID: 33143011 PMCID: PMC7693589 DOI: 10.3390/mi11110974] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/14/2020] [Revised: 10/21/2020] [Accepted: 10/27/2020] [Indexed: 11/16/2022]
Abstract
We report the potential use of non-diffractive Bessel beam for ultrafast laser processing in additive manufacturing environments, its integration into a fast scanning platform, and proof-of-concept side-wall polishing of stainless steel-based additively fabricated parts. We demonstrate two key advantages of the zeroth-order Bessel beam: the significantly long non-diffractive length for large tolerance of sample positioning and the unique self-reconstruction property for un-disrupted beam access, despite the obstruction of metallic powders in the additive manufacturing environment. The integration of Bessel beam scanning platform is constructed by finely adapting the Bessel beam into a Galvano scanner. The beam sustained its good profile within the scan field of 35 × 35 mm2. As a proof of concept, the platform showcases its advanced capacity by largely reducing the side-wall surface roughness of an additively as-fabricated workpiece from Ra 10 μm down to 1 μm. Therefore, the demonstrated Bessel-Scanner configuration possesses great potential for integrating in a hybrid additive manufacturing apparatus.
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Affiliation(s)
- Huu Dat Nguyen
- Laboratoire Hubert Curien, UMR 5516 CNRS, Institute of Optics Graduate School, Université de Lyon, Université Jean Monnet, 42000 Saint-Etienne, France; (H.D.N.); (X.S.); (N.F.); (E.M.); (J.-P.C.); (R.S.)
| | - Xxx Sedao
- Laboratoire Hubert Curien, UMR 5516 CNRS, Institute of Optics Graduate School, Université de Lyon, Université Jean Monnet, 42000 Saint-Etienne, France; (H.D.N.); (X.S.); (N.F.); (E.M.); (J.-P.C.); (R.S.)
- GIE Manutech-USD, 42000 Saint-Etienne, France;
| | - Cyril Mauclair
- Laboratoire Hubert Curien, UMR 5516 CNRS, Institute of Optics Graduate School, Université de Lyon, Université Jean Monnet, 42000 Saint-Etienne, France; (H.D.N.); (X.S.); (N.F.); (E.M.); (J.-P.C.); (R.S.)
- GIE Manutech-USD, 42000 Saint-Etienne, France;
| | | | - Nicolas Faure
- Laboratoire Hubert Curien, UMR 5516 CNRS, Institute of Optics Graduate School, Université de Lyon, Université Jean Monnet, 42000 Saint-Etienne, France; (H.D.N.); (X.S.); (N.F.); (E.M.); (J.-P.C.); (R.S.)
| | - Enrique Moreno
- Laboratoire Hubert Curien, UMR 5516 CNRS, Institute of Optics Graduate School, Université de Lyon, Université Jean Monnet, 42000 Saint-Etienne, France; (H.D.N.); (X.S.); (N.F.); (E.M.); (J.-P.C.); (R.S.)
| | - Jean-Philippe Colombier
- Laboratoire Hubert Curien, UMR 5516 CNRS, Institute of Optics Graduate School, Université de Lyon, Université Jean Monnet, 42000 Saint-Etienne, France; (H.D.N.); (X.S.); (N.F.); (E.M.); (J.-P.C.); (R.S.)
| | - Razvan Stoian
- Laboratoire Hubert Curien, UMR 5516 CNRS, Institute of Optics Graduate School, Université de Lyon, Université Jean Monnet, 42000 Saint-Etienne, France; (H.D.N.); (X.S.); (N.F.); (E.M.); (J.-P.C.); (R.S.)
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Lü JQ, Wang XL, Zhang GL, Tu C, Li Y, Wang HT. Bessel-like beams with controllable rotating local linear polarization during propagation. OPTICS LETTERS 2020; 45:1738-1741. [PMID: 32235987 DOI: 10.1364/ol.385069] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/04/2019] [Accepted: 02/07/2020] [Indexed: 06/11/2023]
Abstract
Bessel-like beams with controllable rotation of local linear polarization upon propagation are generated, which in fact achieve the evolution of polarization states along the equator of the Poincaré sphere during propagation. Based on the amplitude-phase joint modulation method, the rotation direction and rate of polarizations of the Bessel-like beam can be controlled easily by adjusting the radial indices and intensity ratio of two superposed beams. A rotation angle of $\sim$∼800 deg has been achieved after a propagation distance of 120 mm, corresponding to a rotation rate of $\sim$∼6.7 deg/mm, which is about three times higher than in previous works.
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11
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Shi Z, Preece D, Zhang C, Xiang Y, Chen Z. Generation and probing of 3D helical lattices with tunable helix pitch and interface. OPTICS EXPRESS 2019; 27:121-131. [PMID: 30645353 DOI: 10.1364/oe.27.000121] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2018] [Accepted: 12/19/2018] [Indexed: 06/09/2023]
Abstract
We propose a method for generation of tunable three-dimensional (3D) helical lattices with varying helix pitch. In order to change only the lattice helix pitch, a periodically varying phase along the propagation direction is added to the central beam - one of the interference beams for lattice construction. The phase periodicity determines the helix pitch, which can be reconfigured at ease. Furthermore, a helical lattice structure with an interface (domain wall) is also achieved by changing the phase structure of the lateral beams, leading to opposite rotating direction (helicity) on different sides of the interface. When a Gaussian beam is used to probe the bulk lattice, it can evolve into a spiral beam with its helicity varying in accordance with that of the lattice. Probing along the interface with two dipole-like optical beams leads to unusual propagation dynamics, depending on the phase and size of the two beams. This approach could be further explored for studies of nonlinear interface solitons and topological interface states. In addition, the helical lattices may find applications in dynamical multi-beam optical tweezers.
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Nape I, Otte E, Vallés A, Rosales-Guzmán C, Cardano F, Denz C, Forbes A. Self-healing high-dimensional quantum key distribution using hybrid spin-orbit Bessel states. OPTICS EXPRESS 2018; 26:26946-26960. [PMID: 30469772 DOI: 10.1364/oe.26.026946] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/30/2018] [Accepted: 09/12/2018] [Indexed: 06/09/2023]
Abstract
Using spatial modes for quantum key distribution (QKD) has become highly topical due to their infinite dimensionality, promising high information capacity per photon. However, spatial distortions reduce the feasible secret key rates and compromise the security of a quantum channel. In an extreme form such a distortion might be a physical obstacle, impeding line-of-sight for free-space channels. Here, by controlling the radial degree of freedom of a photon's spatial mode, we are able to demonstrate hybrid high-dimensional QKD through obstacles with self-reconstructing single photons. We construct high-dimensional mutually unbiased bases using spin-orbit hybrid states that are radially modulated with a non-diffracting Bessel-Gaussian (BG) profile, and show secure transmission through partially obstructed quantum links. Using a prepare-measure protocol we report higher quantum state self-reconstruction and information retention for the non-diffracting BG modes as compared to Laguerre-Gaussian modes, obtaining a quantum bit error rate (QBER) that is up to 3× lower. This work highlights the importance of controlling the radial mode of single photons in quantum information processing and communication as well as the advantages of QKD with hybrid states.
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Mphuthi N, Botha R, Forbes A. Are Bessel beams resilient to aberrations and turbulence? JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2018; 35:1021-1027. [PMID: 29877347 DOI: 10.1364/josaa.35.001021] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2018] [Accepted: 04/28/2018] [Indexed: 06/08/2023]
Abstract
It is understood from the conical wave picture that Bessel beams may self-heal after certain opaque obstructions, but the extrapolation to transparent phase screens is not self-evident. Here we consider the propagation of Bessel beams through aberrated obstacles and show that the self-healing is not guaranteed, but rather a function of the severity of the aberration. Paradoxically, we explain why strong aberrations may show self-healing while weak aberrations will not, and highlight the parameters that influence this. Finally, we combine aberrations to pass the Bessel beam through turbulence, and debunk the myth that Bessel beams are resilient to such perturbations.
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Cao Z, Zhai C, Xu S, Chen Y. Propagation of on-axis and off-axis Bessel beams in a gradient-index medium. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2018; 35:230-235. [PMID: 29400889 DOI: 10.1364/josaa.35.000230] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/09/2017] [Accepted: 11/13/2017] [Indexed: 06/07/2023]
Abstract
Bessel beams have been increasingly used for their advantages of non-diffraction and long focal depth. In this paper, we studied the propagation of on-axis and off-axis Bessel beams in a gradient-index medium. By expressing a Bessel beam in integral form, the analytical expression of an on-axis, decentered, and tilted Bessel beam through a paraxial optical system is derived with the ABCD matrix method and Collins diffraction integral formula. Main lobe size and trajectory of the zeroth- and second-order Bessel beam are obtained, demonstrating that the Bessel beam is focused by the gradient-index medium and its main lobe trajectory is exactly the same as the corresponding geometrical ray for both the decentered and tilted Bessel beam. Effects of beam apodization are finally studied by the Fourier beam propagation method, showing that the side lobes of the Bessel beam vanish when the beam is focused inside the medium as only part of the beam enters the lens.
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15
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Zhang Y, Li P, Ma C, Liu S, Cheng H, Han L, Zhao J. Efficient generation of vector beams by calibrating the phase response of a spatial light modulator. APPLIED OPTICS 2017; 56:4956-4960. [PMID: 29047641 DOI: 10.1364/ao.56.004956] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2017] [Accepted: 05/16/2017] [Indexed: 06/07/2023]
Abstract
The spatial light modulator (SLM) is considered as an effective device to create beams with inhomogeneous phases and polarizations, such as vortex beams and vector beams. However, the nonlinear responses of SLM severely reduce the generation efficiency of these beams. In this paper, by calibrating the SLM to present a linear phase response in the scope of 0-2π, we propose a convenient and efficient method of creating vector beams with arbitrary polarizations based on phase encoding. Compared with the common methods of generating vector beams, our approach can distinctly enhance the generation efficiency.
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