Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light

Milione, Giovanni; Sztul, H. I.; Nolan, Daniel A.; Alfano, R. R.

doi:10.1103/physrevlett.107.053601

Cited by 704 publications

(449 citation statements)

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“…More recently, the geometric representation of higher order paraxial modes have been discussed in Refs. [7,8]. Another fundamental contribution to the theory of geometric phases was given by Mukunda and Simon in Refs.…”

Section: Introductionmentioning

confidence: 99%

Topological phase structure of entangled qudits

Khoury¹,

Oxman²

2014

Phys. Rev. A

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We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. 106, 240503 (2011) is detailed and extended to qudits of different dimensions. The topological nature of the phase evolution and its restriction to fractional values are related to both the structure of the projective space of states and entanglement. For maximally entangled states of qudits with the same Hilbert space dimension, the fractional geometric phases are the only ones attainable under local SU(d) operations, an effect that can be experimentally observed through conditional interference.

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Section: Introductionmentioning

confidence: 99%

Topological phase structure of entangled qudits

Khoury¹,

Oxman²

2014

Phys. Rev. A

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“…At the quantum level, these hybrid modes provide larger Hilbert spaces for encoding information [13]. An investigation of polarization-spatial light modes is also essential for understanding this type of imaging at a deeper level [14].C-points are the umbilical points of the line singularities in the polarization of light because they connect the apex of two opposite cones (a diabolo): of semi-major and semi-minor axis lengths [2,15]. They consist of a state of circular polarization surrounded by a field of polarization ellipses in the optical field, with orientations that rotate about the C-point [16].…”

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confidence: 99%

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confidence: 99%

Generation of isolated asymmetric umbilics in light's polarization

et al. 2014

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Polarization-singularity C-points, a form of line singularities, are the vectorial counterparts of the optical vortices of spatial modes and fundamental optical features of polarization-spatial modes. Their generation in tailored beams has been limited to lemon and star C-points that contain symmetric dislocations in state-of-polarization patterns. In this article we present the theory and laboratory measurements of two complementary methods to generate isolated asymmetric C-points in tailored beams, of which symmetric lemons and stars are limiting cases; and we report on the generation of monstars, an asymmetric C-point with characteristics of both lemons and stars. So far, the study of line singularities relies on the diagnosis of natural occurrences. Non-separable superpositions of polarization and spatial mode of light can provide a vehicle for deliberately creating line-singularity patterns for their study. This polarization-spatial-mode hybridization also adds a new dimension to imaging, where polarization provides additional sensing information [10,11]. Different species exploit polarization-spatial combinations for their survival [12], and line singularities may provide the means to characterize them. At the quantum level, these hybrid modes provide larger Hilbert spaces for encoding information [13]. An investigation of polarization-spatial light modes is also essential for understanding this type of imaging at a deeper level [14].C-points are the umbilical points of the line singularities in the polarization of light because they connect the apex of two opposite cones (a diabolo): of semi-major and semi-minor axis lengths [2,15]. They consist of a state of circular polarization surrounded by a field of polarization ellipses in the optical field, with orientations that rotate about the C-point [16]. C-points are singular points of ellipse orientation. They are intimately linked to the optical vortices of scalar fields, but encode the optical dislocations in the state of polarization instead of the phase [17]. The production of the full spectrum of C-points is of interest in its own right, as it reveals a new domain of complex light not investigated before. The production and analysis of C-points are the basis for new techniques to produce and diagnose optical vortices, which are of interest in metrology due to their high sensitivity to perturbations [18].The two symmetric types of C-point singularities, known as lemons and stars, correspond to dislocations where the ellipse orientation varies linearly with and counter to the angle about the singularity, respectively. Yet, the generation of beams bearing isolated C-points (i.e., alone in a light beam) has been limited to these two cases [19][20][21]. The larger class of asymmetric C-points containing orientations evolving nonlinearly have been produced only in speckle patterns [6][7][8][9], or as C-point pairs (dipoles) in tailored beams [22].The two symmetric cases are the ends of a spectrum of C-points where the pattern of orientations in the ellipse f...

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“…For example, the radially polarized light, a subset of the CV beams, can lead to a strong longitudinal field in the case of strong focusing 2,3 . Because of these particularities, CV beams are expected with a broad applications such as particle trapping 4 , high resolution imaging 2 , particle acceleration 5 , and microscopy 6 .Similar to the geometric representation of homogeneous polarizations on Poincaré sphere, a prominent geometric representation of the CV beams is provided by the so-called higher-order Poincaré sphere (HOPS) 7,8 . In this geometrical representation rule, higher-order Pancharatnam-Berry phase is demonstrated by cyclic transformation of the CV beams on the HOPS 9,10 .…”

mentioning

confidence: 99%

“…Similar to the geometric representation of homogeneous polarizations on Poincaré sphere, a prominent geometric representation of the CV beams is provided by the so-called higher-order Poincaré sphere (HOPS) 7,8 . In this geometrical representation rule, higher-order Pancharatnam-Berry phase is demonstrated by cyclic transformation of the CV beams on the HOPS 9,10 .…”

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confidence: 99%

Realization of polarization evolution on higher-order Poincaré sphere with metasurface

Liu

Ling

et al. 2014

Applied Physics Letters

127

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We present a simple and convenient method to yield cylindrical vector (CV) beams and realize its polarization evolution on higher-order Poincaré sphere based on inhomogeneous birefringent metasurface. By means of local polarization transformation of the metasurface, it is possible to convert a light beam with homogeneous elliptical polarization into a vector beam with any desired polarization distribution. The Stokes parameters of the output light are measured to verify our scheme, which show well agreement with the theoretical prediction. Our method may provide a convenient way to generate CV beams, which is expected to have potential applications in encoding information and quantum computation.Cylindrical vector (CV) beams are light beams of which the polarization states are arranged with cylindrical symmetry in the beam cross section 1 . A plenty of unique properties originated from their special intrinsic symmetry have distinguished the CV beams from general optical beams with homogeneous polarization. For example, the radially polarized light, a subset of the CV beams, can lead to a strong longitudinal field in the case of strong focusing 2,3 . Because of these particularities, CV beams are expected with a broad applications such as particle trapping 4 , high resolution imaging 2 , particle acceleration 5 , and microscopy 6 .Similar to the geometric representation of homogeneous polarizations on Poincaré sphere, a prominent geometric representation of the CV beams is provided by the so-called higher-order Poincaré sphere (HOPS) 7,8 . In this geometrical representation rule, higher-order Pancharatnam-Berry phase is demonstrated by cyclic transformation of the CV beams on the HOPS 9,10 . This phase is geometric in nature and differs significantly from a dynamic phase, which is proportional to light's total angular momentum. This state evolution will provide an advantage solution to create optical qubits, a single photon carrying several bits of information, which is expected to improve the flexibility of information encoding and simplify quantum computation 11 . Nevertheless, there is still not an effective method to generate all the states on HOPS and realize the state evolution. Most efforts including using subwavelength nanostructure 12-14 , orientation-tailored liquid crystal 15-17 , interferometry 18,19 , laser intracavity devices 20 , and fiber laser 21,22 have been made to obtain the radial and azimuthal polarized beams, however, the other states are seldom referred to.In this work, we demonstrate a simple and convenient method to generate the CV beams and realize the evolution of polarization states on the HOPS. It is well known that the cascaded polarizer, quarter-wave plate (QWP), and halfwave plate (HWP) can generate any elliptical polarization state at will 23 . Furthermore, by modulating the direction of the optical axis of the QWP/HWP, the polarization can evolve along the longitude/latitude on the surface of the fundamental Poincaré sphere. Analogously, while it comes to the CV beams whose pola...

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Higher-Order Poincaré Sphere, Stokes Parameters, and the Angular Momentum of Light

Cited by 704 publications

References 29 publications

Topological phase structure of entangled qudits

Topological phase structure of entangled qudits

Generation of isolated asymmetric umbilics in light's polarization

Realization of polarization evolution on higher-order Poincaré sphere with metasurface

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