Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Bliokh, Konstantin Y.; Alonso, Miguel A.; Dennis, Mark R.

doi:10.1088/1361-6633/ab4415

Cited by 106 publications

(101 citation statements)

References 155 publications

(470 reference statements)

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“…So, SoP along any circle around one of C-points traces a circle around one of the pole. The position, orientation and tilt of the contour on the PS, about the equator is a qualitative measure of the local structure of the C-point singularity as it describes the variation of the SoP around the C-point [37,49]. The unfolding area, defined by the region at the boundary of which the SoP projects to the half of diametrically opposite SoP on the PS from the SoP at the centre of the beam [50].…”

Section: Resultsmentioning

confidence: 99%

Localized geometric phase analogue associated with Poincaré beams due to unfolding of fractional optical vortex beams through a birefringent crystal

Maji¹,

Pattanayak²,

Brundavanam³

2020

J. Opt.

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Fractional optical vortex beam is generated by the diffraction of a Gaussian beam using computer generated hologram embedded with mixed screw-edge dislocation. Unfolding of the generated fractional vortex beam into eigen-polarization components with orthogonal polarization results in the conversion of scalar phase singularity to vector polarization singularities in the beam cross-section. The evolution of the singularities of the ellipse field namely C-points (points of undefined major axis) and L-lines (lines of undefined handedness) in the state of polarization distribution on a transverse plane quantifies the transformation. The effect of the phase morphology dictated by the fractional order of the dislocation, transverse spatial separation and longitudinal relative phase of the two eigen-polarization components on determining the complex transverse polarization structure is investigated. The nature of the generated Poincaré beam is also indicated by projecting the states of polarization on to the Poincaré sphere. With increasing order of dislocation from 0.0 to 1.0 in fractional steps and with increasing relative phase, the partial Poincaré beam is transformed to a full Poincaré beam. The transformation of the local structure around the C-points is measured through the geometric phase due to the Poincaré sphere contour around the C-points for different dynamic phase difference of the unfolded FOV beams generated from different fractional order of dislocation. This study can be useful for different geometric phase based application of optical vortex beams.

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Section: Resultsmentioning

confidence: 99%

Localized geometric phase analogue associated with Poincaré beams due to unfolding of fractional optical vortex beams through a birefringent crystal

Maji¹,

Pattanayak²,

Brundavanam³

2020

J. Opt.

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“…For the normal mode,

Φ_{B}^{nor}

is a spin‐redirection‐Berry phase gained by the wave with k i undergoing the refraction process (i.e., the path 1‐2‐3 defined in Figure 3a), and can be rewritten as

\begin{matrix} true \\ right Φ_{B}^{nor} ({boldk}^{t}) & = & left \int_{1 - 2 - 3} A (k) \cdot d boldk \\ = & left - \int_{0}^{ϕ_{k}} {normalA}_{ϕ_{k}}^{i} false(k^{i} false) \sin θ_{k}^{i} d ϕ_{k} + 0 + \int_{0}^{ϕ_{k}} {normalA}_{ϕ_{k}}^{t} false(k^{t} false) k^{t} \sin θ_{k}^{t} d ϕ_{k}, \\ = & left - σ ((), \cos θ_{k}^{t} - \cos θ_{k}^{i}) ϕ_{k} \end{matrix}

where

{boldA}^{a} false(k^{a} false) = - i {({\overset{v}{true}}_{σ}^{a})}^{*} \cdot false(\nabla_{k} false) {\overset{v}{true}}_{σ}^{a}

is the Berry connection with solely azimuthal component

{boldA}_{ϕ_{k}}^{a} false(k^{a} false) = - σ \frac{\cot θ_{k}^{a}}{k^{a}} {\overset{e}{true}}_{ϕ_{k}}

. [ 1,24,25 ] Obviously,

Φ_{B}^{nor}

is nonzero only as light changes its propagation direction, but disappears when

…”

Section: Underlying Physics Of the Topology‐induced Phase Transitionsmentioning

confidence: 99%

Topology‐Induced Phase Transitions in Spin‐Orbit Photonics

Ling

Guan

Cai

et al. 2021

Laser & Photonics Reviews

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Spin‐controlled vortex generation and spin‐Hall effect, two distinct effects discovered in optics, have been extensively studied recently. However, while physical origins of two effects are both due to spin‐orbit interactions, their inherent connections remain obscure which also hinders further explorations on the manipulations of them. Here, in studying the scattering of a spin‐polarized light beam at sharp interfaces, an intriguing phase transition between vortex generation and spin‐Hall shift trigged by varying the incidence angle is revealed. After reflection/refraction, the beam contains two components: normal and abnormal modes acquiring spin‐redirection‐Berry phases and Pancharatnam–Berry phases, respectively. Inside the abnormal beam, two classes of wave components gain Pancharatnam–Berry phases with distinct topological natures, generating intrinsic and extrinsic orbital angular momenta (OAM), respectively. Enlarging incidence angle changes the relative portions of these two contributions, making the abnormal beam undergo a phase transition from vortex generation to spin‐Hall shift. Such intriguing effect is experimentally observed at a purposely designed metamaterial slab, exhibiting efficiency enhanced by several‐thousand times compared to that at a conventional slab. These findings unify two previously discovered effects in a single framework, reinterpret previous results with clearer pictures, and shed light on understanding other physical effects involving the competition between intrinsic and extrinsic OAM.

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“…We thank Professor J H Hannay for a helpful suggestion. We are also pleased to acknowledge the influence of [20], which appeared online after our first draft was submitted; this led to the paragraph at the end of section 3, rectifying an omission concerning the geometric phases associated with the wavevectors.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Geometry of 3D monochromatic light: local wavevectors, phases, curl forces, and superoscillations

Berry

Shukla

2019

J. Opt.

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This is an exploration of some geometric properties, and their interconnections, for nonparaxial electromagnetic waves. The properties involve the electric field alone, and also in combination with the magnetic field ('electric-magnetic democracy'). The orbital part of the Poynting vector, represented in terms of the electric field, is proportional to the nonconservative 'curl force' exerted on small absorbing polarisable particles; its circuit integral represents the work done transporting a particle. Normalised versions of the electric, magnetic, and electric-magnetic orbital Poynting vectors are natural candidates for wavevectors representing the direction of the wave at each point, generalising the phase gradient for scalar waves; there are associated total, dynamical and geometric phases. For isotropic ensembles of random waves, the probability distributions of the different wavevectors are estimated by codimension arguments and calculated exactly for statistically isotropic superpositions of plane waves. The superoscillation probability, that the magnitude of the local wavevector exceeds that of the waves in the superposition, is 0.031 40 for the electric wavevector and 0.000 109 for the electric-magnetic wavevector. Both values are much smaller than the known superoscillation probability 0.350 48 for scalar waves in three-dimensions, illustrating a general phenomenon: interference detail is weaker for electric properties than for scalar, and weaker still for electric-magnetic properties.

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Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Cited by 106 publications

References 155 publications

Localized geometric phase analogue associated with Poincaré beams due to unfolding of fractional optical vortex beams through a birefringent crystal

Localized geometric phase analogue associated with Poincaré beams due to unfolding of fractional optical vortex beams through a birefringent crystal

Topology‐Induced Phase Transitions in Spin‐Orbit Photonics

Geometry of 3D monochromatic light: local wavevectors, phases, curl forces, and superoscillations

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