The DOI matches its Crossref record; 159 of the 162 references it cites were found in a registry or an index; 10 of the 184 sources its claims cite were checked for support.
Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
Open accessAbstract
We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin-orbit coupling of light which consists of (i) the Berry phase responsible for a trajectory-dependent polarization variations and (ii) the spin Hall effect representing polarization-dependent trajectory perturbations. These mutual phenomena are described within universal geometrical structures underlying the problem and are explained by the dynamics of the intrinsic angular momentum carried by the wave. Such close geometro-dynamical interrelations illuminate a dual physical nature of the phenomena.
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TL;DR
This review develops a unified geometrical-optics description of spin-orbit coupling of light in a gradient-index dielectric, where the Berry phase and spin Hall effect are mutual consequences of a Coriolis-type term in the ray-accompanying frame. It shows that polarization evolution and polarization-dependent ray deflection are governed by Berry connection/curvature and by conservation of total angular momentum.
Key findings
- The Berry phase and spin Hall effect of light are two sides of the same spin-orbit interaction: the Berry phase describes the trajectory’s effect on polarization, while the spin Hall effect describes polarization’s reaction on the ray trajectory; both follow from a single spin-orbit Lagrangian.
- The Berry curvature takes the form of a topological monopole in momentum space and equals \(F = t\) on the unit \(t\)-sphere, indicating unit Gaussian curvature; the Berry phase for a cyclic evolution equals the solid angle \(\Theta\) cut by the loop on the \(t\)-sphere, up to a \(2\pi\) frame-rotation difference.
- The spin Hall effect adds a helicity-dependent topological term to the ray equations, producing a transverse deflection orthogonal to both the wave momentum \(p\) and the inhomogeneity gradient \(\nabla n\); its magnitude is estimated as the wavelength \(\lambda\) for a complete \(2\pi\) turn of the propagation direction, and the splitting between right- and left-hand circularly polarized beams is \(\Delta = 2\delta r_0\).
- For a helical ray in a cylindrically symmetric medium, the Berry phase grows linearly with propagation distance and rotates the polarization ellipse uniformly; the spin Hall displacement is directed along the binormal and accumulates over repeated cyclical trajectories.
Methods
- Theoretical review using short-wavelength geometrical optics for a monochromatic electromagnetic wave in a smoothly inhomogeneous isotropic dielectric, with small parameter \(\mu\) comparing wavelength to medium inhomogeneity scale.
- Maxwell equations are projected onto the plane transverse to the ray, transformed to a ray-accompanying rotating coordinate frame, and diagonalized in the circular-polarization basis; the resulting Coriolis term is treated to first order in \(\mu\).
- The analysis uses Berry connection/curvature, Jones-vector and Stokes/Poincaré representations, Euler-Lagrange ray equations, and a worked example of a helical ray in a cylindrical gradient-index medium.
Limitations
- The paper states that it considers only the spin-redirection Rytov–Vladimirskii–Berry phase in inhomogeneous media and does not cover generalizations to step-index interfaces, anisotropic media, or higher-order states of light carrying orbital angular momentum.
- It notes that geometrical optics is rigorously inapplicable in single-mode waveguides, although the polarization evolution and Berry phase of waveguide modes obey the same geometrical formalism.
- It states that the spin Hall displacement is typically much smaller than the width of a paraxial optical beam, though observable because beam centroids can be measured with subwavelength accuracy; it also notes that the Imbert–Fedorov shift cannot generally be described within the Berry-phase formalism because of non-adiabatic evolution at sharp interfaces.
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Claims the paper makes
62 Own interpretation · 54 No basis given · 42 Not checked yet · 3 Partly supported · 2 Own result · accuracy not yet measured
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“At the same time, Eq. (3.14) shows that it can be treated as the angular Doppler effect term, which describes the phase shift of the wave carrying intrinsic angular momentum Σ and undergoing rotational evolution with angular frequency Ω [68 -80].”
What the sources say
- Not checked yetcites [68] source
- Partly supportedcites [69] sourceExperimental — accuracy not yet measured
The Introduction (p. 2) reports a phase shift associated with spin rotation, and General Consideration (pp. 4–5) relates angular momentum to the rotation frequency. Our copy does not identify a spin-orbit Lagrangian as an angular Doppler effect term, so that specific interpretation is not supported. (LLM, conf=0.82)
- Partly supportedcites [70] sourceExperimental — accuracy not yet measured
In the paper’s discussion of the Coriolis frequency shift and unified geometric phase (page unavailable in our copy), a term in the wave Hamiltonian is linked to spin-orbit interaction, and the resulting phase arises as the reference frame rotates. The paper says this shift is similar to an angular Doppler shift, but explicitly distinguishes it from a real angular Doppler shift; it does not identify the term as a spin-orbit Lagrangian. (LLM, conf=0.84)
- Not checked yetcites [71] source
- Not checked yetcites [72] source
- Not checked yetcites [73] source
- Not checked yetcites [74] source
- Partly supportedcites [75] sourceExperimental — accuracy not yet measured
In the discussion of the rotating quarter-wave plate and Figs. 3–4 (page not provided), the paper reports a polarization-dependent geometric phase that changes with rotation rate Ω and produces a frequency shift. It does not identify a spin-orbit Lagrangian or an angular Doppler effect term involving intrinsic angular momentum Σ; the rotating element in its experiment is a wave plate. (LLM, conf=0.86)
- Not checked yetcites [76] source
- Not checked yetcites [77] source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“By differentiating expression (3.36) and using Eq. (3.29) we find that the Stokes vector obeys the following precession equation [34,35]:”
What the sources say
- Could not verifycites [34] sourceExperimental — accuracy not yet measured
Section D gives ray equations for circularly polarized light, and the passage following Eq. (28) says the Berry phase rotates the polarization plane. Neither passage states a precession equation for the Stokes vector; searches for “Stokes” and polarization precession found no such equation in our copy. (LLM, conf=0.72)
- Partly supportedcites [35] sourceExperimental — accuracy not yet measured
On p. 2, the paper gives a cross-product evolution equation for the spin vector, which has a precession form. But it does not identify that vector as the Stokes vector or give a Stokes-vector precession equation; on p. 3, it says polarization was not considered in its framework. (LLM, conf=0.78)
plaindirect- Asserted: passes — The authors put it forward as true.
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- Could not verify
The cited sources support only part of this claim — read each source’s verdict below.
In the paper
“For a cyclic evolution in momentum space (which corresponds to a ray trajectory with the coincident input and output directions of propagation), the Berry phase (3.26) equals [4 -20]”
What the sources say
- Supportedcites [4] Vinitskii S I, 1990, Usp. Fiz. Nauk source
Section 3.3 relates the Berry phase of circularly polarized light to a closed path of propagation directions and its solid angle. It also says that, for adiabatic evolution, the spin-direction and propagation-direction spheres give equivalent descriptions. The cited paper therefore supports the claim in this optical setting. (LLM, conf=0.85)
- Partly supportedcites [5] Vinitskii S I, 1990, Sov. Phys. Usp. sourceExperimental — accuracy not yet measured
Section 3.1 describes a photon’s momentum returning to its initial value and the resulting geometrical phase. Section 3.6 gives the Berry phase as −mΩ(C), where m = ±1 is the photon’s helicity. The claim captures the solid-angle relationship but omits the helicity-dependent sign. (LLM, conf=0.83)
- Not checked yetcites [6] source
- Supportedcites [7] Ben-Aryeh Y, 2004, J. Opt. B: Quantum Semiclass. Opt. source
In the section labeled “Following” (page unavailable), the paper states that when a light wave’s propagation direction cycles along a closed path, its topological phase equals the solid angle of the circuit in the space of wavevector directions. This supports the claim for the optical momentum-space evolution described. (LLM, conf=0.93)
- Not checked yetcites [8] source
- Not checked yetcites [9] Malykin G B, 2004, Phys.-Usp. source
- Not checked yetcites [10] Rytov S M, 1938, Dokl. Akad. Nauk. SSSR
- Not checked yetcites [11] Vladimirskii V V, 1941, Dokl. Akad. Nauk. SSSR
- Not checked yetcites [12] source
- Not checked yetcites [13] source
plaindirect- Asserted: passes — The authors put it forward as true.
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- Supported
None of the sources cited for this claim have been checked yet.
In the paper
“The conservation of the total angular momentum, Eq. (3.42), links the spin Hall effect of light to another remarkable phenomenon - the transverse Imbert-Fedorov shift [24,27,99 -118].”
What the sources say
- Not checked yetcites [24] Pancharatnam S, 1975, Collected Works
- Not checked yetcites [27] source
- Not checked yetcites [99] source
- Could not verifycites [100] sourceExperimental — accuracy not yet measured
The cited paper’s Sections 2 and 4 discuss electromagnetic potentials and electron-beam interference and scattering. Searches for the spin Hall effect of light, the Imbert–Fedorov shift, and conservation of angular momentum found no passage linking those optical phenomena in our copy. Page numbers were not available for the retrieved passages. (LLM, conf=0.76)
- Not checked yetcites [101] source
- Not checked yetcites [102] source
- Could not verifycites [103] sourceExperimental — accuracy not yet measured
The paper’s discussion of Stokes parameters and pseudospin (p. 2) and its applications to polarization changes (pp. 3–4) do not address the claimed link. Searches for the Imbert–Fedorov shift, the spin Hall effect of light, and conservation of total angular momentum found no passage establishing it. (LLM, conf=0.72)
- Not checked yetcites [104] Fedorov F I, 1955, Dokl. Akad. Nauk SSSR
- Not checked yetcites [105] source
- Not checked yetcites [106] source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray.”
hedgeddirect- Asserted: passes — The authors put it forward as true.
- Checkable: passes — It can be checked against evidence.
- Load-bearing: passes — The paper’s conclusions depend on it.
- Based: passes — The paper gives a reason why it holds.
- The authors state this as an assumption: The inhomogeneity of the medium is smooth, i.e., its characteristic scale L is large compared with the wavelength.
- The authors state this as an assumption: Higher-order terms proportional to Ω^2 and Ω dot are neglected.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The spin-orbit Lagrangian (3.12) brings about an additional polarization-dependent wave phase.”
plaindirect- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The spin-orbit Lagrangian is proportional to the longitudinal component of the angular velocity of the co-moving coordinate frame, which is”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Here the second term describes the Coriolis effect caused by the rotation of the ray coordinate frame.”
plaindirect- Asserted: passes — The authors put it forward as true.
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- The authors state this as an assumption: Higher-order terms proportional to Ω^2 and Ω dot are neglected.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“The angle of the resulting rotation of e equals the Berry phase B Φ .”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“A cyclical evolution on the t sphere, Fig. 2, corresponds to the rotation on the angle 0 2 B Φ on the Poincaré sphere.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- It may state two separate claims as one. 44
- The quote only partly states this claim. 5
- Probably not a substantial claim. 18
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“According to Eq. (3.10), in the first approximation of the geometrical optics, these two states evolve independently, and the zero-order polarization degeneracy is lifted by the Coriolis term.”
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In the paper
“This term is small: 0 ~ µ Ω Ż , but should be taken into account in the first-order approximation in µ .”
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In the paper
“Its third component, [ ] 2 2 3 1,1 S e e + -= -∈ -, indicates the wave helicity and represents a continuous analogue of the quantized helicity 1 s = ± .”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“It is equal to the contour integral of the effective vector-potential A or to the flux of the 'magnetic field' F through this contour.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“In contrast to the previous Eqs. (3.25) -(3.29), equation (3.32) is independent of the local coordinate frame ( ) , , v w t and describes the polarization dynamics in a universal way.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Equation (3.32) is non-integrable , i.e., its solution ( ) l e is non-local due to the non-integrability of the Berry phase (3.25) and (3.26).”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“On the surface of the unit t -sphere (i.e., at 1 p = ), the Berry curvature equals = F t indicating the unit Gaussian curvature of the surface.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Therefore, displacement δ r is directed locally orthogonal to inhomogeneity, 0 δ ≡ p , and we can use Eqs. (3.45) and (3.46) for calculation of δ r .”
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In the paper
“In the Stokes-vector formalism, Eq. (3.37), the Stokes vector precesses uniformly with angular velocity, Fig. 3:”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Thus, the Berry phase grows linearly with the propagation distance l , and polarization ellipse experience a uniform rotation with angular velocity (4.7) in the ray reference frame, see Fig. 1.”
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In the paper
“Indeed, the spin-dependent term of Eqs. (3.40) is proportional to the curvature of the ray and directed orthogonally to the local propagation plane (see Section A.2).”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Equations (3.40) depend on the Berry curvature F and therefore are gauge-invariant, i.e., independent on the coordinate frame.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“There had been a number of remarkable experiment [120 -123] which observed the spin-orbit coupling and polarization transport of light in complex speckle fields of multimode optical fibers (see also [24]),”
What the sources say
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“Note that 1 2 1 sin K ρ ϑ --= is the curvature of the helical ray, and Eq. (4.14) agrees with Eq. (A12).”
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In the paper
“The Berry phase (the angle of rotation of the polarization ellipse) per one period of the helix, 2 / sin l π ρ ϑ = , equals”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Recently, the spin Hall effect of light and the ray equations (3.40) were verified by direct measurements for a helical trajectories as in Fig. 4 [35].”
What the sources say
- Not checked yetcites [35] source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The spin-orbit term in Eqs. (3.40) is proportional to 0 Ż , and, thus, can be treated as a ' semiclassical ' correction to the ray equations.”
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In the paper
“The shift per one period of helix, 2 / sin l π ρ ϑ = , equals”
- Also stated in: § 4.4. Spin Hall effect · p. 16 · plain
“whereas the splitting between the centers of right-hand, 1 s = , and left-hand, 1 s = -, polarized beams is, evidently, 0 2 δ ∆ = r , see Fig. 4.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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- Also stated in: § 4.4. Spin Hall effect · p. 16 · plain
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Thus, the torsion characterizes local rotation of this frame about t , and the Berry phase in this frame is”
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In the paper
“Here the Berry curvature is the monopole (3.20), whereas the Berry connection becomes Eq. (3.35) after gauge transformation (3.23) with α = -φ .”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Indeed, the topological term in equations (3.40) can be written as [35]”
What the sources say
- Not checked yetcites [35] source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“In particular, the central wave phase 0 Φ ( 0 i e ψ Φ ∝ ) in this approximation is given by the WKB integral along the ray:”
plaindirect- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
None of the sources cited for this claim have been checked yet.
In the paper
“In the short-wavelength (semiclassical) approximation, the spin-orbit coupling can be described within the Berry-phase formalism, which has a universal geometrical character and can be applied to a diversity of quantum and classical wave systems [1 -3].”
What the sources say
- Not checked yetcites [1] Shapere A, 1989, Geometric Phases in Physics
- Not checked yetcites [2] Markovski B, 1989, Topological Phases in Quantum Theory
- Not checked yetcites [3] Bohm A, 2003, Geometrical Phase in Quantum Systems source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The rays are curvilinear because of the wave refraction in the medium, and the gradient n ∇ plays the role of an 'external force' affecting the motion of the particle.”
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In the paper
“This effect is known as the spin Hall effect of light or optical Magnus effect [24 -35]”
What the sources say
- Not checked yetcites [24] Pancharatnam S, 1975, Collected Works
- Not checked yetcites [25] source
- Not checked yetcites [26] source
- Not checked yetcites [27] source
- Not checked yetcites [28] source
- Not checked yetcites [29] source
- Not checked yetcites [30] source
- Not checked yetcites [31] source
- Not checked yetcites [32] source
- Not checked yetcites [33] source
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“This term describes the spin-orbit coupling of light which consists of (i) the Berry phase responsible for a trajectory-dependent polarization variations and (ii) the spin Hall effect representing polarizationdependent trajectory perturbations.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In the zero -order approximation in µ , Eq. (3.1) results in the scalar Hamiltonian and the ray equations (2.3) -(2.6). However, polarization is indeterminate in this approximation.”
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In the paper
“It will be shown that the Berry phase and spin Hall effect are closely related to the dynamics of the spin angular momentum carried by the wave and can be described in terms of the Coriolis effect or the angular Doppler effect.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Evolution of vector waves, e.g., electromagnetic or elastic ones, requires more sophisticated approaches, since it involves an additional, internal degree of freedom -polarization (spin).”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“These mutual phenomena are described within universal geometrical structures underlying the problem”
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In the paper
“Such close geometro-dynamical interrelations illuminate a dual physical nature of the phenomena.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“This polarization term is small in a gradient-index medium (of the order of µ ) and can be treated perturbatively within the geometrical optics approach.”
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In the paper
“In a more general context, the Berry phase and the accompanying geometric reaction forces arise from a coupling between the fast and slow degrees of freedom [44]”
What the sources say
- Not checked yetcites [44] source
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The polarization rotation corresponding to the Berry phase (3.33) and (3.34) has been measured experimentally in single-mode optical fibers coiled in a helix similar to Fig. 1 [10,11] and for helical rays in a multimode rectilinear waveguide [20,35], cf. Section 4.”
What the sources say
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“This evidences adiabatic regime of the wave evolution [4,12,14,17], i.e., independence of the right- and left-hand circular polarizations.”
What the sources say
boosted- Asserted: passes — The authors put it forward as true.
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In the paper
“At the same time, it shows that the Berry phase is analogous to the Aharonov -Bohm (or Dirac) phase in quantum mechanics [94 -96].”
What the sources say
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“In fact, the spin Hall effect in a gradient-index medium and the Imbert-Fedorov shift represent, respectively, the weak- and strong-scattering limits of the polarization transport induced by the spin-orbit interaction of light.”
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In the paper
“In contrast, the spin Hall effect represents a real deflection of the ray trajectory, which is independent on the observation frame.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“but all of them (apart from numerical simulations in [123]) dealt with step-index index fibers, so that these results should rather be associated with the Imbert-Fedorov shifts upon the reflection at sharp inhomogeneities.”
What the sources say
- Not checked yetcites [123] source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“Here J is obviously associated with the total angular momentum of light, consisting of the extrinsic orbital angular momentum = × L r p and the intrinsic spin angular momentum Σ .”
boostedcorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim.
In the paper
“It is worth remarking that the pseudospin S arrowrightnosp completely describes the polarization state of the wave, while the real spin angular momentum 0 s = Σ t Ż does not [97].”
What the sources say
- Not checked yetcites [97] source
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“In addition, propagation of light in optical fibers does not allow one to observe the geometricaloptics ray trajectories hidden in the complex speckle patterns of the interfering modes.”
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Thus, akin to the Berry phase (3.26) and (3.33), the ray displacement takes the form of a nonlocal contour integral in momentum space, which can grow unlimitedly with the length of the trajectory.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Important to note that the Berry curvature appears in momentum rather than coordinate space and takes the form of the topological monopole as in the case of massless spinning particles.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“In the spin Hall effect, the Berry curvature manifests itself dynamically - the polarization term in Eq. (3.40) represents a ' Lorentz force ' from the 'magnetic monopole' (3.20).”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The latter effect is a similar polarization-dependent displacement of a wave beam reflected or transmitted at a plane dielectric interface.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In the zero-order (scalar) approximation the light propagates along a smooth trajectory which ensures the adiabatic regime of the evolution.”
plaindirect- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The first-order corrections involve the wave polarization and bring about two mutual phenomena -the Berry phase and the spin Hall effect of light.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Since the Euler-angles and Frenet frames coincide with each other, the Berry-phase expressions are equivalent as well.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“The Berry phase can be associated with the inertia of the wave field which remains locally non-rotating, and can be eliminated in the proper inertial coordinate frame (see Section A3).”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“The Jones and Stokes representations characterize the polarization state of light, respectively, by the complex two-component vector ψ and the real three-component vector S arrowrightnosp . In the generic case, they obey ( ) SU 2 and ( ) SO 3 evolutions and correspond, respectively, to the Schrödinger and Heisenberg representations of spin in quantum mechanics [34,98].”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The Berry phase represents the effect of the trajectory on the polarization of light, while the spin Hall effect is the inverse effect which accounts for the reaction of polarization on the trajectory of propagation.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“It can be treated as an effective circular birefringence of the inhomogeneous medium [25,26], but, in fact, it arises because of the intrinsic property (spin) of light coupled to a curved ray trajectory.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Thus, while the Berry phase is an artifact of a particular rotating ray-accompanying coordinate frame, the spinHall effect is a Coriolis-type transverse deflection induced by a real bending of spinning light.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“However, the parallel-transport frame is non-local -equation (A14) contains the phase which depends on the integral evolution of t .”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“In this case the intrinsic orbital angular momentum behaves, in the geometrical optics approximation, very much like spin and the vortex charge determines spin-like helicity of the beam.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“Thus, although the rotation of the ray-accompanying frame about t can be eliminated, rotation associated with the ray bending and the ray curvature is unremovable.”
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“A number of effects related to the spin-orbit coupling of light take place in multimode optical fibers [24,120 -123,141 -144].”
What the sources say
- Not checked yetcites [24] Pancharatnam S, 1975, Collected Works
- Not checked yetcites [120] source
- Not checked yetcites [121] source
- Not checked yetcites [122] source
- Not checked yetcites [123] source
- Not checked yetcites [141] Kravtsov Y A, 1996, Phys.-Usp. source
- Not checked yetcites [142] source
- Not checked yetcites [143] source
- Not checked yetcites [144] source
plaincorrelational- Asserted: passes — The authors put it forward as true.
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In the paper
“These basis vectors characterize local properties of the curve and are independent on the laboratory coordinate frame.”
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“The Berry phase is the phase of the central plane wave in the packet.”
plain- Asserted: passes — The authors put it forward as true.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Thus, the spin-orbit-type interaction occurs between the intrinsic and extrinsic orbital angular momentums of light beams, which induces the corresponding Berry phase and orbital Hall effect.”
plaindirect- Asserted: passes — The authors put it forward as true.
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In the paper
“This shows that the spin-induced ray deflection is determined solely by the ray curvature and is directed along the binormal, i.e., orthogonal to the local propagation plane ( , ) t n .”
plaindirect- Asserted: passes — The authors put it forward as true.
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The authors state this as an assumption.
The inhomogeneity of the medium is smooth, i.e., its characteristic scale L is large compared with the wavelength.
“We assume that inhomogeneity of the medium is smooth, i.e., its characteristic scale, L , is large as compared with the wavelength:”
The authors state this as an assumption.
The dielectric constant of the medium is real.
“where 2 n ε = is the dielectric constant of the medium, which is assumed to be real.”
The authors state this as an assumption.
Higher-order terms proportional to Ω^2 and Ω dot are neglected.
“Neglecting higher-order terms proportional to 2 Ω and Ω ɺ , we arrive at”
The authors state this as an assumption.
The wave beams or packets are Gaussian-type and do not bear an intrinsic orbital angular momentum.
“We imply Gaussian-type wave beams or packets which do not bear an intrinsic orbital angular momentum.”
The paper relies on this without support.
The position of the center of gravity of the beam can be measured with subwavelength accuracy.
“since the position of center of gravity of the beam can be measured with a subwavelength accuracy.”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Therefore, the Berry connection and Berry curvature immediately appear in all intrinsic SOI phenomena, such as the spin-Hall effect.”
From Spin–orbit interactions of light (2015) · cites this paper as [7]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“The intrinsic SOI of light originate from fundamental properties of the Maxwell equations 7,8 and are analogous to the spin-orbit interactions of relativistic quantum particles 2,9,10 and electrons in solids 11,12 .”
From Spin–orbit interactions of light (2015) · cites this paper as [7]
The cited source says what the claim attributes to it.
In the citing paper
“The last term in Eq. (1) describes the transverse spin-dependent displacement of the trajectory, i.e., the spin-Hall effect of light (Fig. 1a).”
From Spin–orbit interactions of light (2015) · cites this paper as [7]
The cited source says what the claim attributes to it.
In the citing paper
“Later, it was shown that the helicity-dependent term in Eq. (1) can be considered as a 'Lorentz force' produced by the Berry curvature F σ P ( ) acting in momentum space 7,13,14,17 (Box 2).”
From Spin–orbit interactions of light (2015) · cites this paper as [7]
Citations
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Significance of Electromagnetic Potentials in the Quantum Theory
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Quantised singularities in the electromagnetic field,
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The Classical Theory of Fields
LANDAU, L. D., LIFSHITZ, E. M., & Holbrow, C. H. (1963) · Physics Today · doi:10.1063/1.3050989 · Cited by 2,322
Universal Intrinsic Spin Hall Effect
Sinova, J., Culcer, D., Niu, Q., Sinitsyn, N. A., Jungwirth, T., & MacDonald, A. H. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.126603 · Cited by 2,180
Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media
Marrucci, L., Manzo, C., & Paparo, D. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.163905 · Cited by 2,115
Observation of the Spin Hall Effect of Light via Weak Measurements
Hosten, O., & Kwiat, P. (2008) · Science · doi:10.1126/science.1152697 · Cited by 2,026
Dissipationless Quantum Spin Current at Room Temperature
Murakami, S., Nagaosa, N., & Zhang, S. (2003) · Science · doi:10.1126/science.1087128 · Cited by 1,952
Wilczek, F. A., & Shapere, A. D. (1989) · Advanced series in mathematical physics · doi:10.1142/0613 · Cited by 1,616
Research works printed but not linked: 14
- Rytov S M, 1938, Dokl. Akad. Nauk. SSSR, 18, 263
- Vladimirskii V V, 1941, Dokl. Akad. Nauk. SSSR, 31, 222
- Pancharatnam S, 1975, Collected Works
- Berry M V, 1989, Geometric Phases in Physics, 7
- Horváthy P A, 2006, SIGMA, 2, 090
- Dandoloff R, 1989, J. Physique, 22, L461
- Fedorov F I, 1955, Dokl. Akad. Nauk SSSR, 105, 465
- Punko N N, 1984, JETP Lett., 39, 20
- Fedoseev V G, 1985, Opt. Spectrosc. (USSR), 58, 296
- Volyar A V, 1992, Ukr. Fiz. Zh., 37, 1468
- Volyar A V, 1998, Opt. Atmos. Okeana, 11, 1199
- Volyar A V, 1999, Opt. Spektrosc., 86, 593
- Baranova N B, 1994, JETP Lett., 59, 232
- Zel’dovich B Y, 1994, JETP Lett., 59, 766
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Non-Abelian Gauge Field Optics in the Time Domain
Lai, Y., Zhang, Y., & Chang, K. (2025) · Physical Review Letters · doi:10.1103/fbgc-wkb7 · Cited by 1
“In the electric field ˆ E σ = σ m , the longitudinal shift ξ σ and the central frequency ω σ are given by In contrast to the transverse SHE [23, 24, 48], the temporal gauge field leads to a spin-dependent longitudinal shift, which relates to the spin time delay ∆ T σ = ξ σ / c .”
Quantum Geometry Enabled High-Performance Terahertz Detection
Wu, M., Zhang, M., Zhang, Z., Li, Z., Shi, N., Yu, Y., & Liu, H. (2025) · ACS Applied Materials & Interfaces · doi:10.1021/acsami.5c19447
Ahmad, I., Ullah, A., Ullah, S., Alwadie, N., & Alomar, M. (2026) · Physics Letters A · doi:10.1016/j.physleta.2026.131675
Loss/gain-induced Hall effect of vortex light
Lai, Y., Zhang, Y., & Chang, K. (2026) · Physical review. B./Physical review. B · doi:10.1103/kbtk-sy51
Minkowski and Abraham Momenta Revisited from the Perspective of Photon DynamicsPreprint
Yang, L., Zhang, P., & Feng, L.-L. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.7308352
Spin-orbit interactions of light
Bliokh, K. Y., Rodriguez-Fortuno, F. J., Nori, F., & Zayats, A. V. (2015) · arXiv
Self-citation
Metadata
- Authors
- Bliokh, K. Y.
- Affiliations
- Australian National University (AU)
- Corresponding author
- Bliokh, Konstantin Y
- ORCID
- Bliokh, Konstantin Y
- Venue
- Journal of Optics A: Pure and Applied Optics
- Publisher
- IOP Publishing
- Published
- 2009-08-04
- Volume
- 11
- Issue
- 9
- Pages
- 094009
- ISSN
- 1464-4258 (ISSN-L)
- 1741-3567
- OpenAlex
- W2062673708
- Semantic Scholar
- 9c34209b9b5360bc9bb49a558828f9a34020ee7f
- Cited by
- 217
- References
- 162
- Citations by year
- 2026: 7 · 2025: 17 · 2024: 18 · 2023: 35 · 2022: 21 · 2021: 28 · 2020: 8 · 2019: 16 · 2018: 8 · 2017: 5 · 2016: 8 · 2015: 9 · 2014: 2 · 2013: 10 · 2012: 7
- FWCI
- 4.64
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Optics A Pure and Applied Optics (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- ANU Open Research (Australian National University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Australian Research Council
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and Classical Electrodynamics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Keywords
- Berry phase, spin Hall effect, geometrical optics, polarized light, rotating coordinate system, polarization evolution
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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