Duality and helicity: the photon wave function approach

Elbistan, Mahmut; Horváthy, P. A.; Zhang, P.-M.

doi:10.1016/j.physleta.2017.05.042

Cited by 15 publications

(11 citation statements)

References 23 publications

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“…The main independent dynamical properties of light are: energy, momentum, as well as spin and orbital AM. One can also add here helicity, which is an independent conserved quantity [55,57,59,69,70,[75][76][77][78][79]. The momentum and AM characteristics, both kinetic and canonical, for monochromatic free-space fields are given by equations (1.1) and (1.5)- (1.8).…”

Section: Momentum and Am Of Light In Dispersive Inhomogeneous Mediamentioning

confidence: 99%

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

2017

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We examine the momentum and angular momentum (AM) properties of monochromatic optical fields in dispersive and inhomogeneous isotropic media, using the Abraham-and Minkowski-type approaches, as well as the kinetic (Poynting-like) and canonical (with separate spin and orbital degrees of freedom) pictures. While the kinetic Abraham-Poynting momentum describes the energy flux and the group velocity of the wave, the Minkowski-type quantities, with proper dispersion corrections, describe the actual momentum and AM carried by the wave. The kinetic Minkowski-type momentum and AM densities agree with phenomenological results derived by Philbin. Using the canonical spinorbital decomposition, previously used for free-space fields, we find the corresponding canonical momentum, spin and orbital AM of light in a dispersive inhomogeneous medium. These acquire a very natural form analogous to the Brillouin energy density and are valid for arbitrary structured fields. The general theory is applied to a non-trivial example of a surface plasmon-polariton (SPP) wave at a metal-vacuum interface. We show that the integral momentum of the SPP per particle corresponds to the SPP wave vector, and hence exceeds the momentum of a photon in the vacuum. We also provide the first accurate calculation of the transverse spin and orbital AM of the SPP. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. Importantly, we present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory also predicts a transverse magnetization in the metal (i.e. a magnetic moment for the SPP) as well as the corresponding direct magnetization current, which provides the difference between the Abraham and Minkowski momenta.

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Section: Momentum and Am Of Light In Dispersive Inhomogeneous Mediamentioning

confidence: 99%

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

2017

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“…dimension 3. In contrast the gauge invariant local zilch current of Lipkin, the 0-zilch, has dimension 5, and is often associated with "the optical chirality flow" [29,31]. For a finite radius case, the perfect electric (12) and magnetic (14) conductor boundary conditions do not respect the zilch.…”

Section: Helicity and Zilchmentioning

confidence: 99%

Zilch vortical effect

2018

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We study the question if a helicity transporting current is generated in a rotating photon gas at finite temperature. One problem is that there is no gauge invariant local notion of helicity or helicity current. We circumvent this by studying not only the optical helicity current but also the gauge-invariant "zilch" current. In order to avoid problems of causality, we quantize the system on a cylinder of a finite radius and then discuss the limit of infinite radius. We find that net helicityand zilch currents are only generated in the case of the finite radius and are due to duality violating boundary conditions. A universal result exists for the current density on the axes of rotation in the high-temperature limit. To lowest order in the angular velocity, it takes a form similar to the wellknown temperature dependence of the chiral vortical effect for chiral fermions. We briefly discuss possible relations to gravitational anomalies. arXiv:1807.10705v1 [hep-th] 27 Jul 2018 (T E,T M ) J = ωA (T M,T E) J .We can therefore introduce eigenvectors of the curl operatorwith the eigenvaluesIn terms of electric and magnetic fields these modes fulfill the relationswhich show that these modes correspond to left-and right-circularly polarized electromagnetic fields. The gauge potential can now be quantized in this basis as follows:with ω 2 J = k 2 z + k 2 ⊥ as in Eq. (25). The projection of the angular momentum on the z axis can be computed from the expression of the Poynting vector P = i 2 E × E † as3 x : h := J α (+) † J α (+) J − α (−) † J α (−) J , (72) Q ζ = d 3 x : ζ := J ω 2 J α (+) † J α (+) J − α (−) † J α (−) J

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“…Indeed, in [30], a Berry phase 6 was derived through the adiabatic change of the parameters like Θ from a Lagrangian similar to (33). This phase accompanies the photon states and interestingly its explicit calculation results inχ (4).…”

Section: Applications Of the Hertz Vectors 41 Evolution Of The Opticmentioning

confidence: 96%

“…Moreover, replacing electromagnetic fields with their curls, one can get higher order Lagrangians which are again dual symmetric. As it is noted in [33], one can derive infinitely many conserved charges of free electromagnetism (see [13] and the references therein). In our procedure, with the definitions (40) and (41), it is clear that those charges are all related to the duality symmetry.…”

Section: A Dual Symmetric Hertz Vector Lagrangianmentioning

confidence: 99%

Optical helicity and Hertz vectors

Elbistan

2018

Physics Letters A

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We study the conserved quantity associated with the dual symmetry of the Maxwell equations, called the optical helicity, by means of transverse Hertz vectors. In the presence of charges, its evolution yields the integral of E · B which is the anomaly term for chiral fermions. We also discuss the helicity change in condensed matter systems where topological magnetoelectric effect emerges. An alternative expression of the optical helicity is also found. Lastly, a dual symmetric Hertz Lagrangian is constructed and its conserved charge is derived.

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Duality and helicity: the photon wave function approach

Cited by 15 publications

References 23 publications

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

Optical momentum and angular momentum in complex media: from the Abraham–Minkowski debate to unusual properties of surface plasmon-polaritons

Zilch vortical effect

Optical helicity and Hertz vectors

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