The helicity of the free electromagnetic field and its physical meaning

Afanasiev, G. N.; Stepanovsky, Yu. P.

doi:10.1007/bf02731014

Cited by 102 publications

(135 citation statements)

References 13 publications

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“…We indicate quantities determined by the transverse fields E ⊥ and B by the suffix "rad." The helicity density of the radiation field is defined by [24,25] …”

Section: B Continuity Of the Optical Helicity And Its Fluxmentioning

confidence: 99%

Conservation laws and symmetry transformations of the electromagnetic field with sources

Nienhuis

2016

Phys. Rev. A

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In classical electrodynamics, the universal conservation laws of energy, momentum, and angular momentum are expressed by well-known continuity equations for the densities of these quantities. In the presence of charges and currents source terms must be added. These terms describe the exchange of energy and (linear or angular) momentum between field and matter. Recently, other conserved quantities of the electromagnetic field have been introduced and discussed. Examples are the pseudoscalars chirality and helicity, which are related to the handedness of the field. Even though these quantities have no obvious definition for matter, their conservation laws can still be presented in the form of continuity equations with source terms added. We show that these terms shed light on the interaction of chiral light with matter. A different role of conserved quantities is that they generate symmetry transformations of the system. The spatial transformations translation and rotation of the radiation field are generated by differential operators acting on mode functions. These operators are identical in form to the operators for the momentum and angular momentum of a quantum particle with spin 1. Also, for the total helicity and spin angular momentum of the field such operators on mode functions can be identified. A quite different picture arises in a quantum description of the electromagnetic field. The operator nature of the conserved quantities then arises from the commutation rules of photon creation and annihilation operators. We analyze the relation between these two pictures of symmetry transformations of the electromagnetic field.

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“…We indicate quantities determined by the transverse fields E ⊥ and B by the suffix "rad." The helicity density of the radiation field is defined by [24,25] …”

Section: B Continuity Of the Optical Helicity And Its Fluxmentioning

confidence: 99%

Conservation laws and symmetry transformations of the electromagnetic field with sources

Nienhuis

2016

Phys. Rev. A

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“…It then emerges that the volume integrals of both χ(r) and j(r) are directly related to a conserved quantity [69], the scalar field helicity [70],…”

Section: Quantized Fieldsmentioning

confidence: 99%

Quantum formulation for nanoscale optical and material chirality: symmetry issues, space and time parity, and observables

Andrews

2018

J. Opt.

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To properly represent the interplay and coupling of optical and material chirality at the photonmolecule or photon-nanoparticle level invites a recognition of quantum facets in the fundamental aspects and mechanisms of light-matter interaction. It is therefore appropriate to cast theory in a general quantum form, one that is applicable to both linear and nonlinear optics as well as various forms of chiroptical interaction including chiral optomechanics. Such a framework, fully accounting for both radiation and matter in quantum terms, facilitates the scrutiny and identification of key issues concerning spatial and temporal parity, scale, dissipation and measurement. Furthermore it fully provides for describing the interactions of structured or twisted light beams with a vortex character, and it leads to the complete identification of symmetry conditions for materials to provide for chiral discrimination. Quantum considerations also lend a distinctive perspective to the very different senses in which other aspects of chirality are recognized in metamaterials. Duly attending to the symmetry principles governing allowed or disallowed forms of chiral discrimination supports an objective appraisal of the experimental possibilities and developing applications.

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“…The associated conserved charge is the space integral of the zeroth component, 9) by (3.1) -where we recognize (1.2), the "double Chern-Simons" expression of helicity [2,3,5,8,10,11]. Conversely, the charge (3.9) [i.e.…”

Section: A Wave Function Composed Of Potentialsmentioning

confidence: 99%

“…The century-old problem of symmetry of the vacuum Maxwell equations under duality transformations [1], E → cos θ E + sin θ B, B → − sin θ E + cos θ B, (1.1) has attracted considerable recent attention [2][3][4][5][6][7][8][9]. In particular, the associated Noether quantity is the (optical) helicity [10], expressed as the integral of two Chern-Simons terms…”

Section: Introductionmentioning

confidence: 99%

Duality and helicity: the photon wave function approach

2017

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The photon wave equation proposed in terms of the Riemann-Silberstein vector is derived from a first-order Dirac/Weyl-type action principle. It is symmetric w.r.t. duality transformations, but the associated Noether quantity vanishes. Replacing the fields by potentials and using instead a quadratic Klein-Gordon-type Lagrangian allows us to recover the double-Chern-Simons expression of conserved helicity and is shown to be equivalent to recently proposed alternative frameworks. Applied to the potential-modified theory the Dirac/Weyl-type approach yields again zero conserved charge, whereas the Klein-Gordon-type approach applied to the original setting yields Lipkin's "zilch".

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The helicity of the free electromagnetic field and its physical meaning

Cited by 102 publications

References 13 publications

Conservation laws and symmetry transformations of the electromagnetic field with sources

Conservation laws and symmetry transformations of the electromagnetic field with sources

Quantum formulation for nanoscale optical and material chirality: symmetry issues, space and time parity, and observables

Duality and helicity: the photon wave function approach

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