Analysis of the new conservation law in electromagnetic theory

Candlin, D. J.

doi:10.1007/bf02783348

Cited by 54 publications

(62 citation statements)

References 1 publication

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“…with A ⊥ = A ⊥ (r, t) and C ⊥ = C ⊥ (r, t) the transverse, gauge-invariant pieces [23] of the familiar magnetic vector potential [24,25] and an analogous electric pseudovector potential [68,69] defined here such that E = −Ȧ ⊥ = −∇ × C ⊥ / 0 µ 0 and B = ∇ × A ⊥ = −Ċ ⊥ . Helicity is a property of light that is familiar from particle physics, where it is recognized as being the value taken by the component of a photon's spin angular momentum in the direction of propagation: the helicity H = h dV of an optical field assumes a value equivalent to ±h per circularly polarized plane-wave-mode photon, in particular [26,[70][71][72][73]. Locally, h is found to be time independent for a strictly monochromatic optical field and may exhibit other interesting characteristics besides [26].…”

Section: )mentioning

confidence: 99%

Discriminatory optical force for chiral molecules

2014

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We suggest that the force F exerted upon a chiral molecule by light assumes the form F = a∇w + b∇h under appropriate circumstances, where a and b pertain to the molecule whilst w and h are the local densities of electric energy and helicity in the optical field; the gradients ∇ of these quantities thus governing the molecule's centre-of-mass motion. Whereas a is identical for the mirrorimage forms or enantiomers of the molecule, b has opposite signs; the associated contribution to F therefore pointing in opposite directions. A simple optical field is presented for which ∇w vanishes but ∇h does not, so that F is absolutely discriminatory. We then present two potential applications: a Stern-Gerlach-type deflector capable of spatially separating the enantiomers of a chiral molecule and a diffraction grating to which chiral molecules alone are sensitive; the resulting diffraction patterns thus encoding information about their chiral geometry.

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Section: )mentioning

confidence: 99%

Discriminatory optical force for chiral molecules

2014

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“…The duality action (3.7) goes over into that on the e.m. fields, eqn. (1.1), whereas the "true" helicity, (1.2), goes over into the "zilch", (4.8) [15][16][17].…”

Section: Resultsmentioning

confidence: 99%

“…We note also that while using the Dirac/Weyl-type first-order Lagrangian in the potentialsetting would yield again zero charge, our quadratic Klein-Gordon-type approach applied to the original framework yields, instead, Lipkin's "zilches" [15][16][17], -which is thus another manifestation of duality symmetry.…”

Section: Introductionmentioning

confidence: 95%

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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“…At the heart of this collection is the helicity [48], with the magnetic field, C ⊥ the solenodial electric pseudovector potential and the electric field [36,49–51]. Here and elsewhere ⋅ denotes the scalar product.…”

Section: The Angular Momentum Of Lightmentioning

confidence: 99%

“…It follows immediately that each of the angular momenta described above has an infinite number of higher and lower extensions [45,47], as do other quantities, including energy and linear momentum. If we consider the helicity, for example, and replace, superficially, the fields with their time derivatives, we obtain This is the 00-zilch [48,60,80], which was discovered before the helicity, in fact, and takes on a value equivalent to per photon, with the ω 2 here deriving from the product of two time derivatives. That the 00-zilch is conserved follows from the Maxwell-like equations (2.22) in the same way that the conservation of helicity follows from Maxwell’s equations themselves (2.20) [45,47].…”

Section: The Angular Momentum Of Lightmentioning

confidence: 99%

Chirality and the angular momentum of light

Cameron

Götte

Barnett

et al. 2017

Phil. Trans. R. Soc. A.

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Chirality is exhibited by objects that cannot be rotated into their mirror images. It is far from obvious that this has anything to do with the angular momentum of light, which owes its existence to rotational symmetries. There is nevertheless a subtle connection between chirality and the angular momentum of light. We demonstrate this connection and, in particular, its significance in the context of chiral light–matter interactions.This article is part of the themed issue ‘Optical orbital angular momentum’.

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Analysis of the new conservation law in electromagnetic theory

Cited by 54 publications

References 1 publication

Discriminatory optical force for chiral molecules

Discriminatory optical force for chiral molecules

Duality and helicity: the photon wave function approach

Chirality and the angular momentum of light

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