Beams of electromagnetic radiation carrying angular momentum: The Riemann–Silberstein vector and the classical–quantum correspondence

Bialynicki‐Birula, Iwo; Bialynicka‐Birula, Zofia

doi:10.1016/j.optcom.2005.11.071

Cited by 61 publications

(71 citation statements)

References 22 publications

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“…These mode operatorsL mod andŜ mod have the same form as the quantum operators for the orbital angular momentum and spin of a particle with spin 1 [29]. They obey the commutation rules for angular momentum, in the general form…”

Section: Mode Operators For Conserved Quantitiesmentioning

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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Section: Mode Operators For Conserved Quantitiesmentioning

confidence: 99%

Conservation laws and symmetry transformations of the electromagnetic field with sources

Nienhuis

2016

Phys. Rev. A

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“…This is a general characteristic of all beams of radiation endowed with angular momentum [3]. For m = 0, we obtain the standard plane wave.…”

Section: Exponential Beamsmentioning

confidence: 86%

“…We named this vector in [4] the Riemann-Silberstein (RS) vector because it made its first appearance in [5] and was more extensively analysed in [6]. The RS vector was occasionally used in the past [7,8] in classical electrodynamics, but we believe that its power lies also in bridging a gap between the classical and the quantum theory of the electromagnetic field [3].…”

Section: Whittaker Representation Of the Rs Vectormentioning

confidence: 99%

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Exponential beams of electromagnetic radiation

Bialynicki‐Birula

Bialynicka‐Birula

2006

J. Phys. B: At. Mol. Opt. Phys.

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We show that in addition to well-known Bessel, Hermite-Gauss and LaguerreGauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of ρ. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker representation of the solutions of the Maxwell equations in terms of just one complex function. The connection between the Bessel beams and the exponential beams is made explicit by constructing the exponential beams as wave packets of Bessel beams.

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“…Is a two-dimensional localization of the one-photon state also restricted with the Paley-Wiener criterion? As shown in (Saari et al, 2005) the answer to the latter question is NO, if we construct the wave functions from certain so-called localized waves (Besieris et al, 1998;Bialynicki-Birula & Bialynicka-Birula, 2006;Hernández-Figueroa et al, 2008;Recami et al, 2003;Salo et al, 2000), which are recently discovered solutions to the linear wave equation. This Section reproduces examples from (Saari et al, 2005).…”

Section: Localization In Two Dimensionsmentioning

confidence: 99%

Photon Localization Revisited

Saari¹

2012

Quantum Optics and Laser Experiments

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Beams of electromagnetic radiation carrying angular momentum: The Riemann–Silberstein vector and the classical–quantum correspondence

Cited by 61 publications

References 22 publications

Conservation laws and symmetry transformations of the electromagnetic field with sources

Conservation laws and symmetry transformations of the electromagnetic field with sources

Exponential beams of electromagnetic radiation

Photon Localization Revisited

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