### Abstract

The usual description in basic electromagnetic theory of the linear and angular momenta of light is centred upon the identification of Poynting's vector as the linear momentum density and its cross product with position, or azimuthal component, as the angular momentum density. This seemingly reasonable approach brings with it peculiarities, however, in particular with regards to the separation of angular momentum into orbital and spin contributions, which has sometimes been regarded as contrived. In the present paper, we observe that densities are not unique, which leads us to ask whether the usual description is, in fact, the most natural choice. To answer this, we adopt a fundamental rather than heuristic approach by first identifying appropriate symmetries of Maxwell's equations and subsequently applying Noether's theorem to obtain associated conservation laws. We do not arrive at the usual description. Rather, an equally acceptable one in which the relationship between linear and angular momenta is nevertheless more subtle and in which orbital and spin contributions emerge separately and with transparent forms.

Language | English |
---|---|

Article number | 125610 |

Number of pages | 8 |

Journal | Journal of Optics |

Volume | 17 |

Issue number | 12 |

DOIs | |

Publication status | Published - 29 Oct 2015 |

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### Keywords

- electrodynamics
- noether
- OAM

### Cite this

*Journal of Optics*,

*17*(12), [125610]. https://doi.org/10.1088/2040-8978/17/12/125610

}

*Journal of Optics*, vol. 17, no. 12, 125610. https://doi.org/10.1088/2040-8978/17/12/125610

**The azimuthal component of Poynting's vector and the angular momentum of light.** / Cameron, Robert P; Speirits, Fiona C; Gilson, Claire R; Allen, L; Barnett, Stephen M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The azimuthal component of Poynting's vector and the angular momentum of light

AU - Cameron, Robert P

AU - Speirits, Fiona C

AU - Gilson, Claire R

AU - Allen, L

AU - Barnett, Stephen M

PY - 2015/10/29

Y1 - 2015/10/29

N2 - The usual description in basic electromagnetic theory of the linear and angular momenta of light is centred upon the identification of Poynting's vector as the linear momentum density and its cross product with position, or azimuthal component, as the angular momentum density. This seemingly reasonable approach brings with it peculiarities, however, in particular with regards to the separation of angular momentum into orbital and spin contributions, which has sometimes been regarded as contrived. In the present paper, we observe that densities are not unique, which leads us to ask whether the usual description is, in fact, the most natural choice. To answer this, we adopt a fundamental rather than heuristic approach by first identifying appropriate symmetries of Maxwell's equations and subsequently applying Noether's theorem to obtain associated conservation laws. We do not arrive at the usual description. Rather, an equally acceptable one in which the relationship between linear and angular momenta is nevertheless more subtle and in which orbital and spin contributions emerge separately and with transparent forms.

AB - The usual description in basic electromagnetic theory of the linear and angular momenta of light is centred upon the identification of Poynting's vector as the linear momentum density and its cross product with position, or azimuthal component, as the angular momentum density. This seemingly reasonable approach brings with it peculiarities, however, in particular with regards to the separation of angular momentum into orbital and spin contributions, which has sometimes been regarded as contrived. In the present paper, we observe that densities are not unique, which leads us to ask whether the usual description is, in fact, the most natural choice. To answer this, we adopt a fundamental rather than heuristic approach by first identifying appropriate symmetries of Maxwell's equations and subsequently applying Noether's theorem to obtain associated conservation laws. We do not arrive at the usual description. Rather, an equally acceptable one in which the relationship between linear and angular momenta is nevertheless more subtle and in which orbital and spin contributions emerge separately and with transparent forms.

KW - electrodynamics

KW - noether

KW - OAM

UR - http://www.scopus.com/inward/record.url?scp=84947975866&partnerID=8YFLogxK

U2 - 10.1088/2040-8978/17/12/125610

DO - 10.1088/2040-8978/17/12/125610

M3 - Article

VL - 17

JO - Journal of Optics

T2 - Journal of Optics

JF - Journal of Optics

SN - 0972-8821

IS - 12

M1 - 125610

ER -