### Abstract

We derive exact expressions, in the form of Fourier integrals over the (k,ω) domain, for the energy, momentum, and angular momentum of a light pulse propagating in free space. The angular momentum is seen to split naturally into two parts. The spin contribution of each plane-wave constituent of the pulse, representing the difference between its right- and left-circular polarization content, is aligned with the corresponding k-vector. In contrast, the orbital angular momentum associated with each plane-wave is orthogonal to its k-vector. In general, the orbital angular momentum content of the wavepacket is the sum of an intrinsic part, due, for example, to phase vorticity, and an extrinsic part, r_{CM} × p, produced by the linear motion of the center-of-mass r_{CM} of the light pulse in the direction of its linear momentum p.

Original language | English (US) |
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Article number | 033838 |

Journal | Physical Review A |

Volume | 84 |

Issue number | 3 |

DOIs | |

State | Published - Sep 20 2011 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

**Spin and orbital angular momenta of electromagnetic waves in free space.** / Mansuripur, Masud.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 84, no. 3, 033838. https://doi.org/10.1103/PhysRevA.84.033838

}

TY - JOUR

T1 - Spin and orbital angular momenta of electromagnetic waves in free space

AU - Mansuripur, Masud

PY - 2011/9/20

Y1 - 2011/9/20

N2 - We derive exact expressions, in the form of Fourier integrals over the (k,ω) domain, for the energy, momentum, and angular momentum of a light pulse propagating in free space. The angular momentum is seen to split naturally into two parts. The spin contribution of each plane-wave constituent of the pulse, representing the difference between its right- and left-circular polarization content, is aligned with the corresponding k-vector. In contrast, the orbital angular momentum associated with each plane-wave is orthogonal to its k-vector. In general, the orbital angular momentum content of the wavepacket is the sum of an intrinsic part, due, for example, to phase vorticity, and an extrinsic part, rCM × p, produced by the linear motion of the center-of-mass rCM of the light pulse in the direction of its linear momentum p.

AB - We derive exact expressions, in the form of Fourier integrals over the (k,ω) domain, for the energy, momentum, and angular momentum of a light pulse propagating in free space. The angular momentum is seen to split naturally into two parts. The spin contribution of each plane-wave constituent of the pulse, representing the difference between its right- and left-circular polarization content, is aligned with the corresponding k-vector. In contrast, the orbital angular momentum associated with each plane-wave is orthogonal to its k-vector. In general, the orbital angular momentum content of the wavepacket is the sum of an intrinsic part, due, for example, to phase vorticity, and an extrinsic part, rCM × p, produced by the linear motion of the center-of-mass rCM of the light pulse in the direction of its linear momentum p.

UR - http://www.scopus.com/inward/record.url?scp=80053148328&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevA.84.033838

DO - 10.1103/PhysRevA.84.033838

M3 - Article

VL - 84

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 033838

ER -