### Abstract

In this paper, we use Clifford (geometric) algebra Cl3,0 to verify if electromagnetic energy-momentum density is still conserved for oblique superposition of two elliptically polarized plane waves with the same frequency. We show that energy-momentum conservation is valid at any time only for the superposition of two counterpropagating elliptically polarized plane waves. We show that the time-average energy-momentum of the superposition of two circularly polarized waves with opposite handedness is conserved regardless of the propagation directions of the waves. And, we show that the resulting momentum density of the superposed waves generally has a vector component perpendicular to the momentum densities of the individual waves.

Original language | English |
---|---|

Pages (from-to) | 2468-2479 |

Number of pages | 12 |

Journal | Journal of the Optical Society of America A: Optics and Image Science, and Vision |

Volume | 27 |

Issue number | 11 |

DOIs | |

Publication status | Published - Jan 1 2010 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Atomic and Molecular Physics, and Optics
- Computer Vision and Pattern Recognition

### Cite this

*Journal of the Optical Society of America A: Optics and Image Science, and Vision*,

*27*(11), 2468-2479. https://doi.org/10.1364/JOSAA.27.002468

**Oblique superposition of two elliptically polarized lightwaves using geometric algebra : Is energy-momentum conserved?** / Sze, Michelle Wynne C.; Sugon, Quirino Jr Mallorca; McNamara, Daniel J.

Research output: Contribution to journal › Article

*Journal of the Optical Society of America A: Optics and Image Science, and Vision*, vol. 27, no. 11, pp. 2468-2479. https://doi.org/10.1364/JOSAA.27.002468

}

TY - JOUR

T1 - Oblique superposition of two elliptically polarized lightwaves using geometric algebra

T2 - Is energy-momentum conserved?

AU - Sze, Michelle Wynne C.

AU - Sugon, Quirino Jr Mallorca

AU - McNamara, Daniel J.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - In this paper, we use Clifford (geometric) algebra Cl3,0 to verify if electromagnetic energy-momentum density is still conserved for oblique superposition of two elliptically polarized plane waves with the same frequency. We show that energy-momentum conservation is valid at any time only for the superposition of two counterpropagating elliptically polarized plane waves. We show that the time-average energy-momentum of the superposition of two circularly polarized waves with opposite handedness is conserved regardless of the propagation directions of the waves. And, we show that the resulting momentum density of the superposed waves generally has a vector component perpendicular to the momentum densities of the individual waves.

AB - In this paper, we use Clifford (geometric) algebra Cl3,0 to verify if electromagnetic energy-momentum density is still conserved for oblique superposition of two elliptically polarized plane waves with the same frequency. We show that energy-momentum conservation is valid at any time only for the superposition of two counterpropagating elliptically polarized plane waves. We show that the time-average energy-momentum of the superposition of two circularly polarized waves with opposite handedness is conserved regardless of the propagation directions of the waves. And, we show that the resulting momentum density of the superposed waves generally has a vector component perpendicular to the momentum densities of the individual waves.

UR - http://www.scopus.com/inward/record.url?scp=78149301810&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78149301810&partnerID=8YFLogxK

U2 - 10.1364/JOSAA.27.002468

DO - 10.1364/JOSAA.27.002468

M3 - Article

C2 - 21045912

AN - SCOPUS:78149301810

VL - 27

SP - 2468

EP - 2479

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 1084-7529

IS - 11

ER -