Motion of photons in a gravitational wave background

Zhe Chang; Chao-Guang Huang; Zhi-Chao Zhao

doi:10.1088/1674-1137/41/9/093108

Chinese Physics C> 2017, Vol. 41> Issue(9) : 093108 DOI: 10.1088/1674-1137/41/9/093108

Motion of photons in a gravitational wave background

Zhe Chang ^1,2,, ,
Chao-Guang Huang ^1,2,, ,
Zhi-Chao Zhao ^1,2,,

1.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
2.
School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China

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Abstract：
Photon motion in a Michelson interferometer is re-analyzed in terms of both geometrical optics and wave optics. The classical paths of the photons in the background of a gravitational wave are derived from the Fermat principle, which is the same as the null geodesics in general relativity. The deformed Maxwell equations and the wave equations of electric fields in the background of a gravitational wave are presented in a flat-space approximation. Both methods show that even the envelope of the response of an interferometer depends on the frequency of a gravitational wave, but it is almost independent of the frequency of the mirror's vibrations.
- Fermat principle ,
- modified Maxwell equations ,
- time variation ,
- frequency dependency ,
- gravitational wave vs mirror swing

References

[1]	B. P. Abbott et al (LIGO Scientific Collaboration), Phys. Rev. Lett., 116:061102(2016)
[2]	B. P. Abbott et al (LIGO Scientific Collaboration), Phys. Rev. Lett., 116:241103(2016)
[3]	E. D. Black and R. N. Gutenkunst, Am. J. Phys., 71:365(2003)
[4]	B. Allen, W. G. Anderson, P. R. Brady, D. A. Brown, and J. D. E. Creighton, Phys. Rev. D, 85:122006(2012)
[5]	J. Aasi et al, Class. Quant. Grav., 32:074001(2015)
[6]	Z. Chang, C. G. Huang, and Z. C. Zhao, Sci. China-Phys. Mech. Astro., 59:100421(2016)
[7]	Z. Chang, C. G. Huang, and Z. C. Zhao, Chin. Phys. C, 41(2):025001(2017)
[8]	J. Mizuno, A. Rdiger, R. Schilling, W. Winkler, and K. Danzmann, Optics Commun., 138:383-393(1997)
[9]	E. D. Black and R. N. Gutenkunst, Am. J. Phys., 69:79-87(2001)
[10]	M. Rakhmanov, R. L. Savage, D. H. Reitze et al, Phys. Lett. A, 305:239-244(2002)
[11]	J. Markowitz, R. Savage, and P. Schwinberg, LIGO Technical Document T030186-00-W (2003)
[12]	M. Rakhmanov, F. Bondu, O. Debieu et al, Class. Quantum Grav., 21:S487(2004)
[13]	M. Rakhmanov, Phys. Rev. D, 71:084003(2005)
[14]	M. Rakhmanov, J. D. Romano, and J. T. Whelan, Class. Quantum Grav., 25:184017(2008)
[15]	B. P. Abbott (LIGO Scientific Collaboration), arXiv:1602.03845
[16]	J. Mizuno, Comparison of optical configurations for laser-interferomettric gravitational-wave detectors, Ph.D. Thesis, (Hannover University)
[17]	L. D. Landau and E. M. Lifshitz, The classical theory of fields, 4th edition (Amsterdam:Butterworth-Heinemann, 1980)
[18]	K. S. Thorne, Gravitational radiation in Three hundred years of gravitation, ed by S. W. Hawking and W. Israel, (Cambridge:Cambridge University Press, 1987)

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Zhe Chang, Chao-Guang Huang and Zhi-Chao Zhao. Motion of photons in a gravitational wave background[J]. Chinese Physics C, 2017, 41(9): 093108. doi: 10.1088/1674-1137/41/9/093108

Zhe Chang, Chao-Guang Huang and Zhi-Chao Zhao. Motion of photons in a gravitational wave background[J]. Chinese Physics C, 2017, 41(9): 093108. doi: 10.1088/1674-1137/41/9/093108 shu

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Received: 2017-06-12

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Supported by National Natural Science Foundation of China (11275207, 11375203, 11690022, 11675182) and Strategic Priority Research Program of the Chinese Academy of Sciences Multi-waveband Gravitational Wave Universe (XDB23040000)

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通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Motion of photons in a gravitational wave background

Corresponding author: Zhe Chang,

Corresponding author: Chao-Guang Huang,

Corresponding author: Zhi-Chao Zhao,

1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

2. School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China

Received Date: 2017-06-12

Available Online: 2017-09-05

Fund Project: Supported by National Natural Science Foundation of China (11275207, 11375203, 11690022, 11675182) and Strategic Priority Research Program of the Chinese Academy of Sciences Multi-waveband Gravitational Wave Universe (XDB23040000)

Abstract: Photon motion in a Michelson interferometer is re-analyzed in terms of both geometrical optics and wave optics. The classical paths of the photons in the background of a gravitational wave are derived from the Fermat principle, which is the same as the null geodesics in general relativity. The deformed Maxwell equations and the wave equations of electric fields in the background of a gravitational wave are presented in a flat-space approximation. Both methods show that even the envelope of the response of an interferometer depends on the frequency of a gravitational wave, but it is almost independent of the frequency of the mirror's vibrations.

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Motion of photons in a gravitational wave background

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通讯作者: 陈斌, bchen63@163.com

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