Abstract
We describe the general method for calculating the Casimir energy of two diffraction gratings periodic in one spatial direction and separated by a vacuum gap. We express the Casimir energy in terms of the Rayleigh coefficients.
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H. B. G. Casimir, Proc. K. Ned. Akad. Wet., 51, 793–795 (1948).
K. A. Milton, J. Phys. A, 37, R209–R277 (2004); arXiv:hep-th/0406024v1 (2004).
V. N. Marachevsky, J. Phys. A, 45, 374021 (2012).
R. L. Jaffe, Phys. Rev. D, 72, 021301 (2005); arXiv:hep-th/0503158v1 (2005).
A. Edery and V. N. Marachevsky, JHEP, 0812, 035 (2008); arXiv:0810.3430v2 [hep-th] (2008).
V. N. Marachevsky and Yu. M. Pis’mak, Phys. Rev. D, 81, 065005 (2010); arXiv:0907.1985v2 [hep-th] (2009).
I. V. Fialkovsky, V. N. Marachevsky, and D. V. Vassilevich, Phys. Rev. B, 84, 035446 (2011); arXiv:1102.1757v2 [hep-th] (2011).
A. W. Rodriguez, F. Capasso, and S. G. Johnson, Nature Photonics, 5, 211–221 (2011).
V. V. Nesterenko and I. G. Pirozhenko, Phys. Rev. Lett., 86, 052503 (2012).
A. Lambrecht and V. N. Marachevsky, Phys. Rev. Lett., 101, 160403 (2008); arXiv:0806.3142v2 [quant-ph] (2008).
S. J. Rahi, T. Emig, N. Graham, R. L. Jaffe, and M. Kardar, Phys. Rev. D, 80, 085021 (2009); arXiv:0908.2649v1 [quant-ph] (2009).
M. Bordag and I. Pirozhenko, Phys. Rev. D, 81, 085023 (2010); arXiv:0912.4047v2 [quant-ph] (2009).
A. Roy and U. Mohideen, Phys. Rev. Lett., 82, 4380–4383 (1999); V. N. Marachevsky, “The Casimir effect: Medium and geometry,” arXiv:1211.5056v1 [quant-ph] (2012).
F. Chen, U. Mohideen, G. L. Klimchitskaya, and V. M. Mostepanenko, Phys. Rev. Lett., 88, 101801 (2002); arXiv:quant-ph/0201087v1 (2002); Phys. Rev. A, 66, 032113 (2002); arXiv:quant-ph/0209167v1 (2002).
E. Lifshitz, Sov. Phys. JETP, 2, 73–83 (1956).
H. B. Chan, Y. Bao, J. Zou, R. A. Cirelli, F. Klemens, W. M. Mansfield, and C. S. Pai, Phys. Rev. Lett., 101, 030401 (2008).
R. Büscher, and T. Emig, Phys. Rev. A., 69, 062101 (2004); arXiv:cond-mat/0401451v2 (2004); Phys. Rev. Lett., 94, 133901 (2005).
A. Lambrecht and V. N. Marachevsky, Internat. J. Mod. Phys. A, 24, 1789–1795 (2009).
H.-C. Chiu, G. L. Klimchitskaya, V. N. Marachevsky, V. M. Mostepanenko, and U. Mohideen, Phys. Rev. B, 80, 121402 (2009); arXiv:0909.2161v1 [quant-ph] (2009); 81, 115417 (2010); arXiv:1002.3936v1 [quant-ph] (2010).
Y. Bao, R. Guérout, J. Lussange, A. Lambrecht, R. A. Cirelli, F. Klemens, W. M. Mansfield, C. S. Pai, and H. B. Chan, Phys. Rev. Lett., 105, 250402 (2010); arXiv:1009.3487v1 [quant-ph] (2010).
O. M. Rayleigh, Proc. Roy. Soc. A., 79, 399–416 (1907).
D. Maystre, ed., Selected Papers on Diffraction Gratings (Gdansk-Jurata, Poland, 1992), SPIE, Bellingham (1993); R. Petit, ed., Electromagnetic Theory of Gratings, Springer, Berlin (1980); M. C. Hutley, Diffraction Gratings, Acad. Press, London (1982); E. G. Loewen and E. Popov, Diffraction Gratings and Applications, Marcel Dekker, New York (1997).
K. Schram, Phys. Lett. A., 43, 282–284 (1973).
Yu. S. Barash and V. L. Ginzburg, Sov. Phys. Usp., 18, No. 5 (1975).
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 176, No. 1, pp. 117–126, July, 2013.
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Marachevsky, V.N. Casimir effect for periodic systems separated by a vacuum gap. Theor Math Phys 176, 929–936 (2013). https://doi.org/10.1007/s11232-013-0081-6
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DOI: https://doi.org/10.1007/s11232-013-0081-6