Towards a piecewise-homogeneous metamaterial model of the collision of two linearly polarized gravitational plane waves

IEEE Transactions on Antennas and Propagation

Volumn 62, Issue 12, 2014, Pages 6149-6154

  Mackay, Tom G ^a,b   Lakhtakia, Akhlesh ^b  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

^b The Pennsylvania State University   (United States)

Author keywords

Colliding gravitational plane waves; homogenization; inverse Bruggeman formalism; Killing Cauchy horizon; metamaterial

Indexed keywords

EID: 84914125494     PISSN: 0018926X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAP.2014.2358689     Document Type: Article

References (35)

1. Metamaterials: Theory, Design, Applications, T. J. Cui, D. R. Smith, and R. Liu, Eds.. New York, NY, USA: Springer, 2010.
2. G. V. Skrotskii, "The influence of gravitation on the propagation of light," Soviet Phys.-Dokl, vol. 2, pp. 226-229, 1957.
3. J. Plébanski, "Electromagnetic waves in gravitational fields," Phys. Rev., vol. 118, pp. 1396-1408, 1960.
4. "General relativity and modern optics," in New Trends in Atomic Physics, W. Schleich, M. O. Scully, G. Grynberg, and R. Stora, Eds.. Amsterdam, The Netherlands: Elsevier, 1984, pp. 995-1124.
5. I. I. Smolyaninov, "Surface plasmon toy model of a rotating black hole," New J. Phys., vol. 5, no. 147, 2003.
6. M. Li, R.-X. Miao, and Y. Pang, "Casimir energy, holographic dark energy and electromagnetic metamaterial mimicking de sitter," Phys. Lett. B, vol. 689, pp. 55-59, 2010.
7. M. Li, R.-X.Miao, and Y. Pang, "More studies on metamaterials mimicking de sitter space," Opt. Express, vol. 18, pp. 9026-9033, 2010.
8. T. G. Mackay and A. Lakhtakia, "Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial," Phys. Rev. B, vol. 83, no. 195424, 2011.
9. R.-X. Miao, R. Zheng, and M. Li, "Metamaterials mimicking dynamic spacetime, d-brane and noncommutativity in string theory," Phys. Lett. B, vol. 696, pp. 550-555, 2011.
10. T. G. Mackay and A. Lakhtakia, "Towards a metamaterial simulation of a spinning cosmic string," Phys. Lett. A, vol. 374, pp. 2305-2308, 2010.
11. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, "Cloaking devices, electromagnetic wormholes, and transformation optics," SIAM Rev., vol. 51, pp. 3-33, 2009.
12. W. Lu, J. Jin, Z. Lin, and H. Chen, "A simple design of an artificial electromagnetic black hole," J. Appl. Phys., vol. 108, no. 064517, 2010.
13. J. B. Griffiths, Colliding Plane Waves in General Relativity. Oxford, U.K.: Clarendon, 1991.
14. D.Bini, A. Geralico, andM. Haney, "Refraction index analysis of light propagation in a colliding gravitational wave spacetime," Gen. Relativ. Gravit., vol. 46, no. 1644, 2014.
15. A. Ori, "Structure of the singularity inside a realistic rotating black hole," Phys. Rev. Lett., vol. 68, pp. 2117-2120, 1992.
16. U. Yurtsever, "Comments on the instability of black-hole inner horizons," Class. Quantum Grav., vol. 10, pp. L17-L24, 1993.
17. H. J. de Vega and N. Sánchez, "Strings falling into spacetime singularities," Phys. Rev. D, vol. 45, pp. 2783-2793, 1992.
18. O. Jofre and C. Núñuz, "Strings in plane wave backgrounds reexamined," Phys. Rev. D, vol. 50, pp. 5232-5240, 1992.
19. V. Ferrari, P. Pendenza, and G. Veneziano, "Beam-like gravitational waves and their geodesies," Gen. Relativ. Gravit., vol. 20, pp. 1185-1191, 1988.
20. D. Garfinkle and T. Vachaspati, "Cosmic-string traveling waves," Phys. Rev. D, vol. 42, pp. 1960-1963, 1990.
21. V. Ferrari and J. Ibãez, "A new exact solution for colliding gravitational plane waves," Gen. Relativ. Gravit., vol. 19, pp. 383-404, 1987.
22. V. Ferrari and J. Ibãez, "On the collision of gravitational plane waves: A class of soliton solutions," Gen. Relativ. Gravit., vol. 19, pp. 405-425, 1987.
23. V. Ferrari and J. Ibañez, "Type-D solutions describing the collision of plane-fronted gravitational waves," Proc. R. Soc. Lond. A, vol. 417, pp. 417-431, 1988.
24. T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide. Singapore: World Scientific, 2010.
25. W. S.Weiglhofer, A. Lakhtakia, and B. Michel, "Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium," Microw. Opt. Technol. Lett., vol. 22, pp. 263-266, 1999, corrections: vol. 22, p. 221, 1999.
26. B. Michel, "A Fourier space approach to the pointwise singularity of an anisotropic dielectric medium," Int. J. Appl. Electromagn. Mech., vol. 8, pp. 219-227, 1997.
27. B. Michel and W. S. Weiglhofer, "Pointwise singularity of dyadic Green function in a general bianisotropic medium," Arch. Elektr. Ubertrag., vol. 52, pp. 219-223, 1998, corrections: vol. 52, p. 310, 1998.
28. W. S.Weiglhofer, "Electromagnetic depolarization dyadics and elliptic integrals," J. Phys. A: Math. Gen., vol. 31, pp. 7191-7196, 1998.
29. T. G. Mackay and A. Lakhtakia, "Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization," J. Nanophotonics, vol. 4, no. 041535, 2010.
30. T. G. Mackay, "On extended homogenization formalisms for nanocomposites," J. Nanophotonics, vol. 2, no. 021850, 2008.
31. T. G. Mackay and W. S. Weiglhofer, "Homogenization of biaxial composite materials: Nondissipative dielectric properties," Electromagnetics, vol. 21, pp. 15-26, 2001.
32. J. Shin, J.-T. Shen, and S. Fan, "Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth," Phys. Rev. Lett., vol. 102, no. 093903, 2009.
33. M. Navarro-Cia, M. Beruete, I. Campillo, and M. Sorolla, "Enhanced lens by and near-zero metamaterial boosted by extraordinary optical transmission," Phys Rev. B, vol. 83, no. 115112, 2011.
34. A. H. Gevorgyan, "Magneto-optics of a thin film layer with helical structure and enormous anisotropy," Mol. Cryst. Liq. Cryst., vol. 382, pp. 1-19, 2002.
35. T. G.Mackay, "Towards metamaterials with giant dielectric anisotropy via ho- mogenization: An analytical study," Photon. Nanostruct.: Fundam. Appl., 2014 [Online]. Available: http://dx.doi.org/10.1016/j.photonics.2014.10.005