Abstract

Within the framework of quantum electrodynamics (QED), vacuum is a nonlinear medium that can be linearized for a rapidly time-varying electromagnetic field with a small amplitude subjected to a magnetostatic field. The linearized QED vacuum is a uniaxial dielectric-magnetic medium for which the degree of anisotropy is exceedingly small. By implementing an affine transformation of the spatial coordinates, the degree of anisotropy may become sufficiently large as to be readily perceivable. The inverse Bruggeman formalism can be implemented to specify a homogenized composite material (HCM) that is electromagnetically equivalent to the affinely transformed QED vacuum. This HCM can arise from remarkably simple component materials, for example, two isotropic dielectric materials and two isotropic magnetic materials, randomly distributed as oriented spheroidal particles.

© 2012 Optical Society of America

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  1. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
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  3. S. L. Adler, “Vacuum birefringence in a rotating magnetic field: corrigendum,” J. Phys. A 40, 5767 (2007).
    [CrossRef]
  4. Z. Bialynicka-Birula and I. Bialynicki-Birula, “Nonlinear effects in quantum electrodynamics. Photon propagation and photon splitting in an external field,” Phys. Rev. D 2, 2341–2345 (1970).
    [CrossRef]
  5. S. L. Adler, “Photon splitting and photon dispersion in a strong magnetic field,” Ann. Phys. 67, 599–647 (1971).
    [CrossRef]
  6. E. Iacopini and E. Zavattini, “Experimental method to detect the vacuum birefringence induced by a magnetic field,” Phys. Lett. B 85, 151–154 (1979).
    [CrossRef]
  7. E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
    [CrossRef]
  8. E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
    [CrossRef]
  9. T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
    [CrossRef]
  10. T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Towards a cylindrical cloak via inverse homogenization,” J. Opt. Soc. Am. A 29, 239–243 (2012).
    [CrossRef]
  11. H. S. M. Coxeter, Introduction to Geometry, 2nd ed. (Wiley, 1989).
  12. L. Li, J. Chandezon, G. Granet, and J.-P. Plumey, “Rigorous and efficient grating-analysis method made easy for optical engineers,” Appl. Opt. 38, 304–313 (1999).
    [CrossRef]
  13. M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Progr. Opt. 52, 261–304 (2009).
    [CrossRef]
  14. M. N. Chernodub, “Superconductivity of QCD vacuum in strong magnetic field,” Phys. Rev. D 82, 085011 (2010).
    [CrossRef]
  15. I. I. Smolyaninov, “Vacuum in a strong magnetic field as a hyperbolic metamaterial,” Phys. Rev. Lett. 107, 253903 (2011).
    [CrossRef]
  16. A. Lakhtakia and T. G. Mackay, “Integral equation for scattering of light by a strong magnetostatic field in vacuum,” Electromagnetics 27, 341–354 (2007).
    [CrossRef]
  17. W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie des Positrons,” Z. Phys. 98, 714–732 (1936).
    [CrossRef]
  18. J. Schwinger, “On gauge invariance and vacuum polarization,” Phys. Rev. 82, 664–679 (1951).
    [CrossRef]
  19. I. V. Lindell, Methods for Electromagnetic Field Analysis(Clarendon, 1992).
  20. G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
    [CrossRef]
  21. 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. 15, 263–266 (1997).
    [CrossRef]
  22. W. S. Weiglhofer, A. Lakhtakia, and B. Michel, “Correction to ‘Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium’ ,” Microw. Opt. Technol. Lett. 22, 221 (1999).
    [CrossRef]
  23. T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide (World Scientific, 2010).
  24. A. Lakhtakia, “Orthogonal symmetries of polarizability dyadics of bianisotropic ellipsoids,” Microw. Opt. Technol. Lett. 27, 175–177 (2000).
    [CrossRef]
  25. W. S. Weiglhofer, “On the inverse homogenization problem of linear composite materials,” Microw. Opt. Technol. Lett. 28, 421–423 (2001).
    [CrossRef]
  26. E. Cherkaev, “Inverse homogenization for evaluation of effective properties of a mixture,” Inverse Probl. 17, 1203–1218 (2001).
    [CrossRef]
  27. T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
    [CrossRef]
  28. S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
    [CrossRef]
  29. T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A 2, 426–432 (2000).
    [CrossRef]
  30. A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
    [CrossRef]
  31. G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
    [CrossRef]
  32. M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
    [CrossRef]

2012

2011

T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
[CrossRef]

I. I. Smolyaninov, “Vacuum in a strong magnetic field as a hyperbolic metamaterial,” Phys. Rev. Lett. 107, 253903 (2011).
[CrossRef]

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

2010

T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
[CrossRef]

S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
[CrossRef]

M. N. Chernodub, “Superconductivity of QCD vacuum in strong magnetic field,” Phys. Rev. D 82, 085011 (2010).
[CrossRef]

2009

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Progr. Opt. 52, 261–304 (2009).
[CrossRef]

2007

A. Lakhtakia and T. G. Mackay, “Integral equation for scattering of light by a strong magnetostatic field in vacuum,” Electromagnetics 27, 341–354 (2007).
[CrossRef]

S. L. Adler, “Vacuum birefringence in a rotating magnetic field,” J. Phys. A 40, F143–F152 (2007).
[CrossRef]

S. L. Adler, “Vacuum birefringence in a rotating magnetic field: corrigendum,” J. Phys. A 40, 5767 (2007).
[CrossRef]

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

2006

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

2001

W. S. Weiglhofer, “On the inverse homogenization problem of linear composite materials,” Microw. Opt. Technol. Lett. 28, 421–423 (2001).
[CrossRef]

E. Cherkaev, “Inverse homogenization for evaluation of effective properties of a mixture,” Inverse Probl. 17, 1203–1218 (2001).
[CrossRef]

2000

T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A 2, 426–432 (2000).
[CrossRef]

A. Lakhtakia, “Orthogonal symmetries of polarizability dyadics of bianisotropic ellipsoids,” Microw. Opt. Technol. Lett. 27, 175–177 (2000).
[CrossRef]

1999

L. Li, J. Chandezon, G. Granet, and J.-P. Plumey, “Rigorous and efficient grating-analysis method made easy for optical engineers,” Appl. Opt. 38, 304–313 (1999).
[CrossRef]

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, “Correction to ‘Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium’ ,” Microw. Opt. Technol. Lett. 22, 221 (1999).
[CrossRef]

1997

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. 15, 263–266 (1997).
[CrossRef]

1979

E. Iacopini and E. Zavattini, “Experimental method to detect the vacuum birefringence induced by a magnetic field,” Phys. Lett. B 85, 151–154 (1979).
[CrossRef]

1971

S. L. Adler, “Photon splitting and photon dispersion in a strong magnetic field,” Ann. Phys. 67, 599–647 (1971).
[CrossRef]

1970

Z. Bialynicka-Birula and I. Bialynicki-Birula, “Nonlinear effects in quantum electrodynamics. Photon propagation and photon splitting in an external field,” Phys. Rev. D 2, 2341–2345 (1970).
[CrossRef]

1951

J. Schwinger, “On gauge invariance and vacuum polarization,” Phys. Rev. 82, 664–679 (1951).
[CrossRef]

1936

W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie des Positrons,” Z. Phys. 98, 714–732 (1936).
[CrossRef]

Adler, S. L.

S. L. Adler, “Vacuum birefringence in a rotating magnetic field: corrigendum,” J. Phys. A 40, 5767 (2007).
[CrossRef]

S. L. Adler, “Vacuum birefringence in a rotating magnetic field,” J. Phys. A 40, F143–F152 (2007).
[CrossRef]

S. L. Adler, “Photon splitting and photon dispersion in a strong magnetic field,” Ann. Phys. 67, 599–647 (1971).
[CrossRef]

Alù, A.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Anderson, T. H.

Beruete, M.

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

Bialynicka-Birula, Z.

Z. Bialynicka-Birula and I. Bialynicki-Birula, “Nonlinear effects in quantum electrodynamics. Photon propagation and photon splitting in an external field,” Phys. Rev. D 2, 2341–2345 (1970).
[CrossRef]

Bialynicki-Birula, I.

Z. Bialynicka-Birula and I. Bialynicki-Birula, “Nonlinear effects in quantum electrodynamics. Photon propagation and photon splitting in an external field,” Phys. Rev. D 2, 2341–2345 (1970).
[CrossRef]

Bregant, M.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Briane, M.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Burghignoli, P.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Campillo, I.

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

Cantatore, G.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Capolino, F.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Carusotto, S.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Chandezon, J.

Cherkaev, E.

E. Cherkaev, “Inverse homogenization for evaluation of effective properties of a mixture,” Inverse Probl. 17, 1203–1218 (2001).
[CrossRef]

Chernodub, M. N.

M. N. Chernodub, “Superconductivity of QCD vacuum in strong magnetic field,” Phys. Rev. D 82, 085011 (2010).
[CrossRef]

Cimino, R.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Coxeter, H. S. M.

H. S. M. Coxeter, Introduction to Geometry, 2nd ed. (Wiley, 1989).

Della Valle, F.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Di Domenico, G.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Engheta, N.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Euler, H.

W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie des Positrons,” Z. Phys. 98, 714–732 (1936).
[CrossRef]

Gastaldi, U.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Granet, G.

Heisenberg, W.

W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie des Positrons,” Z. Phys. 98, 714–732 (1936).
[CrossRef]

Iacopini, E.

E. Iacopini and E. Zavattini, “Experimental method to detect the vacuum birefringence induced by a magnetic field,” Phys. Lett. B 85, 151–154 (1979).
[CrossRef]

Jackson, D. R.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Jamaian, S. S.

S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
[CrossRef]

Karuza, M.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Lakhtakia, A.

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Towards a cylindrical cloak via inverse homogenization,” J. Opt. Soc. Am. A 29, 239–243 (2012).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
[CrossRef]

A. Lakhtakia and T. G. Mackay, “Integral equation for scattering of light by a strong magnetostatic field in vacuum,” Electromagnetics 27, 341–354 (2007).
[CrossRef]

A. Lakhtakia, “Orthogonal symmetries of polarizability dyadics of bianisotropic ellipsoids,” Microw. Opt. Technol. Lett. 27, 175–177 (2000).
[CrossRef]

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, “Correction to ‘Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium’ ,” Microw. Opt. Technol. Lett. 22, 221 (1999).
[CrossRef]

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. 15, 263–266 (1997).
[CrossRef]

T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide (World Scientific, 2010).

Li, L.

Lindell, I. V.

I. V. Lindell, Methods for Electromagnetic Field Analysis(Clarendon, 1992).

Lovat, G.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Mackay, T. G.

T. H. Anderson, T. G. Mackay, and A. Lakhtakia, “Towards a cylindrical cloak via inverse homogenization,” J. Opt. Soc. Am. A 29, 239–243 (2012).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
[CrossRef]

S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
[CrossRef]

A. Lakhtakia and T. G. Mackay, “Integral equation for scattering of light by a strong magnetostatic field in vacuum,” Electromagnetics 27, 341–354 (2007).
[CrossRef]

T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A 2, 426–432 (2000).
[CrossRef]

T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide (World Scientific, 2010).

Michel, B.

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, “Correction to ‘Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium’ ,” Microw. Opt. Technol. Lett. 22, 221 (1999).
[CrossRef]

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. 15, 263–266 (1997).
[CrossRef]

Milotti, E.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Milton, G. W.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Navarro-Cía, M. N.

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

Plumey, J.-P.

Polacco, E.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Qiu, M.

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Progr. Opt. 52, 261–304 (2009).
[CrossRef]

Ruoso, G.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Salandrino, A.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Schwinger, J.

J. Schwinger, “On gauge invariance and vacuum polarization,” Phys. Rev. 82, 664–679 (1951).
[CrossRef]

Silveirinha, M.

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

Smolyaninov, I. I.

I. I. Smolyaninov, “Vacuum in a strong magnetic field as a hyperbolic metamaterial,” Phys. Rev. Lett. 107, 253903 (2011).
[CrossRef]

Sorolla, M.

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

Weiglhofer, W. S.

W. S. Weiglhofer, “On the inverse homogenization problem of linear composite materials,” Microw. Opt. Technol. Lett. 28, 421–423 (2001).
[CrossRef]

T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A 2, 426–432 (2000).
[CrossRef]

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, “Correction to ‘Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium’ ,” Microw. Opt. Technol. Lett. 22, 221 (1999).
[CrossRef]

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. 15, 263–266 (1997).
[CrossRef]

Willis, J. R.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Yan, M.

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Progr. Opt. 52, 261–304 (2009).
[CrossRef]

Yan, W.

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Progr. Opt. 52, 261–304 (2009).
[CrossRef]

Zavattini, E.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

E. Iacopini and E. Zavattini, “Experimental method to detect the vacuum birefringence induced by a magnetic field,” Phys. Lett. B 85, 151–154 (1979).
[CrossRef]

Zavattini, G.

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

Ann. Phys.

S. L. Adler, “Photon splitting and photon dispersion in a strong magnetic field,” Ann. Phys. 67, 599–647 (1971).
[CrossRef]

Appl. Opt.

Electromagnetics

A. Lakhtakia and T. G. Mackay, “Integral equation for scattering of light by a strong magnetostatic field in vacuum,” Electromagnetics 27, 341–354 (2007).
[CrossRef]

IET Microw. Antennas Propagat.

G. Lovat, P. Burghignoli, F. Capolino, and D. R. Jackson, “Combinations of low/high permittivity and/or permeability substrates for highly directive planar metamaterial antennas,” IET Microw. Antennas Propagat. 1, 177–183 (2007).
[CrossRef]

Inverse Probl.

E. Cherkaev, “Inverse homogenization for evaluation of effective properties of a mixture,” Inverse Probl. 17, 1203–1218 (2001).
[CrossRef]

J. Nanophoton.

T. G. Mackay and A. Lakhtakia, “Determination of constitutive and morphological parameters of columnar thin films by inverse homogenization,” J. Nanophoton. 4, 041535 (2010).
[CrossRef]

S. S. Jamaian and T. G. Mackay, “On limitations of the Bruggeman formalism for inverse homogenization,” J. Nanophoton. 4, 043510 (2010).
[CrossRef]

J. Opt. A

T. G. Mackay and W. S. Weiglhofer, “Homogenization of biaxial composite materials: dissipative anisotropic properties,” J. Opt. A 2, 426–432 (2000).
[CrossRef]

J. Opt. Soc. Am. A

J. Phys. A

S. L. Adler, “Vacuum birefringence in a rotating magnetic field,” J. Phys. A 40, F143–F152 (2007).
[CrossRef]

S. L. Adler, “Vacuum birefringence in a rotating magnetic field: corrigendum,” J. Phys. A 40, 5767 (2007).
[CrossRef]

Microw. Opt. Technol. Lett.

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. 15, 263–266 (1997).
[CrossRef]

W. S. Weiglhofer, A. Lakhtakia, and B. Michel, “Correction to ‘Maxwell Garnett and Bruggeman formalisms for a particulate composite with bianisotropic host medium’ ,” Microw. Opt. Technol. Lett. 22, 221 (1999).
[CrossRef]

A. Lakhtakia, “Orthogonal symmetries of polarizability dyadics of bianisotropic ellipsoids,” Microw. Opt. Technol. Lett. 27, 175–177 (2000).
[CrossRef]

W. S. Weiglhofer, “On the inverse homogenization problem of linear composite materials,” Microw. Opt. Technol. Lett. 28, 421–423 (2001).
[CrossRef]

New J. Phys.

G. W. Milton, M. Briane, and J. R. Willis, “On cloaking for elasticity and physical equations with a transformation invariant form,” New J. Phys. 8, 248 (2006).
[CrossRef]

Phys. Lett. B

E. Iacopini and E. Zavattini, “Experimental method to detect the vacuum birefringence induced by a magnetic field,” Phys. Lett. B 85, 151–154 (1979).
[CrossRef]

Phys. Rev.

J. Schwinger, “On gauge invariance and vacuum polarization,” Phys. Rev. 82, 664–679 (1951).
[CrossRef]

Phys. Rev. B

A. Alù, M. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[CrossRef]

M. N. Navarro-Cía, M. Beruete, I. Campillo, and M. Sorolla, “Enhanced lens by ϵ and μ near-zero metamaterial boosted by extraordinary optical transmission,” Phys. Rev. B 83, 115112 (2011).
[CrossRef]

T. G. Mackay and A. Lakhtakia, “Towards a realization of Schwarzschild-(anti-)de Sitter spacetime as a particulate metamaterial,” Phys. Rev. B 83, 195424 (2011).
[CrossRef]

Phys. Rev. D

Z. Bialynicka-Birula and I. Bialynicki-Birula, “Nonlinear effects in quantum electrodynamics. Photon propagation and photon splitting in an external field,” Phys. Rev. D 2, 2341–2345 (1970).
[CrossRef]

M. N. Chernodub, “Superconductivity of QCD vacuum in strong magnetic field,” Phys. Rev. D 82, 085011 (2010).
[CrossRef]

Phys. Rev. Lett.

I. I. Smolyaninov, “Vacuum in a strong magnetic field as a hyperbolic metamaterial,” Phys. Rev. Lett. 107, 253903 (2011).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Experimental observation of optical rotation generated in vacuum by a magnetic field,” Phys. Rev. Lett. 96, 110406 (2006).
[CrossRef]

E. Zavattini, G. Zavattini, G. Ruoso, E. Polacco, E. Milotti, M. Karuza, U. Gastaldi, G. Di Domenico, F. Della Valle, R. Cimino, S. Carusotto, G. Cantatore, and M. Bregant, “Editorial note: Experimental observation of optical rotation generated in vacuum by a magnetic field [Phys. Rev. Lett. 96, 110406 (2006)],” Phys. Rev. Lett. 99, 129901(E) (2007).
[CrossRef]

Progr. Opt.

M. Yan, W. Yan, and M. Qiu, “Invisibility cloaking by coordinate transformation,” Progr. Opt. 52, 261–304 (2009).
[CrossRef]

Z. Phys.

W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie des Positrons,” Z. Phys. 98, 714–732 (1936).
[CrossRef]

Other

I. V. Lindell, Methods for Electromagnetic Field Analysis(Clarendon, 1992).

T. G. Mackay and A. Lakhtakia, Electromagnetic Anisotropy and Bianisotropy: A Field Guide (World Scientific, 2010).

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

H. S. M. Coxeter, Introduction to Geometry, 2nd ed. (Wiley, 1989).

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Figures (4)

Fig. 1.
Fig. 1.

Relative permittivity parameters ϵs (dashed curve) and ϵt (solid curve) plotted versus |B̲s| (T).

Fig. 2.
Fig. 2.

Implementation I. The common shape parameter U (thick, solid curve) and volume fractions fa (dashed curve), fb (dashed–dotted curve), and fc (thin solid curve) plotted versus |B̲s| (T). The relative permittivities ϵa=4, ϵb=0.3, μc=3.4, and μd=0.4.

Fig. 3.
Fig. 3.

Implementation II. The shape parameters Ua (thick, solid curve), Ub (dashed curve), Uc (dashed–dotted curve), and Ud (thin solid curve) plotted versus |B̲s| (T). Relative permittivities ϵa=4, ϵb=0.3, μc=3.4, and μd=0.4. Volume fractions fa=0.15, fb=0.25, and fc=0.21.

Fig. 4.
Fig. 4.

Implementation III. The relative permittivities ϵa (thick, solid curve) and ϵb (dashed curve) and the relative permeabilities μc (dashed–dotted curve) and μd (thin solid curve) plotted versus |B̲s| (T). Shape parameter U=Ua,b,c,d=5. Volume fractions fa,b,c=0.25.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

D̲(x̲)=ϵ0ϵ̲̲·E̲(x̲)B̲(x̲)=μ0μ̲̲·H̲(x̲)}.
ϵ̳=(18a|B̲s|2)(B^̲sB^̲s)+(1+20a|B̲s|2)B^̲sB^̲sμ̳=118a|B̲s|2(B^̲sB^̲s)+1124a|B̲s|2B^̲sB^̲s},
x̲x̲·x̲
=p(B^̲sB^̲s)+qB^̲sB^̲s
p=(18a|B̲s|2)(1+20a|B̲s|2)(12δ|B̲s|)(1+5δ|B̲s|)q=18a|B̲s|212δ|B̲s|}
ϵ̳1detϵ̳·ϵ̳·T
=(12δ|B̲s|)(B^̲sB^̲s)+(1+5δ|B̲s|)B^̲sB^̲s
ϵt(B^̲sB^̲s)+ϵsB^̲sB^̲s
μ̳1detμ̳·μ̳·T
=12δ|B̲s|(18a|B̲s|2)2(B^̲sB^̲s)+1+5δ|B̲s|14a|B̲s|2(1+120a|B̲s|2)B^̲sB^̲s
μt(B^̲sB^̲s)+μsB^̲sB^̲s.
r̲s=ρ·r^̲,
=(B^̲sB^̲s)+UB^̲sB^̲s,(=a,b,c,d),
τ̳HCM=τtHCM(B^̲sB^̲s)+τsHCMB^̲sB^̲s,(τ=ϵ,μ).
Δ=[(ϵ̆sHCMϵsϵs)2+(ϵ̆tHCMϵtϵt)2+(μ̆sHCMμsμs)2+(μ̆tBrμtμt)2]1/2.

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