Abstract

In a preceding paper [J. Opt. Soc. Am. A 21, 122 (2004) ], we proposed proof of the nonexistence of harmonic solutions for a perfectly homogeneous left-handed material with both relative permittivity and relative permeability equal to 1 using the theorem of analytic continuation of an analytic function. The use of this theorem of analyticity has been questioned in a recent paper [Phys. Rev. E 73, 046608 (2006) ], arguing the possible inadequacy of the conditions of application of the theorem. We avoid the use of the analyticity theorem and propose a direct and simple proof of the nonexistence of such solutions. Furthermore, this proof is extended to any left-handed material with negative permeability and permittivity.

© 2008 Optical Society of America

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  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  2. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 86, 3966-3969 (2000).
    [CrossRef]
  3. G. W. 't Hooft, “Comment on negative refraction makes a perfect lens,” Phys. Rev. Lett. 87, 249701 (2001).
    [CrossRef] [PubMed]
  4. J. B. Pendry, “Pendry replies:” Phys. Rev. Lett. 87, 249702 (2001).
    [CrossRef]
  5. J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703 (2001).
    [CrossRef] [PubMed]
  6. J. B. Pendry, “Pendry replies:” Phys. Rev. Lett. 87, 249704 (2001).
    [CrossRef]
  7. D. Maystre, “Electromagnetic analysis of ultra-refraction and negative refraction,” J. Mod. Opt. 50, 1431-1444 (2003).
    [CrossRef]
  8. S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
    [CrossRef] [PubMed]
  9. J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap material,” J. Mod. Opt. 41, 345-351 (1994).
    [CrossRef]
  10. R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589-1617 (1987).
    [CrossRef]
  11. S. Y. Lin, V. M. Hietala, L. Wang, and E. D. Jones, “Highly dispersive photonic band-gap prism,” Opt. Lett. 21, 1771-1773 (1996).
    [CrossRef] [PubMed]
  12. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
    [CrossRef]
  13. C. M. Soukoulis, Photonic Band-Gap Materials (Kluwer, 1996).
  14. S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171-176 (1999).
    [CrossRef]
  15. B. Gralak, S. Enoch, and G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012-1020 (2000).
    [CrossRef]
  16. P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: Always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
    [CrossRef] [PubMed]
  17. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  18. N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
    [CrossRef] [PubMed]
  19. G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479-8482 (1994).
    [CrossRef]
  20. D. Maystre and S. Enoch, “Perfect lenses made with left-handed materials: Alice's mirror?” J. Opt. Soc. Am. A 21, 122-131 (2004).
    [CrossRef]
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  22. A. D. Yaghjian and T. B. Hansen, “Plane-wave solutions to frequency domain and time-domain scattering from magnetodielectric slabs,” Phys. Rev. E 73, 046608 (2006).
    [CrossRef]
  23. D. Maystre, Diffraction Gratings (SPIE, 1993).
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    [CrossRef]
  25. D. Maystre, “Rigorous vector theories of gratings,” in Progress in Optics, Vol. 21E.Wolf, ed. (Elsevier, North-Holland, 1984).
    [CrossRef]
  26. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  27. R. F. Cybulski and M. P. Silverman, “Enhanced internal reflection from an exponential amplifying region,” Opt. Lett. 8, 142-144 (1983).
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  28. G. Gomez-Santos, “Universal features of the time-evolution of evanescent modes in a left-handed perfect lens,” Phys. Rev. Lett. 90, 077401 (2003).
    [CrossRef] [PubMed]
  29. G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Opaque perfect lenses,” Physica B 394, 171-175 (2007).
    [CrossRef]
  30. G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
    [CrossRef]
  31. R. H. T. Bates, “Analytic constraints on electromagnetic field computations,” IEEE Trans. Microwave Theory Tech. 23, 605-623 (1975).
    [CrossRef]
  32. J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zellinger, “Experimental realization of freely propagating teleported qubits,” Nature 421, 721-725 (2003).
    [CrossRef] [PubMed]
  33. G. W. Milton, The Theory of Composites (Cambridge U. Press, 2002).
    [CrossRef]

2007 (1)

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Opaque perfect lenses,” Physica B 394, 171-175 (2007).
[CrossRef]

2006 (1)

A. D. Yaghjian and T. B. Hansen, “Plane-wave solutions to frequency domain and time-domain scattering from magnetodielectric slabs,” Phys. Rev. E 73, 046608 (2006).
[CrossRef]

2005 (1)

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

2004 (1)

2003 (3)

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zellinger, “Experimental realization of freely propagating teleported qubits,” Nature 421, 721-725 (2003).
[CrossRef] [PubMed]

G. Gomez-Santos, “Universal features of the time-evolution of evanescent modes in a left-handed perfect lens,” Phys. Rev. Lett. 90, 077401 (2003).
[CrossRef] [PubMed]

D. Maystre, “Electromagnetic analysis of ultra-refraction and negative refraction,” J. Mod. Opt. 50, 1431-1444 (2003).
[CrossRef]

2002 (4)

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: Always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

G. W. Milton, The Theory of Composites (Cambridge U. Press, 2002).
[CrossRef]

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

2001 (6)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
[CrossRef]

G. W. 't Hooft, “Comment on negative refraction makes a perfect lens,” Phys. Rev. Lett. 87, 249701 (2001).
[CrossRef] [PubMed]

J. B. Pendry, “Pendry replies:” Phys. Rev. Lett. 87, 249702 (2001).
[CrossRef]

J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703 (2001).
[CrossRef] [PubMed]

J. B. Pendry, “Pendry replies:” Phys. Rev. Lett. 87, 249704 (2001).
[CrossRef]

2000 (2)

1999 (1)

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171-176 (1999).
[CrossRef]

1998 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

1996 (2)

1994 (2)

J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap material,” J. Mod. Opt. 41, 345-351 (1994).
[CrossRef]

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

1993 (1)

D. Maystre, Diffraction Gratings (SPIE, 1993).

1987 (1)

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589-1617 (1987).
[CrossRef]

1984 (1)

D. Maystre, “Rigorous vector theories of gratings,” in Progress in Optics, Vol. 21E.Wolf, ed. (Elsevier, North-Holland, 1984).
[CrossRef]

1983 (1)

1980 (1)

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
[CrossRef]

1975 (1)

R. H. T. Bates, “Analytic constraints on electromagnetic field computations,” IEEE Trans. Microwave Theory Tech. 23, 605-623 (1975).
[CrossRef]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1962 (1)

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, 1962), Vol. 2, p. 501.

Aspelmeyer, M.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zellinger, “Experimental realization of freely propagating teleported qubits,” Nature 421, 721-725 (2003).
[CrossRef] [PubMed]

Bates, R. H. T.

R. H. T. Bates, “Analytic constraints on electromagnetic field computations,” IEEE Trans. Microwave Theory Tech. 23, 605-623 (1975).
[CrossRef]

Bowden, C. M.

J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap material,” J. Mod. Opt. 41, 345-351 (1994).
[CrossRef]

Courant, R.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, 1962), Vol. 2, p. 501.

Cybulski, R. F.

Dowling, J. P.

J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap material,” J. Mod. Opt. 41, 345-351 (1994).
[CrossRef]

Enoch, S.

D. Maystre and S. Enoch, “Perfect lenses made with left-handed materials: Alice's mirror?” J. Opt. Soc. Am. A 21, 122-131 (2004).
[CrossRef]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

B. Gralak, S. Enoch, and G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012-1020 (2000).
[CrossRef]

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171-176 (1999).
[CrossRef]

Garcia, N.

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

Gasparoni, S.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zellinger, “Experimental realization of freely propagating teleported qubits,” Nature 421, 721-725 (2003).
[CrossRef] [PubMed]

Gomez-Santos, G.

G. Gomez-Santos, “Universal features of the time-evolution of evanescent modes in a left-handed perfect lens,” Phys. Rev. Lett. 90, 077401 (2003).
[CrossRef] [PubMed]

Gralak, B.

Guérin, N.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Hansen, T. B.

A. D. Yaghjian and T. B. Hansen, “Plane-wave solutions to frequency domain and time-domain scattering from magnetodielectric slabs,” Phys. Rev. E 73, 046608 (2006).
[CrossRef]

Heyman, E.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
[CrossRef]

Hietala, V. M.

Hilbert, D.

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, 1962), Vol. 2, p. 501.

Jennewein, T.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zellinger, “Experimental realization of freely propagating teleported qubits,” Nature 421, 721-725 (2003).
[CrossRef] [PubMed]

Jones, E. D.

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Lin, S. Y.

Maystre, D.

D. Maystre and S. Enoch, “Perfect lenses made with left-handed materials: Alice's mirror?” J. Opt. Soc. Am. A 21, 122-131 (2004).
[CrossRef]

D. Maystre, “Electromagnetic analysis of ultra-refraction and negative refraction,” J. Mod. Opt. 50, 1431-1444 (2003).
[CrossRef]

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171-176 (1999).
[CrossRef]

D. Maystre, Diffraction Gratings (SPIE, 1993).

D. Maystre, “Rigorous vector theories of gratings,” in Progress in Optics, Vol. 21E.Wolf, ed. (Elsevier, North-Holland, 1984).
[CrossRef]

McPhedran, R. C.

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Opaque perfect lenses,” Physica B 394, 171-175 (2007).
[CrossRef]

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Milton, G. W.

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Opaque perfect lenses,” Physica B 394, 171-175 (2007).
[CrossRef]

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

G. W. Milton, The Theory of Composites (Cambridge U. Press, 2002).
[CrossRef]

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Nicorovici, N. A. P.

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

Nicorovici, N.-A. P.

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Opaque perfect lenses,” Physica B 394, 171-175 (2007).
[CrossRef]

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

Nieto-Vesperinas, M.

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

Notomi, M.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Pan, J. W.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zellinger, “Experimental realization of freely propagating teleported qubits,” Nature 421, 721-725 (2003).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, “Pendry replies:” Phys. Rev. Lett. 87, 249704 (2001).
[CrossRef]

J. B. Pendry, “Pendry replies:” Phys. Rev. Lett. 87, 249702 (2001).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 86, 3966-3969 (2000).
[CrossRef]

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
[CrossRef]

Podolskiy, V. A.

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

Sabouroux, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Silverman, M. P.

Smith, D. R.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

C. M. Soukoulis, Photonic Band-Gap Materials (Kluwer, 1996).

't Hooft, G. W.

G. W. 't Hooft, “Comment on negative refraction makes a perfect lens,” Phys. Rev. Lett. 87, 249701 (2001).
[CrossRef] [PubMed]

Tamamura, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Tayeb, G.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

B. Gralak, S. Enoch, and G. Tayeb, “Anomalous refractive properties of photonic crystals,” J. Opt. Soc. Am. A 17, 1012-1020 (2000).
[CrossRef]

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171-176 (1999).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Valanju, A. P.

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: Always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

Valanju, P. M.

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: Always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Vincent, P.

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

Walser, R. M.

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: Always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

Wang, L.

Williams, J. M.

J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703 (2001).
[CrossRef] [PubMed]

Yaghjian, A. D.

A. D. Yaghjian and T. B. Hansen, “Plane-wave solutions to frequency domain and time-domain scattering from magnetodielectric slabs,” Phys. Rev. E 73, 046608 (2006).
[CrossRef]

Zellinger, A.

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zellinger, “Experimental realization of freely propagating teleported qubits,” Nature 421, 721-725 (2003).
[CrossRef] [PubMed]

Zengerle, R.

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589-1617 (1987).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

R. H. T. Bates, “Analytic constraints on electromagnetic field computations,” IEEE Trans. Microwave Theory Tech. 23, 605-623 (1975).
[CrossRef]

J. Mod. Opt. (3)

J. P. Dowling and C. M. Bowden, “Anomalous index of refraction in photonic bandgap material,” J. Mod. Opt. 41, 345-351 (1994).
[CrossRef]

R. Zengerle, “Light propagation in singly and doubly periodic planar waveguides,” J. Mod. Opt. 34, 1589-1617 (1987).
[CrossRef]

D. Maystre, “Electromagnetic analysis of ultra-refraction and negative refraction,” J. Mod. Opt. 50, 1431-1444 (2003).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (1)

J. W. Pan, S. Gasparoni, M. Aspelmeyer, T. Jennewein, and A. Zellinger, “Experimental realization of freely propagating teleported qubits,” Nature 421, 721-725 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

S. Enoch, G. Tayeb, and D. Maystre, “Numerical evidence of ultrarefractive optics in photonic crystals,” Opt. Commun. 161, 171-176 (1999).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. B (2)

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Optical and dielectric properties of partially resonant composites,” Phys. Rev. B 49, 8479-8482 (1994).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, 10096-10099 (1998).
[CrossRef]

Phys. Rev. E (2)

R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
[CrossRef]

A. D. Yaghjian and T. B. Hansen, “Plane-wave solutions to frequency domain and time-domain scattering from magnetodielectric slabs,” Phys. Rev. E 73, 046608 (2006).
[CrossRef]

Phys. Rev. Lett. (9)

G. Gomez-Santos, “Universal features of the time-evolution of evanescent modes in a left-handed perfect lens,” Phys. Rev. Lett. 90, 077401 (2003).
[CrossRef] [PubMed]

N. Garcia and M. Nieto-Vesperinas, “Left-handed materials do not make a perfect lens,” Phys. Rev. Lett. 88, 207403 (2002).
[CrossRef] [PubMed]

P. M. Valanju, R. M. Walser, and A. P. Valanju, “Wave refraction in negative-index media: Always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
[CrossRef] [PubMed]

S. Enoch, G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, “A metamaterial for directive emission,” Phys. Rev. Lett. 89, 213902 (2002).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 86, 3966-3969 (2000).
[CrossRef]

G. W. 't Hooft, “Comment on negative refraction makes a perfect lens,” Phys. Rev. Lett. 87, 249701 (2001).
[CrossRef] [PubMed]

J. B. Pendry, “Pendry replies:” Phys. Rev. Lett. 87, 249702 (2001).
[CrossRef]

J. M. Williams, “Some problems with negative refraction,” Phys. Rev. Lett. 87, 249703 (2001).
[CrossRef] [PubMed]

J. B. Pendry, “Pendry replies:” Phys. Rev. Lett. 87, 249704 (2001).
[CrossRef]

Physica B (1)

G. W. Milton, N.-A. P. Nicorovici, and R. C. McPhedran, “Opaque perfect lenses,” Physica B 394, 171-175 (2007).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

G. W. Milton, N. A. P. Nicorovici, R. C. McPhedran, and V. A. Podolskiy, “A proof of superlensing in the quasistatic regime, and limitations of superlenses in this regime due to anomalous localized resonance,” Proc. R. Soc. London, Ser. A 461, 3999-4034 (2005).
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative value of ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

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C. M. Soukoulis, Photonic Band-Gap Materials (Kluwer, 1996).

R. Courant and D. Hilbert, Methods of Mathematical Physics (Interscience, 1962), Vol. 2, p. 501.

D. Maystre, Diffraction Gratings (SPIE, 1993).

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
[CrossRef]

D. Maystre, “Rigorous vector theories of gratings,” in Progress in Optics, Vol. 21E.Wolf, ed. (Elsevier, North-Holland, 1984).
[CrossRef]

G. W. Milton, The Theory of Composites (Cambridge U. Press, 2002).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Notations.

Fig. 2
Fig. 2

Fourier–Bessel expansion of G inside the circle Γ + ; G vanishes inside the gray region.

Equations (22)

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E S = H 0 ( 1 ) ( k 0 S M )
2 E s + k 0 2 E s = 4 i δ ( x ) δ ( y y s )
2 E + k 0 2 E = 4 i δ ( x ) δ ( y y s ) if y > 0 ,
2 E + k 0 2 E = 0 if e < y < 0 ,
2 E + k 0 2 E = 0 if y < e .
H 0 ( 1 ) { k 0 Q M } = 1 π + 1 β ( α ) exp { i α x + i β ( α ) y y Q } d α
β ( α ) = k 0 2 α 2 or i α 2 k 0 2 .
E S ( M ) = 1 π + 1 β ( α ) exp { i α x + i β ( α ) ( y S y ) } d α = 1 π + 1 β ( α ) exp ( i β ( α ) y S ) exp ( i α x i β ( α ) y ) .
in the slab , E S ( M ) = 1 π + 1 β ( α ) exp ( i β ( α ) y S ) exp ( i α x + i β ( α ) y ) d α ,
below the slab , y < e , E = 1 π + 1 β ( α ) exp ( i β ( α ) y F ) exp ( i α x i β ( α ) y ) d α .
if y S < y < 0 , E ( M ) = H 0 ( 1 ) ( k 0 S M ) ,
if y < y F , E ( M ) = H 0 ( 1 ) ( k 0 F M ) .
U ( x , y ) = { E ( x , y ) if y > 0 E ( x , y ) if e < y < 0 } .
if y > e , 2 G + k 0 2 G = 0 ,
except perhaps at S ( 0 , y S ) .
G ( r , θ ) = + G n ( r ) exp ( i n θ ) .
+ [ d 2 G n d r 2 + 1 r G n r + ( 1 n 2 r 2 ) G n ] exp ( i n θ ) = 0
G n ( r ) = a n J n ( r ) + b n Y n ( r )
G ( r , θ ) = + a n J n ( k 0 r ) exp ( i n θ ) .
E ( x , y ) = U ( x , y ) = E ( x , y ) .
E S = H 0 ( 1 ) ( k 0 S M ) .
E F = H 0 ( 1 ) ( k 0 F M ) .

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