Abstract

The demonstration and confirmation of metamaterials with simultaneous negative permittivity and permeability, and thus a negative refractive index, has resulted in a surge of interest in the reflection and refraction phenomena at the interfaces of these so-called negative-index materials (NIMs). We present a systematic study of the Brewster angle, i.e., the angle of incidence at which no reflection occurs, for both TE and TM waves scattering at the interface between two semi-infinite planar media, one of which may be a NIM. Detailed physical explanations that account for the Brewster angle for a plane wave incident upon a NIM are provided under the framework of the Ewald–Oseen extinction theorem, considering the re-emission of induced electric and magnetic dipoles. The conditions under which the Brewster angle exists are concisely summarized in a map of different material parameter regimes.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys. Usp. 10, 509–514 (1968).
    [CrossRef]
  2. R. A. Shelby, D. R. Smith, S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77–79 (2001).
    [CrossRef] [PubMed]
  3. R. W. Ziolkowski, E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
    [CrossRef]
  4. J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002).
    [CrossRef] [PubMed]
  5. A. A. Houck, J. B. Brock, I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett. 90, 137401 (2003).
    [CrossRef]
  6. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003).
    [CrossRef]
  7. S. Foteinopoulou, E. N. Economou, C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003).
    [CrossRef] [PubMed]
  8. P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404–404 (2003).
    [CrossRef]
  9. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [CrossRef] [PubMed]
  10. A. L. Pokrovsky, A. L. Efros, “Lens based on the use of left-handed materials,” Appl. Opt. 42, 5701–5705 (2003).
    [CrossRef] [PubMed]
  11. Z. M. Zhang, C. J. Fu, “Unusual photon tunneling in the presence of a layer with a negative refractive index,” Appl. Phys. Lett. 80, 1097–1099 (2002).
    [CrossRef]
  12. C. J. Fu, Z. M. Zhang, “Transmission enhancement using a negative-refraction layer,” Microscale Thermophys. Eng. 7, 221–234 (2003).
    [CrossRef]
  13. D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
    [CrossRef]
  14. W. T. Lu, J. B. Sokoloff, S. Sridhar, “Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative,” Phys. Rev. E 69, 026604 (2004).
    [CrossRef]
  15. Z. M. Zhang, K. Park, “On the group front and group velocity in a dispersive medium upon refraction from a non-dispersive medium,” J. Heat Transfer 126, 244–249 (2004).
    [CrossRef]
  16. J. A. Kong, B.-I. Wu, Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084–2086 (2002).
    [CrossRef]
  17. P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
    [CrossRef]
  18. A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
    [CrossRef]
  19. D.-K. Qing, G. Chen, “Goos-Hänchen shifts at the interfaces between left- and right-handed media,” Opt. Lett. 29, 872–874 (2004).
    [CrossRef] [PubMed]
  20. J. A. Kong, Electromagnetic Wave Theory, 2nd ed. (Wiley, 1990).
  21. S. G. Kaplan, L. M. Hanssen, “FT-IR based ellipsometer using high-quality Brewster-angle polarizers,” in Polarization: Measurement, Analysis, and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 285–293 (1999).
  22. A. H. Sihvola, I. V. Lindell, “Novel effects in wave reflection from biisotropic media,” Microwave Opt. Technol. Lett. 6, 581–584 (1993).
    [CrossRef]
  23. X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
    [CrossRef]
  24. T. A. Leskova, A. A. Maradudin, I. Simonsen, “Scattering of electromagnetic waves from the random surface of a left-handed medium,” in Surface Scattering and Diffraction for Advanced Metrology, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE4447, 6–16 (2001).
    [CrossRef]
  25. T. A. Leskova, A. A. Maradudin, I. Simonsen, “Coherent scattering of an electromagnetic wave from, and its transmission through, a slab of a left-handed medium with a randomly rough illuminated surface,” in Surface Scattering and Diffraction III, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE5189, 22–35 (2003).
    [CrossRef]
  26. M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 2.
    [CrossRef]
  27. R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 1963), Vol. 1, Secs. 31 and 30-7.
  28. M. Schwartz, Principles of Electrodynamics (McGraw-Hill, 1972), Chap. 7.
  29. H. M. Lai, Y. P. Lau, W. H. Wong, “Understanding wave characteristics via linear superposition of retarded fields,” Am. J. Phys. 70, 173–179 (2002).
    [CrossRef]
  30. G. N. Henderson, T. K. Gaylord, E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
    [CrossRef]

2004

W. T. Lu, J. B. Sokoloff, S. Sridhar, “Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative,” Phys. Rev. E 69, 026604 (2004).
[CrossRef]

Z. M. Zhang, K. Park, “On the group front and group velocity in a dispersive medium upon refraction from a non-dispersive medium,” J. Heat Transfer 126, 244–249 (2004).
[CrossRef]

D.-K. Qing, G. Chen, “Goos-Hänchen shifts at the interfaces between left- and right-handed media,” Opt. Lett. 29, 872–874 (2004).
[CrossRef] [PubMed]

2003

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

A. L. Pokrovsky, A. L. Efros, “Lens based on the use of left-handed materials,” Appl. Opt. 42, 5701–5705 (2003).
[CrossRef] [PubMed]

C. J. Fu, Z. M. Zhang, “Transmission enhancement using a negative-refraction layer,” Microscale Thermophys. Eng. 7, 221–234 (2003).
[CrossRef]

A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
[CrossRef]

A. A. Houck, J. B. Brock, I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

S. Foteinopoulou, E. N. Economou, C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404–404 (2003).
[CrossRef]

2002

J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002).
[CrossRef] [PubMed]

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

J. A. Kong, B.-I. Wu, Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084–2086 (2002).
[CrossRef]

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
[CrossRef]

Z. M. Zhang, C. J. Fu, “Unusual photon tunneling in the presence of a layer with a negative refractive index,” Appl. Phys. Lett. 80, 1097–1099 (2002).
[CrossRef]

H. M. Lai, Y. P. Lau, W. H. Wong, “Understanding wave characteristics via linear superposition of retarded fields,” Am. J. Phys. 70, 173–179 (2002).
[CrossRef]

2001

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

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

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

1993

A. H. Sihvola, I. V. Lindell, “Novel effects in wave reflection from biisotropic media,” Microwave Opt. Technol. Lett. 6, 581–584 (1993).
[CrossRef]

1991

G. N. Henderson, T. K. Gaylord, E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

1968

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

Berman, P. R.

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
[CrossRef]

Borie, E.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 2.
[CrossRef]

Brock, J. B.

A. A. Houck, J. B. Brock, I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef]

Chen, G.

Chuang, I. L.

A. A. Houck, J. B. Brock, I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef]

Dammertz, G.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Economou, E. N.

S. Foteinopoulou, E. N. Economou, C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Efros, A. L.

Feynman, R. P.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 1963), Vol. 1, Secs. 31 and 30-7.

Foteinopoulou, S.

S. Foteinopoulou, E. N. Economou, C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Fu, C. J.

C. J. Fu, Z. M. Zhang, “Transmission enhancement using a negative-refraction layer,” Microscale Thermophys. Eng. 7, 221–234 (2003).
[CrossRef]

Z. M. Zhang, C. J. Fu, “Unusual photon tunneling in the presence of a layer with a negative refractive index,” Appl. Phys. Lett. 80, 1097–1099 (2002).
[CrossRef]

Gaylord, T. K.

G. N. Henderson, T. K. Gaylord, E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Glytsis, E. N.

G. N. Henderson, T. K. Gaylord, E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Grzegorczyk, T. M.

J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002).
[CrossRef] [PubMed]

Hanssen, L. M.

S. G. Kaplan, L. M. Hanssen, “FT-IR based ellipsometer using high-quality Brewster-angle polarizers,” in Polarization: Measurement, Analysis, and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 285–293 (1999).

Heidinger, R.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Henderson, G. N.

G. N. Henderson, T. K. Gaylord, E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Heyman, E.

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

Houck, A. A.

A. A. Houck, J. B. Brock, I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef]

Kaplan, S. G.

S. G. Kaplan, L. M. Hanssen, “FT-IR based ellipsometer using high-quality Brewster-angle polarizers,” in Polarization: Measurement, Analysis, and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 285–293 (1999).

Koltenbah, B. E. C.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Kong, J. A.

J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002).
[CrossRef] [PubMed]

J. A. Kong, B.-I. Wu, Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084–2086 (2002).
[CrossRef]

J. A. Kong, Electromagnetic Wave Theory, 2nd ed. (Wiley, 1990).

Koppenberg, K.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Lai, H. M.

H. M. Lai, Y. P. Lau, W. H. Wong, “Understanding wave characteristics via linear superposition of retarded fields,” Am. J. Phys. 70, 173–179 (2002).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
[CrossRef]

Lau, Y. P.

H. M. Lai, Y. P. Lau, W. H. Wong, “Understanding wave characteristics via linear superposition of retarded fields,” Am. J. Phys. 70, 173–179 (2002).
[CrossRef]

Leighton, R. B.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 1963), Vol. 1, Secs. 31 and 30-7.

Leskova, T. A.

T. A. Leskova, A. A. Maradudin, I. Simonsen, “Scattering of electromagnetic waves from the random surface of a left-handed medium,” in Surface Scattering and Diffraction for Advanced Metrology, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE4447, 6–16 (2001).
[CrossRef]

T. A. Leskova, A. A. Maradudin, I. Simonsen, “Coherent scattering of an electromagnetic wave from, and its transmission through, a slab of a left-handed medium with a randomly rough illuminated surface,” in Surface Scattering and Diffraction III, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE5189, 22–35 (2003).
[CrossRef]

Leuterer, F.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Lindell, I. V.

A. H. Sihvola, I. V. Lindell, “Novel effects in wave reflection from biisotropic media,” Microwave Opt. Technol. Lett. 6, 581–584 (1993).
[CrossRef]

Lu, W. T.

W. T. Lu, J. B. Sokoloff, S. Sridhar, “Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative,” Phys. Rev. E 69, 026604 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404–404 (2003).
[CrossRef]

Maradudin, A. A.

T. A. Leskova, A. A. Maradudin, I. Simonsen, “Coherent scattering of an electromagnetic wave from, and its transmission through, a slab of a left-handed medium with a randomly rough illuminated surface,” in Surface Scattering and Diffraction III, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE5189, 22–35 (2003).
[CrossRef]

T. A. Leskova, A. A. Maradudin, I. Simonsen, “Scattering of electromagnetic waves from the random surface of a left-handed medium,” in Surface Scattering and Diffraction for Advanced Metrology, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE4447, 6–16 (2001).
[CrossRef]

Pacheco, J.

J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002).
[CrossRef] [PubMed]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404–404 (2003).
[CrossRef]

Park, K.

Z. M. Zhang, K. Park, “On the group front and group velocity in a dispersive medium upon refraction from a non-dispersive medium,” J. Heat Transfer 126, 244–249 (2004).
[CrossRef]

Pendry, J. B.

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Piosczyk, B.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Pokrovsky, A. L.

Qing, D.-K.

Sands, M.

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 1963), Vol. 1, Secs. 31 and 30-7.

Schultz, S.

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

Schurig, D.

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

Schwartz, M.

M. Schwartz, Principles of Electrodynamics (McGraw-Hill, 1972), Chap. 7.

Shelby, R. A.

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

Sihvola, A. H.

A. H. Sihvola, I. V. Lindell, “Novel effects in wave reflection from biisotropic media,” Microwave Opt. Technol. Lett. 6, 581–584 (1993).
[CrossRef]

Simonsen, I.

T. A. Leskova, A. A. Maradudin, I. Simonsen, “Scattering of electromagnetic waves from the random surface of a left-handed medium,” in Surface Scattering and Diffraction for Advanced Metrology, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE4447, 6–16 (2001).
[CrossRef]

T. A. Leskova, A. A. Maradudin, I. Simonsen, “Coherent scattering of an electromagnetic wave from, and its transmission through, a slab of a left-handed medium with a randomly rough illuminated surface,” in Surface Scattering and Diffraction III, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE5189, 22–35 (2003).
[CrossRef]

Smith, D. R.

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

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

Sokoloff, J. B.

W. T. Lu, J. B. Sokoloff, S. Sridhar, “Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative,” Phys. Rev. E 69, 026604 (2004).
[CrossRef]

Soukoulis, C. M.

S. Foteinopoulou, E. N. Economou, C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Sridhar, S.

W. T. Lu, J. B. Sokoloff, S. Sridhar, “Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative,” Phys. Rev. E 69, 026604 (2004).
[CrossRef]

P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404–404 (2003).
[CrossRef]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

Thumm, M.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Veselago, V. G.

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

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404–404 (2003).
[CrossRef]

Wagner, D.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 2.
[CrossRef]

Wong, W. H.

H. M. Lai, Y. P. Lau, W. H. Wong, “Understanding wave characteristics via linear superposition of retarded fields,” Am. J. Phys. 70, 173–179 (2002).
[CrossRef]

Wu, B.-I.

J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002).
[CrossRef] [PubMed]

J. A. Kong, B.-I. Wu, Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084–2086 (2002).
[CrossRef]

Yang, X.

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

Zhang, Y.

J. A. Kong, B.-I. Wu, Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084–2086 (2002).
[CrossRef]

J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002).
[CrossRef] [PubMed]

Zhang, Z. M.

Z. M. Zhang, K. Park, “On the group front and group velocity in a dispersive medium upon refraction from a non-dispersive medium,” J. Heat Transfer 126, 244–249 (2004).
[CrossRef]

C. J. Fu, Z. M. Zhang, “Transmission enhancement using a negative-refraction layer,” Microscale Thermophys. Eng. 7, 221–234 (2003).
[CrossRef]

Z. M. Zhang, C. J. Fu, “Unusual photon tunneling in the presence of a layer with a negative refractive index,” Appl. Phys. Lett. 80, 1097–1099 (2002).
[CrossRef]

Ziolkowski, R. W.

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

Am. J. Phys.

H. M. Lai, Y. P. Lau, W. H. Wong, “Understanding wave characteristics via linear superposition of retarded fields,” Am. J. Phys. 70, 173–179 (2002).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Z. M. Zhang, C. J. Fu, “Unusual photon tunneling in the presence of a layer with a negative refractive index,” Appl. Phys. Lett. 80, 1097–1099 (2002).
[CrossRef]

D. R. Smith, D. Schurig, J. B. Pendry, “Negative refraction of modulated electromagnetic waves,” Appl. Phys. Lett. 81, 2713–2715 (2002).
[CrossRef]

J. A. Kong, B.-I. Wu, Y. Zhang, “Lateral displacement of a Gaussian beam reflected from a grounded slab with negative permittivity and permeability,” Appl. Phys. Lett. 80, 2084–2086 (2002).
[CrossRef]

Electromagnetics

A. Lakhtakia, “On planewave remittances and Goos-Hänchen shifts of planar slabs with negative real permittivity and permeability,” Electromagnetics 23, 71–75 (2003).
[CrossRef]

Int. J. Infrared Millim. Waves

X. Yang, D. Wagner, B. Piosczyk, K. Koppenberg, E. Borie, R. Heidinger, F. Leuterer, G. Dammertz, M. Thumm, “Analysis of transmission characteristics for single and double disk windows,” Int. J. Infrared Millim. Waves 24, 619–628 (2003).
[CrossRef]

J. Heat Transfer

Z. M. Zhang, K. Park, “On the group front and group velocity in a dispersive medium upon refraction from a non-dispersive medium,” J. Heat Transfer 126, 244–249 (2004).
[CrossRef]

Microscale Thermophys. Eng.

C. J. Fu, Z. M. Zhang, “Transmission enhancement using a negative-refraction layer,” Microscale Thermophys. Eng. 7, 221–234 (2003).
[CrossRef]

Microwave Opt. Technol. Lett.

A. H. Sihvola, I. V. Lindell, “Novel effects in wave reflection from biisotropic media,” Microwave Opt. Technol. Lett. 6, 581–584 (1993).
[CrossRef]

Nature

P. V. Parimi, W. T. Lu, P. Vodo, S. Sridhar, “Imaging by flat lens using negative refraction,” Nature 426, 404–404 (2003).
[CrossRef]

Opt. Lett.

Phys. Rev. E

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

W. T. Lu, J. B. Sokoloff, S. Sridhar, “Refraction of electromagnetic energy for wave packets incident on a negative-index medium is always negative,” Phys. Rev. E 69, 026604 (2004).
[CrossRef]

P. R. Berman, “Goos-Hänchen shift in negatively refractive media,” Phys. Rev. E 66, 067603 (2002).
[CrossRef]

Phys. Rev. Lett.

J. Pacheco, T. M. Grzegorczyk, B.-I. Wu, Y. Zhang, J. A. Kong, “Power propagation in homogeneous isotropic frequency-dispersive left-handed media,” Phys. Rev. Lett. 89, 257401 (2002).
[CrossRef] [PubMed]

A. A. Houck, J. B. Brock, I. L. Chuang, “Experimental observations of a left-handed material that obeys Snell’s law,” Phys. Rev. Lett. 90, 137401 (2003).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef]

S. Foteinopoulou, E. N. Economou, C. M. Soukoulis, “Refraction in media with a negative refractive index,” Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[CrossRef] [PubMed]

Proc. IEEE

G. N. Henderson, T. K. Gaylord, E. N. Glytsis, “Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics,” Proc. IEEE 79, 1643–1659 (1991).
[CrossRef]

Science

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

Sov. Phys. Usp.

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

Other

J. A. Kong, Electromagnetic Wave Theory, 2nd ed. (Wiley, 1990).

S. G. Kaplan, L. M. Hanssen, “FT-IR based ellipsometer using high-quality Brewster-angle polarizers,” in Polarization: Measurement, Analysis, and Remote Sensing II, D. H. Goldstein, D. B. Chenault, eds., Proc. SPIE3754, 285–293 (1999).

T. A. Leskova, A. A. Maradudin, I. Simonsen, “Scattering of electromagnetic waves from the random surface of a left-handed medium,” in Surface Scattering and Diffraction for Advanced Metrology, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE4447, 6–16 (2001).
[CrossRef]

T. A. Leskova, A. A. Maradudin, I. Simonsen, “Coherent scattering of an electromagnetic wave from, and its transmission through, a slab of a left-handed medium with a randomly rough illuminated surface,” in Surface Scattering and Diffraction III, Z.-H. Gu, A. A. Maradudin, eds., Proc. SPIE5189, 22–35 (2003).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), Chap. 2.
[CrossRef]

R. P. Feynman, R. B. Leighton, M. Sands, The Feynman Lectures on Physics (Addison-Wesley, 1963), Vol. 1, Secs. 31 and 30-7.

M. Schwartz, Principles of Electrodynamics (McGraw-Hill, 1972), Chap. 7.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Schematic of reflection and refraction of a TE wave at the interface of two semi-infinite media: (a) from a PIM to a PIM; (b) from a PIM to a NIM. In (b), the refracted wave vector points opposite to the direction of energy flux. The positive sense for all angles is counterclockwise.

Fig. 2
Fig. 2

Power reflectivity ρs for a TE wave as a function of the incidence angle at the interface of vacuum and a dielectric–magnetic material (either PIM or NIM), with various values of the permittivity and permeability.

Fig. 3
Fig. 3

Radiated electric field amplitudes, normalized by the incident electric field amplitude, for a TE wave incident from vacuum (ε1 = μ1 = 1) into a dielectric–magnetic PIM: (a) ε2 = 1, μ2 = 4; (b) ε2 = 0.5, μ2 = 8. Note that Er0(e) is always zero in (a), since there are no induced electric dipoles.

Fig. 4
Fig. 4

Radiated electric field amplitudes for a TE wave incident into a lossless NIM: (a) ε2 = − 1, μ2 = −4; (b) ε2 = −0.5, μ2 = −8. Although Er0 is identical to the corresponding panel in Fig. 3, the separate contributions of Er0(e) and Er0(m) are entirely different.

Fig. 5
Fig. 5

Radiated electric field amplitudes for a TE wave incident into a PIM with ε2 = 2 and μ2 = 0.125: (a) magnitude; (b) phase. Note that if ε2 = −2 and μ2 = −0.125, both Er0(e) and Er0(m) will be different, but |Er0| remains the same. The phase ϕr0 will be the same if θ1 ≤ θc = 30° but will change sign if θ1 > θc.

Fig. 6
Fig. 6

Radiated electric field amplitudes for a TE wave incident into a NIM with ε2 = − 1 and μ2 = − 0.25: (a) magnitude; (b) phase. Note that if ε2 = 1 and μ2 = 0.25, Er0(e) = 0 and Er0 = Er0(m). The phase ϕr0 will be the same for θ1 ≤ θc = 30° but change sign for θ1 > θc as compared with the curve shown in the figure.

Fig. 7
Fig. 7

Regime map based on parameters X and Y. The Brewster angle exists for TM waves in regions (I) and (IV) and for TE waves in (II) and (III). The curves X = Y and XY = 1 correspond to θ1 ± θ2 = 90°.

Equations (16)

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

r s = E r 0 E i 0 = k 1 z / μ 1 k 2 z / μ 2 k 1 z / μ 1 + k 2 z / μ 2 = ε 1 / μ 1 cos θ 1 ε 2 / μ 2 cos θ 2 ε 1 / μ 1 cos θ 1 + ε 2 / μ 2 cos θ 2 ,
r p = H r 0 H i 0 = k 1 z / ε 1 k 2 z / ε 2 k 1 z / ε 1 + k 2 z / ε 2 = μ 1 / ε 1 cos θ 1 μ 2 / ε 2 cos θ 2 μ 1 / ε 1 cos θ 1 + μ 2 / ε 2 cos θ 2 ,
E rad = E rad ( e ) + E rad ( m ) = { E r < z < 0 E t E i 0 z < + .
E rad ( e ) = ( · Π e ) ε 0 μ 0 2 Π e t 2 ,
E rad ( m ) = μ 0 × Π m t ,
Π e ( r ) = V P ( r ) ε 0 G ( r r ) d r ,
Π m ( r ) = V M ( r ) G ( r r ) d r ,
Π e = { χ E t 0 exp [ i ( k x x k 1 z z ) ] 2 k 1 z ( k t z + k 1 z ) for < z < 0 χ E t 0 [ exp ( i k 1 · r ) 2 k 1 z ( k t z k 1 z ) + exp ( i k t · r ) k t 2 k 1 2 ] for 0 z < + ,
Π m = { χ m H t 0 exp [ i ( k x x k 1 z z ) ] 2 k 1 z ( k t z + k 1 z ) for < z < 0 χ m H t 0 [ exp ( i k 1 · r ) 2 k 1 z ( k t z k 1 z ) + exp ( i k t · r ) k t 2 k 1 2 ] for 0 z < + ,
χ k r × ( k r × E t 0 ) 2 k 1 z ( k 2 z + k 1 z ) + χ m k r × ( k 2 × E t 0 ) 2 k 1 z ( k 2 z + k 1 z ) μ 2 = E r 0 ,
χ k 1 × ( k 1 × E t 0 ) 2 k 1 z ( k 2 z k 1 z ) + χ m k 1 × ( k 2 × E t 0 ) 2 k 1 z ( k 2 z k 1 z ) μ 2 = E i 0 .
H r 0 = 1 μ 0 ω k r × E r 0 = H r 0 ŷ , H i 0 = 1 μ 0 ω k 1 × E i 0 = H i 0 ŷ , H t 0 = 1 μ 2 μ 0 ω k 2 × E t 0 = H t 0 ŷ .
1 ω μ 0 k 1 × E t 0 = k x 2 + k 1 z k 2 z ε 2 k 1 2 1 ω μ 2 μ 0 k 2 × E t 0 = k x 2 + k 1 z k 2 z ε 2 k 1 2 H t 0 , 1 ω μ 0 k r × E t 0 = k x 2 k 1 z k 2 z ε 2 k 1 2 H t 0 .
( μ 2 1 ) ( k 1 z k 2 z k x 2 ) = μ 2 ( ε 2 1 ) k 1 2 .
k r · k 2 = k x 2 k 1 z k 2 z = μ 2 ( ε 2 1 ) k 1 2 1 μ 2 ,
k 1 · k 2 = k x 2 + k 1 z k 2 z = μ 2 ( ε 2 + 1 ) k 1 2 1 + μ 2 .

Metrics