Abstract

The geometric representation at a fixed frequency of the wave vector (or dispersion) surface ω(k) for lossless, homogeneous, dielectric–magnetic uniaxial materials is explored for the case when the elements of the relative permittivity and permeability tensors of the material can have any sign. Electromagnetic plane waves propagating inside the material can exhibit dispersion surfaces in the form of ellipsoids of revolution, hyperboloids of one sheet, or hyperboloids of two sheets. Furthermore, depending on the relative orientation of the optic axis, the intersections of these surfaces with fixed planes of propagation can be circles, ellipses, hyperbolas, or straight lines. The understanding obtained is used to study the reflection and refraction of electromagnetic plane waves due to a planar interface with an isotropic medium.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  2. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 1074011-1074014 (2003).
    [CrossRef]
  3. A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 1374011-1374014 (2003).
    [CrossRef]
  4. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
    [CrossRef] [PubMed]
  5. J. B. Pendry, A. J. Holden, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  6. A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AEÜ, Int. J. Electron. Commun. 56, 407-410 (2002).
    [CrossRef]
  7. A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Negative phase-velocity mediums," in W.S.Weiglhofer and A.Lakhtakia, eds., Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
    [CrossRef]
  8. A. D. Boardman, N. King, and L. Velasco, "Negative refraction in perspective," Electromagnetics 25, 365-389 (2005).
    [CrossRef]
  9. T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 0266021 (2004).
    [CrossRef]
  10. L. B. Hu and S. T. Chui, "Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials," Phys. Rev. B 66, 0851081 (2002).
    [CrossRef]
  11. A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
    [CrossRef]
  12. D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 0774051 (2003).
    [CrossRef]
  13. D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
    [CrossRef]
  14. O. S. Eritsyan, "On the optical properties of anisotropic media in the presence of negative components of dielectric and (or) magnetic tensors," Crystallogr. Rep. 50, 465-470 (2005).
    [CrossRef]
  15. T. G. Mackay, A. Lakhtakia, and R. A. Depine, "Uniaxial dielectric media with hyperbolic dispersion relations," Microwave Opt. Technol. Lett. 48, 363-367 (2006)
    [CrossRef]
  16. Z. Liu, J. Xu, and Z. Lin, "Omnidirectional reflection from a slab of uniaxially anisotropic negative refractive index materials," Opt. Commun. 240, 19-27 (2004).
    [CrossRef]
  17. R. A. Depine and A. Lakhtakia, "Diffraction by a grating made of an uniaxial dielectric magnetic medium exhibiting negative refraction," New J. Phys. 7, 158 (2005).
    [CrossRef]
  18. R. A. Depine, M. E. Inchaussandague, and A. Lakhtakia, "Application of the differential method to uniaxial gratings with an infinite number of refraction channels: scalar case," Opt. Commun. 258, 90-96 (2006)
    [CrossRef]
  19. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Plane waves and canonical sources in a gyroelectromagnetic uniaxial medium," Int. J. Electron. 71, 853-861 (1991).
    [CrossRef]
  20. A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space," J. Mod. Opt. 38, 649-657 (1991).
    [CrossRef]
  21. H. Lütkepohl, Handbook of Matrices (Wiley, 1996).
  22. H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-free Approach (McGraw-Hill, 1983).
  23. R. A. Depine, A. Lakhtakia, and D. R. Smith, "Enhanced diffraction by a rectangular grating made of a negative phase-velocity (or negative index) material," Phys. Lett. A 337, 155-160 (2005).
    [CrossRef]
  24. A. Lakhtakia and M. W. McCall, "Counterposed phase velocity and energy-transport velocity vectors in a dielectric-magnetic uniaxial medium," Optik (Stuttgart) 115, 28-30 (2004).
    [CrossRef]

2006

T. G. Mackay, A. Lakhtakia, and R. A. Depine, "Uniaxial dielectric media with hyperbolic dispersion relations," Microwave Opt. Technol. Lett. 48, 363-367 (2006)
[CrossRef]

R. A. Depine, M. E. Inchaussandague, and A. Lakhtakia, "Application of the differential method to uniaxial gratings with an infinite number of refraction channels: scalar case," Opt. Commun. 258, 90-96 (2006)
[CrossRef]

2005

R. A. Depine, A. Lakhtakia, and D. R. Smith, "Enhanced diffraction by a rectangular grating made of a negative phase-velocity (or negative index) material," Phys. Lett. A 337, 155-160 (2005).
[CrossRef]

O. S. Eritsyan, "On the optical properties of anisotropic media in the presence of negative components of dielectric and (or) magnetic tensors," Crystallogr. Rep. 50, 465-470 (2005).
[CrossRef]

A. D. Boardman, N. King, and L. Velasco, "Negative refraction in perspective," Electromagnetics 25, 365-389 (2005).
[CrossRef]

R. A. Depine and A. Lakhtakia, "Diffraction by a grating made of an uniaxial dielectric magnetic medium exhibiting negative refraction," New J. Phys. 7, 158 (2005).
[CrossRef]

2004

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 0266021 (2004).
[CrossRef]

Z. Liu, J. Xu, and Z. Lin, "Omnidirectional reflection from a slab of uniaxially anisotropic negative refractive index materials," Opt. Commun. 240, 19-27 (2004).
[CrossRef]

A. Lakhtakia and M. W. McCall, "Counterposed phase velocity and energy-transport velocity vectors in a dielectric-magnetic uniaxial medium," Optik (Stuttgart) 115, 28-30 (2004).
[CrossRef]

D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
[CrossRef]

2003

A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
[CrossRef]

D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 0774051 (2003).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 1074011-1074014 (2003).
[CrossRef]

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 1374011-1374014 (2003).
[CrossRef]

2002

L. B. Hu and S. T. Chui, "Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials," Phys. Rev. B 66, 0851081 (2002).
[CrossRef]

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AEÜ, Int. J. Electron. Commun. 56, 407-410 (2002).
[CrossRef]

2001

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

1999

J. B. Pendry, A. J. Holden, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1996

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

1991

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Plane waves and canonical sources in a gyroelectromagnetic uniaxial medium," Int. J. Electron. 71, 853-861 (1991).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space," J. Mod. Opt. 38, 649-657 (1991).
[CrossRef]

Boardman, A. D.

A. D. Boardman, N. King, and L. Velasco, "Negative refraction in perspective," Electromagnetics 25, 365-389 (2005).
[CrossRef]

Brock, J. B.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 1374011-1374014 (2003).
[CrossRef]

Chen, H. C.

H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-free Approach (McGraw-Hill, 1983).

Chuang, I. L.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 1374011-1374014 (2003).
[CrossRef]

Chui, S. T.

L. B. Hu and S. T. Chui, "Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials," Phys. Rev. B 66, 0851081 (2002).
[CrossRef]

Depine, R. A.

R. A. Depine, M. E. Inchaussandague, and A. Lakhtakia, "Application of the differential method to uniaxial gratings with an infinite number of refraction channels: scalar case," Opt. Commun. 258, 90-96 (2006)
[CrossRef]

T. G. Mackay, A. Lakhtakia, and R. A. Depine, "Uniaxial dielectric media with hyperbolic dispersion relations," Microwave Opt. Technol. Lett. 48, 363-367 (2006)
[CrossRef]

R. A. Depine and A. Lakhtakia, "Diffraction by a grating made of an uniaxial dielectric magnetic medium exhibiting negative refraction," New J. Phys. 7, 158 (2005).
[CrossRef]

R. A. Depine, A. Lakhtakia, and D. R. Smith, "Enhanced diffraction by a rectangular grating made of a negative phase-velocity (or negative index) material," Phys. Lett. A 337, 155-160 (2005).
[CrossRef]

Eritsyan, O. S.

O. S. Eritsyan, "On the optical properties of anisotropic media in the presence of negative components of dielectric and (or) magnetic tensors," Crystallogr. Rep. 50, 465-470 (2005).
[CrossRef]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 1074011-1074014 (2003).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Houck, A. A.

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 1374011-1374014 (2003).
[CrossRef]

Hu, L. B.

L. B. Hu and S. T. Chui, "Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials," Phys. Rev. B 66, 0851081 (2002).
[CrossRef]

Inchaussandague, M. E.

R. A. Depine, M. E. Inchaussandague, and A. Lakhtakia, "Application of the differential method to uniaxial gratings with an infinite number of refraction channels: scalar case," Opt. Commun. 258, 90-96 (2006)
[CrossRef]

King, N.

A. D. Boardman, N. King, and L. Velasco, "Negative refraction in perspective," Electromagnetics 25, 365-389 (2005).
[CrossRef]

Kolinko, P.

Koltenbah, B. E. C.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 1074011-1074014 (2003).
[CrossRef]

Lakhtakia, A.

T. G. Mackay, A. Lakhtakia, and R. A. Depine, "Uniaxial dielectric media with hyperbolic dispersion relations," Microwave Opt. Technol. Lett. 48, 363-367 (2006)
[CrossRef]

R. A. Depine, M. E. Inchaussandague, and A. Lakhtakia, "Application of the differential method to uniaxial gratings with an infinite number of refraction channels: scalar case," Opt. Commun. 258, 90-96 (2006)
[CrossRef]

R. A. Depine and A. Lakhtakia, "Diffraction by a grating made of an uniaxial dielectric magnetic medium exhibiting negative refraction," New J. Phys. 7, 158 (2005).
[CrossRef]

R. A. Depine, A. Lakhtakia, and D. R. Smith, "Enhanced diffraction by a rectangular grating made of a negative phase-velocity (or negative index) material," Phys. Lett. A 337, 155-160 (2005).
[CrossRef]

A. Lakhtakia and M. W. McCall, "Counterposed phase velocity and energy-transport velocity vectors in a dielectric-magnetic uniaxial medium," Optik (Stuttgart) 115, 28-30 (2004).
[CrossRef]

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 0266021 (2004).
[CrossRef]

A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
[CrossRef]

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AEÜ, Int. J. Electron. Commun. 56, 407-410 (2002).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space," J. Mod. Opt. 38, 649-657 (1991).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Plane waves and canonical sources in a gyroelectromagnetic uniaxial medium," Int. J. Electron. 71, 853-861 (1991).
[CrossRef]

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Negative phase-velocity mediums," in W.S.Weiglhofer and A.Lakhtakia, eds., Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 1074011-1074014 (2003).
[CrossRef]

Lin, Z.

Z. Liu, J. Xu, and Z. Lin, "Omnidirectional reflection from a slab of uniaxially anisotropic negative refractive index materials," Opt. Commun. 240, 19-27 (2004).
[CrossRef]

Liu, Z.

Z. Liu, J. Xu, and Z. Lin, "Omnidirectional reflection from a slab of uniaxially anisotropic negative refractive index materials," Opt. Commun. 240, 19-27 (2004).
[CrossRef]

Lütkepohl, H.

H. Lütkepohl, Handbook of Matrices (Wiley, 1996).

Mackay, T. G.

T. G. Mackay, A. Lakhtakia, and R. A. Depine, "Uniaxial dielectric media with hyperbolic dispersion relations," Microwave Opt. Technol. Lett. 48, 363-367 (2006)
[CrossRef]

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 0266021 (2004).
[CrossRef]

McCall, M. W.

A. Lakhtakia and M. W. McCall, "Counterposed phase velocity and energy-transport velocity vectors in a dielectric-magnetic uniaxial medium," Optik (Stuttgart) 115, 28-30 (2004).
[CrossRef]

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AEÜ, Int. J. Electron. Commun. 56, 407-410 (2002).
[CrossRef]

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Negative phase-velocity mediums," in W.S.Weiglhofer and A.Lakhtakia, eds., Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
[CrossRef]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 1074011-1074014 (2003).
[CrossRef]

Pendry, J. B.

J. B. Pendry, A. J. Holden, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Schultz, S.

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

Schurig, D.

D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
[CrossRef]

D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 0774051 (2003).
[CrossRef]

Shelby, R. A.

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

Sherwin, J. A.

A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
[CrossRef]

Smith, D. R.

R. A. Depine, A. Lakhtakia, and D. R. Smith, "Enhanced diffraction by a rectangular grating made of a negative phase-velocity (or negative index) material," Phys. Lett. A 337, 155-160 (2005).
[CrossRef]

D. R. Smith, P. Kolinko, and D. Schurig, "Negative refraction in indefinite media," J. Opt. Soc. Am. B 21, 1032-1043 (2004).
[CrossRef]

D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 0774051 (2003).
[CrossRef]

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

Stewart, W. J.

J. B. Pendry, A. J. Holden, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 1074011-1074014 (2003).
[CrossRef]

Varadan, V. K.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space," J. Mod. Opt. 38, 649-657 (1991).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Plane waves and canonical sources in a gyroelectromagnetic uniaxial medium," Int. J. Electron. 71, 853-861 (1991).
[CrossRef]

Varadan, V. V.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Plane waves and canonical sources in a gyroelectromagnetic uniaxial medium," Int. J. Electron. 71, 853-861 (1991).
[CrossRef]

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space," J. Mod. Opt. 38, 649-657 (1991).
[CrossRef]

Velasco, L.

A. D. Boardman, N. King, and L. Velasco, "Negative refraction in perspective," Electromagnetics 25, 365-389 (2005).
[CrossRef]

Weiglhofer, W. S.

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AEÜ, Int. J. Electron. Commun. 56, 407-410 (2002).
[CrossRef]

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Negative phase-velocity mediums," in W.S.Weiglhofer and A.Lakhtakia, eds., Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
[CrossRef]

Xu, J.

Z. Liu, J. Xu, and Z. Lin, "Omnidirectional reflection from a slab of uniaxially anisotropic negative refractive index materials," Opt. Commun. 240, 19-27 (2004).
[CrossRef]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

AEÜ, Int. J. Electron. Commun.

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Brief overview of recent developments on negative phase-velocity mediums (alias left-handed materials)," AEÜ, Int. J. Electron. Commun. 56, 407-410 (2002).
[CrossRef]

Crystallogr. Rep.

O. S. Eritsyan, "On the optical properties of anisotropic media in the presence of negative components of dielectric and (or) magnetic tensors," Crystallogr. Rep. 50, 465-470 (2005).
[CrossRef]

Electromagnetics

A. D. Boardman, N. King, and L. Velasco, "Negative refraction in perspective," Electromagnetics 25, 365-389 (2005).
[CrossRef]

IEEE Trans. Microwave Theory Tech.

J. B. Pendry, A. J. Holden, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Int. J. Electron.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Plane waves and canonical sources in a gyroelectromagnetic uniaxial medium," Int. J. Electron. 71, 853-861 (1991).
[CrossRef]

Int. J. Infrared Millim. Waves

A. Lakhtakia and J. A. Sherwin, "Orthorhombic materials and perfect lenses," Int. J. Infrared Millim. Waves 24, 19-23 (2003).
[CrossRef]

J. Mod. Opt.

A. Lakhtakia, V. K. Varadan, and V. V. Varadan, "Reflection and transmission of plane waves at the planar interface of a general uniaxial medium and free space," J. Mod. Opt. 38, 649-657 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Microwave Opt. Technol. Lett.

T. G. Mackay, A. Lakhtakia, and R. A. Depine, "Uniaxial dielectric media with hyperbolic dispersion relations," Microwave Opt. Technol. Lett. 48, 363-367 (2006)
[CrossRef]

New J. Phys.

R. A. Depine and A. Lakhtakia, "Diffraction by a grating made of an uniaxial dielectric magnetic medium exhibiting negative refraction," New J. Phys. 7, 158 (2005).
[CrossRef]

Opt. Commun.

R. A. Depine, M. E. Inchaussandague, and A. Lakhtakia, "Application of the differential method to uniaxial gratings with an infinite number of refraction channels: scalar case," Opt. Commun. 258, 90-96 (2006)
[CrossRef]

Z. Liu, J. Xu, and Z. Lin, "Omnidirectional reflection from a slab of uniaxially anisotropic negative refractive index materials," Opt. Commun. 240, 19-27 (2004).
[CrossRef]

Optik (Stuttgart)

A. Lakhtakia and M. W. McCall, "Counterposed phase velocity and energy-transport velocity vectors in a dielectric-magnetic uniaxial medium," Optik (Stuttgart) 115, 28-30 (2004).
[CrossRef]

Phys. Lett. A

R. A. Depine, A. Lakhtakia, and D. R. Smith, "Enhanced diffraction by a rectangular grating made of a negative phase-velocity (or negative index) material," Phys. Lett. A 337, 155-160 (2005).
[CrossRef]

Phys. Rev. B

L. B. Hu and S. T. Chui, "Characteristics of electromagnetic wave propagation in uniaxially anisotropic left-handed materials," Phys. Rev. B 66, 0851081 (2002).
[CrossRef]

Phys. Rev. E

T. G. Mackay and A. Lakhtakia, "Plane waves with negative phase velocity in Faraday chiral mediums," Phys. Rev. E 69, 0266021 (2004).
[CrossRef]

Phys. Rev. Lett.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 1074011-1074014 (2003).
[CrossRef]

A. A. Houck, J. B. Brock, and I. L. Chuang, "Experimental observations of a left-handed material that obeys Snell's law," Phys. Rev. Lett. 90, 1374011-1374014 (2003).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

D. R. Smith and D. Schurig, "Electromagnetic wave propagation in media with indefinite permittivity and permeability tensors," Phys. Rev. Lett. 90, 0774051 (2003).
[CrossRef]

Science

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

Other

A. Lakhtakia, M. W. McCall, and W. S. Weiglhofer, "Negative phase-velocity mediums," in W.S.Weiglhofer and A.Lakhtakia, eds., Introduction to Complex Mediums for Optics and Electromagnetics (SPIE, 2003).
[CrossRef]

H. Lütkepohl, Handbook of Matrices (Wiley, 1996).

H. C. Chen, Theory of Electromagnetic Waves: A Coordinate-free Approach (McGraw-Hill, 1983).

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 (2)

Fig. 1
Fig. 1

Geometrical representations of Eq. (7): (a) A > 0 and B < 0 , hyperboloid of one sheet; (b) A < 0 and B > 0 , hyperboloid of two sheets.

Fig. 2
Fig. 2

Reciprocal space maps for Cases I and II, when φ c = 60 ° . θ c = ( a ) 20°, (b) 52.73°, (c) 55°, (d) 59.06°. The light gray circle represents the dispersion equation for plane waves in the medium of incidence.

Tables (1)

Tables Icon

Table 1 Types of Possible Dispersion Surfaces for Different Combinations among the Eigenvalues ϵ , ϵ , μ , and μ of the Real Symmetric Tensors ϵ ̃ and μ ̃ a

Equations (31)

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

ϵ ̃ = ϵ I ̃ + ( ϵ ϵ ) c ̂ c ̂ , μ ̃ = μ I ̃ + ( μ μ ) c ̂ c ̂ ,
k ϵ ̃ k = k 0 2 μ ϵ ϵ ,
k μ ̃ k = k 0 2 μ ϵ μ .
k ϵ ̃ k = ϵ ( k × c ̂ ) 2 + ϵ ( k c ̂ ) 2 ,
k 2 ϵ + k 2 ϵ = k 0 2 μ .
k 2 μ + k 2 μ = k 0 2 ϵ .
k 2 A + k 2 B = 1 ,
M 11 k x 2 + 2 M 12 k x k y + M 22 k y 2 = F ,
M 11 = ϵ + ( ϵ ϵ ) c x 2
M 12 = ( ϵ ϵ ) c x c y
M 22 = ϵ + ( ϵ ϵ ) c y 2
F = k 0 2 ϵ ϵ μ
M ̃ = [ M 11 M 12 M 12 M 22 ]
λ 1 = ϵ + ( ϵ ϵ ) ( c x 2 + c y 2 ) ,
λ 2 = ϵ ,
λ 1 k 1 2 + λ 2 k 2 2 = F
c ̂ = x ̂ sin θ c cos φ c + y ̂ cos θ c + z ̂ sin θ c sin φ c ,
λ 1 E = ϵ + ( ϵ ϵ ) ( 1 sin 2 θ c sin 2 φ c ) ,
λ 2 E = ϵ .
sin 2 θ c sin 2 φ c < ϵ ϵ ϵ ,
sin 2 θ c sin 2 φ c = ϵ ϵ ϵ ,
sin 2 θ c sin 2 φ c > ϵ ϵ ϵ ,
λ 1 M = μ + ( μ μ ) ( 1 sin 2 θ c sin 2 φ c ) ,
λ 2 M = μ .
sin 2 θ c sin 2 φ c < μ μ μ ,
sin 2 θ c sin 2 φ c = μ μ μ ,
sin 2 θ c sin 2 φ c > μ μ μ ,
sin θ c E = [ ϵ ( ϵ ϵ ) sin 2 φ c ] 1 2 .
sin θ c M = [ μ ( μ μ ) sin 2 φ c ] 1 2
S = ω ϵ 8 π ϵ ( k × c ̂ ) 2 ϵ ̃ k ,
S = ω 8 π k 0 2 ( k × c ̂ ) 2 μ μ μ ̃ k .

Metrics