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Pulsed and CW Gaussian beam interactions with double negative metamaterial slabs

Richard W. Ziolkowski

Open Access Open Access

Abstract

The interactions of pulsed and continuous wave (CW) Gaussian beams with double negative (DNG) metatmaterials are considered. Sub-wavelength focusing of a diverging, normally incident pulsed Gaussian beam with a planar DNG slab is demonstrated. The negative angle of refraction behavior associated with the negative index of refraction exhibited by DNG metamaterials is demonstrated. The transmitted beam resulting from both 3-cycle and CW Gaussian beams that are obliquely incident on a DNG slab are shown to have this property. Gaussian beams that undergo total internal reflection from a DNG metamaterial slab are also shown to experience a negative Goos-Hänchen (lateral) shift. Several potential applications for these effects in the microwave and optical regimes are discussed.

©2003 Optical Society of America

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Corrections

Richard W. Ziolkowski, "Pulsed Gaussian beam interactions with double negative metamaterial slabs: errata," Opt. Express 11, 1596-1597 (2003)
https://opg.optica.org/oe/abstract.cfm?uri=oe-11-13-1596
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References

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  • Publication
  1. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, (Prentice Hall, Englewood Cliffs, NJ, 1991), pp. 36–38.
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    [Crossref]
  3. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with zimultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [Crossref] [PubMed]
  4. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  5. D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
    [Crossref] [PubMed]
  6. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001).
    [Crossref]
  7. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative refractive index of refraction,” Science 292, 77–79 (2001).
    [Crossref] [PubMed]
  8. R. W. Ziolkowski and E. Heyman, “Wave propagation in media having negative permittivity and permeability,” Phys. Rev. E 64, 056625 (2001).
    [Crossref]
  9. C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90, 5483–5486 (2001).
    [Crossref]
  10. J. A. Kong, B.-I. Wu, and Y. Zhang, “A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability,” Microwave Opt. Tech. Lett. 33, 136–139 (2002).
    [Crossref]
  11. P. M. Valanju, R. M. Walter, and A. P. Valanju, “Wave refraction in negative-index media: Always positive and very inhomogeneous,” Phys. Rev. Lett. 88, 187401 (2002).
    [Crossref] [PubMed]
  12. G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702–2712 (2002).
    [Crossref]
  13. K. G. Balmain, A. A. Luttgen, and P. C. Kremer, “Resonance cone formation, reflection, refraction and focusing in a planar, anisotropic metamaterial,” Proceedings of the URSI National Radio Science Meeting, pp. 45, San Antonio, TX, July 2002.
  14. R. W. Ziolkowski, “Design, fabrication, and testing of double negative metamaterials,” to appear in IEEE Trans. Antennas Propagat., June 2003.
    [Crossref]
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  16. A. Taflove, Ed., Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method, (Artech House, Inc., Norwood, MA, 1998).
  17. D. C. Wittwer and R. W. Ziolkowski, “Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy media,” IEEE Trans. Antennas and Propagat. 48, 192–199 (2000).
    [Crossref]
  18. D. C. Wittwer and R. W. Ziolkowski, “Maxwellian material based absorbing boundary conditions for lossy media in 3D,” IEEE Trans. Antennas and Propagat. 48, 200–213 (2000).
    [Crossref]
  19. J. B. Judkins, C. W. Haggans, and R. W. Ziolkowski, “2D-FDTD simulation for rewritable optical disk surface structure design,” Special Issue of Applied Optics on Optical Data Storage Technologies, Appl. Opt.35, 2477–2487 (1996).
    [Crossref] [PubMed]
  20. M. W. Feise, P. J. Bevelacqua, and J. B. Schneider, “Effects of surface waves on behavior of perfect lenses,” Phys. Rev. B 66, 035113 (2002).
    [Crossref]
  21. A. Ishimaru and J. Thomas, “Transmission and focusing of a slab of negative refractive index,” Proceedings of the URSI National Radio Science Meeting, pp. 43, San Antonio, TX, July 2002.
  22. A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002).
    [Crossref]
  23. S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed., Toronto: John Wiley \& Sons, 1994, pp. 257–258.
  24. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, (Prentice Hall, Englewood Cliffs, NJ, 1991), pp. 165–169.
  25. H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096–10099 (1998).
    [Crossref]
  26. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696 (2000).
    [Crossref]
  27. C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
    [Crossref]

2002 (6)

J. A. Kong, B.-I. Wu, and Y. Zhang, “A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability,” Microwave Opt. Tech. Lett. 33, 136–139 (2002).
[Crossref]

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

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702–2712 (2002).
[Crossref]

M. W. Feise, P. J. Bevelacqua, and J. B. Schneider, “Effects of surface waves on behavior of perfect lenses,” Phys. Rev. B 66, 035113 (2002).
[Crossref]

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002).
[Crossref]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[Crossref]

2001 (4)

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001).
[Crossref]

A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative refractive 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]

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90, 5483–5486 (2001).
[Crossref]

2000 (6)

D. C. Wittwer and R. W. Ziolkowski, “Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy media,” IEEE Trans. Antennas and Propagat. 48, 192–199 (2000).
[Crossref]

D. C. Wittwer and R. W. Ziolkowski, “Maxwellian material based absorbing boundary conditions for lossy media in 3D,” IEEE Trans. Antennas and Propagat. 48, 200–213 (2000).
[Crossref]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696 (2000).
[Crossref]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with zimultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[Crossref] [PubMed]

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, R10096–10099 (1998).
[Crossref]

1968 (1)

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

Balmain, K. G.

K. G. Balmain, A. A. Luttgen, and P. C. Kremer, “Resonance cone formation, reflection, refraction and focusing in a planar, anisotropic metamaterial,” Proceedings of the URSI National Radio Science Meeting, pp. 45, San Antonio, TX, July 2002.

Bevelacqua, P. J.

M. W. Feise, P. J. Bevelacqua, and J. B. Schneider, “Effects of surface waves on behavior of perfect lenses,” Phys. Rev. B 66, 035113 (2002).
[Crossref]

Caloz, C.

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90, 5483–5486 (2001).
[Crossref]

Chang, C.-C.

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90, 5483–5486 (2001).
[Crossref]

Eleftheriades, G. V.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702–2712 (2002).
[Crossref]

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002).
[Crossref]

Feise, M. W.

M. W. Feise, P. J. Bevelacqua, and J. B. Schneider, “Effects of surface waves on behavior of perfect lenses,” Phys. Rev. B 66, 035113 (2002).
[Crossref]

Grbic, A.

A. Grbic and G. V. Eleftheriades, “Experimental verification of backward-wave radiation from a negative refractive index metamaterial,” J. Appl. Phys. 92, 5930–5935 (2002).
[Crossref]

Haggans, C. W.

J. B. Judkins, C. W. Haggans, and R. W. Ziolkowski, “2D-FDTD simulation for rewritable optical disk surface structure design,” Special Issue of Applied Optics on Optical Data Storage Technologies, Appl. Opt.35, 2477–2487 (1996).
[Crossref] [PubMed]

Heyman, E.

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

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, (Prentice Hall, Englewood Cliffs, NJ, 1991), pp. 36–38.

A. Ishimaru and J. Thomas, “Transmission and focusing of a slab of negative refractive index,” Proceedings of the URSI National Radio Science Meeting, pp. 43, San Antonio, TX, July 2002.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering, (Prentice Hall, Englewood Cliffs, NJ, 1991), pp. 165–169.

Itoh, T.

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90, 5483–5486 (2001).
[Crossref]

Iyer, A. K.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702–2712 (2002).
[Crossref]

Joannopoulos, J. D.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[Crossref]

Johnson, S. G.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[Crossref]

Judkins, J. B.

J. B. Judkins, C. W. Haggans, and R. W. Ziolkowski, “2D-FDTD simulation for rewritable optical disk surface structure design,” Special Issue of Applied Optics on Optical Data Storage Technologies, Appl. Opt.35, 2477–2487 (1996).
[Crossref] [PubMed]

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, R10096–10099 (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, R10096–10099 (1998).
[Crossref]

Kong, J. A.

J. A. Kong, B.-I. Wu, and Y. Zhang, “A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability,” Microwave Opt. Tech. Lett. 33, 136–139 (2002).
[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, R10096–10099 (1998).
[Crossref]

Kremer, P. C.

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702–2712 (2002).
[Crossref]

K. G. Balmain, A. A. Luttgen, and P. C. Kremer, “Resonance cone formation, reflection, refraction and focusing in a planar, anisotropic metamaterial,” Proceedings of the URSI National Radio Science Meeting, pp. 45, San Antonio, TX, July 2002.

Kroll, N.

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[Crossref] [PubMed]

Luo, C.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[Crossref]

Luttgen, A. A.

K. G. Balmain, A. A. Luttgen, and P. C. Kremer, “Resonance cone formation, reflection, refraction and focusing in a planar, anisotropic metamaterial,” Proceedings of the URSI National Radio Science Meeting, pp. 45, San Antonio, TX, July 2002.

Nemat-Nasser, S. C.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001).
[Crossref]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with zimultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: Refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696 (2000).
[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, R10096–10099 (1998).
[Crossref]

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with zimultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Pendry, J. B.

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104(R) (2002).
[Crossref]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

Ramo, S.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed., Toronto: John Wiley \& Sons, 1994, pp. 257–258.

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, R10096–10099 (1998).
[Crossref]

Schneider, J. B.

M. W. Feise, P. J. Bevelacqua, and J. B. Schneider, “Effects of surface waves on behavior of perfect lenses,” Phys. Rev. B 66, 035113 (2002).
[Crossref]

Schultz, S.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001).
[Crossref]

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

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with zimultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Shelby, A.

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

Shelby, R. A.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001).
[Crossref]

Smith, D. R.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001).
[Crossref]

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

D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. 85, 2933–2936 (2000).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with zimultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[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, R10096–10099 (1998).
[Crossref]

Thomas, J.

A. Ishimaru and J. Thomas, “Transmission and focusing of a slab of negative refractive index,” Proceedings of the URSI National Radio Science Meeting, pp. 43, San Antonio, TX, July 2002.

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, R10096–10099 (1998).
[Crossref]

Valanju, A. P.

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

Van Duzer, T.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed., Toronto: John Wiley \& Sons, 1994, pp. 257–258.

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]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite Medium with zimultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Walter, R. M.

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

Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. Van Duzer, Fields and Waves in Communication Electronics, 3rd ed., Toronto: John Wiley \& Sons, 1994, pp. 257–258.

Wittwer, D. C.

D. C. Wittwer and R. W. Ziolkowski, “Maxwellian material based absorbing boundary conditions for lossy media in 3D,” IEEE Trans. Antennas and Propagat. 48, 200–213 (2000).
[Crossref]

D. C. Wittwer and R. W. Ziolkowski, “Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy media,” IEEE Trans. Antennas and Propagat. 48, 192–199 (2000).
[Crossref]

Wu, B.-I.

J. A. Kong, B.-I. Wu, and Y. Zhang, “A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability,” Microwave Opt. Tech. Lett. 33, 136–139 (2002).
[Crossref]

Zhang, Y.

J. A. Kong, B.-I. Wu, and Y. Zhang, “A unique lateral displacement of a Gaussian beam transmitted through a slab with negative permittivity and permeability,” Microwave Opt. Tech. Lett. 33, 136–139 (2002).
[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]

D. C. Wittwer and R. W. Ziolkowski, “Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy media,” IEEE Trans. Antennas and Propagat. 48, 192–199 (2000).
[Crossref]

D. C. Wittwer and R. W. Ziolkowski, “Maxwellian material based absorbing boundary conditions for lossy media in 3D,” IEEE Trans. Antennas and Propagat. 48, 200–213 (2000).
[Crossref]

J. B. Judkins, C. W. Haggans, and R. W. Ziolkowski, “2D-FDTD simulation for rewritable optical disk surface structure design,” Special Issue of Applied Optics on Optical Data Storage Technologies, Appl. Opt.35, 2477–2487 (1996).
[Crossref] [PubMed]

R. W. Ziolkowski, “Design, fabrication, and testing of double negative metamaterials,” to appear in IEEE Trans. Antennas Propagat., June 2003.
[Crossref]

Appl. Phys. Lett. (1)

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78, 489–491 (2001).
[Crossref]

IEEE Trans. Antennas and Propagat. (2)

D. C. Wittwer and R. W. Ziolkowski, “Two time-derivative Lorentz material (2TDLM) formulation of a Maxwellian absorbing layer matched to a lossy media,” IEEE Trans. Antennas and Propagat. 48, 192–199 (2000).
[Crossref]

D. C. Wittwer and R. W. Ziolkowski, “Maxwellian material based absorbing boundary conditions for lossy media in 3D,” IEEE Trans. Antennas and Propagat. 48, 200–213 (2000).
[Crossref]

IEEE Trans. Microwave Theory Tech. (1)

G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microwave Theory Tech. 50, 2702–2712 (2002).
[Crossref]

J. Appl. Phys. (2)

C. Caloz, C.-C. Chang, and T. Itoh, “Full-wave verification of the fundamental properties of left-handed materials in waveguide configurations,” J. Appl. Phys. 90, 5483–5486 (2001).
[Crossref]

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Supplementary Material (9)

Media 1: GIF (404 KB)     
Media 2: GIF (333 KB)     
Media 3: GIF (414 KB)     
Media 4: GIF (416 KB)     
Media 5: GIF (261 KB)     
Media 6: GIF (458 KB)     
Media 7: GIF (206 KB)     
Media 8: GIF (626 KB)     
Media 9: GIF (528 KB)     

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Figures (18)
Fig. 1.
Fig. 1. Reflection and transmission configuration

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Fig. 2.
Fig. 2. Frequency response of the real part of the index of refraction associated with the lossy Drude models used in the FDTD simulations.

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Fig. 3.
Fig. 3. (413 KB) Electric field intensity distribution for the normally incident Gaussian beam propagation in free space. The location of the slab region in the DNG simulations is shown.

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Fig. 4.
Fig. 4. (341 KB) Electric field intensity distribution for the normally incident Gaussian beam interaction with a DNG slab having n=-1. Focusing at the back surface is observed.

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Fig. 5.
Fig. 5. Gaussian beam interaction with a DNG slab having n=-1. The intensity of the electric field along the beam axis is shown. The DNG slab front and back face locations are indicated by the green lines. Sharp discontinuities in the derivatives of the field across the DPS-DNG interface and focusing at the back surface are observed.

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Fig. 6.
Fig. 6. Gaussian beam interaction with a DNG slab having n=-1. The intensity of the electric field along the front and back faces, orthogonal to the beam axis, are shown. Focusing and narrowing of the beam at the back surface are observed.

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Fig. 7.
Fig. 7. (424 KB) Electric field intensity distribution for the normally incident Gaussian beam interaction with a DNG slab having n=-6. Channeling of the beam in the DNG slab is observed. The energy in the wings of the beam is seen to be directed towards the axis of the beam.

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Fig. 8.
Fig. 8. Gaussian beam interaction with a DNG slab having n=-6. The intensity of the electric field along the beam axis is shown. The DNG slab front and back face locations are indicated by the green lines. Sharp discontinuities in the derivatives of the field across the DPS-DNG interface and maintenance of the center intensity are observed.

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Fig. 9.
Fig. 9. Gaussian beam interaction with a DNG slab having n=-6. The intensity of the electric field along the front and back faces, orthogonal to the beam axis, are shown. There is only a slight narrowing in the width of the beam after its propagation through the entire DNG slab.

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Fig. 10.
Fig. 10. (426 KB) Electric field intensity distribution for the interaction of a CW Gaussian beam that is incident at 20° to a DNG slab having n=-1. A negative angle of refraction equal and opposite to the angle of incidence is observed.

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Fig. 11.
Fig. 11. (267 KB) Electric field intensity distribution for the interaction of a 3-cycle pulsed Gaussian beam that is incident at 20° to a DNG slab having n=-1. A negative angle of refraction of the transmitted pulsed beam is observed. A backward wave is generated at the front interface.

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Fig. 12.
Fig. 12. (469 KB) Electric field intensity distribution for the interaction of a Gaussian beam that is incident at 20° to a DNG slab having n=-6. A shallow negative angle of refraction is observed. The beam is compressed in the DNG slab because of the higher refractive index.

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Fig. 13.
Fig. 13. (211 KB) Electric field intensity distribution for the interaction of a 3-cycle pulsed Gaussian beam that is incident at 20° to a DNG slab having n=-6. A negative angle of refraction and compression of the transmitted pulsed beam is observed.

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Fig. 14.
Fig. 14. A Gaussian beam obliquely incident from a higher refractive index magnitude medium to a lower one with an angle of incidence beyond the critical angle (blue) will generate a reflected beam that experiences a positive Goos-Hänchen lateral shift (green) in a DPS medium or a negative Goos-Hänchen lateral shift (red) in a DNG medium.

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Fig. 15.
Fig. 15. (641 KB) Electric field intensity distribution for the interaction of a CW Gaussian beam that is incident at 40° in a DPS medium with ε r =9.0 and µ r =+1, i.e., n=+3 onto a DPS slab having ε r =+3.0 and µ r =+1, i.e., n=+√3. The positive Goös-Hachen shift of this beam is observed. Some penetration of the beam into the slab occurs. The total field-scattered field boundary where the beam is generated is apparent. The total-internal-reflected beam propagates out of the FDTD total field region into the FDTD scattered field region as it passes this boundary.

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Fig. 16.
Fig. 16. (541 KB) Electric field intensity distribution for the interaction of a CW Gaussian beam that is incident at 40° in a DPS medium with ε r =9.0 and µ r =+1, i.e., n=+3 onto a DNG slab having ε r =-3.0 and µ r =-1, i.e., n=-√3. The total field-scattered field boundary where the beam is generated is apparent. The total-internal-reflected beam propagates out of the FDTD total field region into the FDTD scattered field region as it passes this boundary.

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Fig. 17.
Fig. 17. The electric field intensity distribution measured at t=6000Δt at two cells in front of the TF-SF plane for the total internal reflection DPS slab case. The positions of the incident beam center and the specularly-reflected beam center are indicated by the vertical black lines. The theoretical positive Goös-Hachen shift is indicated by the vertical green line.

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Fig. 18.
Fig. 18. The electric field intensity distribution measured at t=6000Δt at two cells in front of the TF-SF plane for the total internal reflection DNG slab case. The positions of the incident beam center and the specularly-reflected beam center are indicated by the vertical black lines. The theoretical negative Goäs-Hachen shift is indicated by the vertical green line.

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Equations (28)

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

θ refl = θ inc
n trans sin ⁡ θ trans = n inc sin ⁡ θ inc
n i = ε i ε 0 μ i μ 0 = ε r μ r
R = η trans cos ⁡ θ inc − η inc cos ⁡ θ trans η trans cos ⁡ θ inc + η inc cos ⁡ θ trans
T = 2 η trans cos ⁡ θ inc η trans cos ⁡ θ inc + η inc cos ⁡ θ trans
η i = μ i ε i
ε ( ω ) = ε 0 ( 1 − ω pe 2 ω ( ω + i Γ e ) )
μ ( ω ) = μ 0 ( 1 − ω pm 2 ω ( ω + i Γ m ) )
∂ t 2 P y + Γ e ∂ t P y = ε 0 ω pe 2 E y
∂ t 2 M nx + Γ m ∂ t M nx = μ 0 ω pm 2 H x
∂ t 2 M nz + Γ m ∂ t M nz = μ 0 ω pm 2 H z
K x = ∂ t M nx
K z = ∂ t M nz
J y = ∂ t P y
∂ t H x = + 1 μ 0 ( ∂ z E y − K x )
∂ t K x + Γ m K x = μ 0 ω pm 2 H x
∂ t H z = − 1 μ 0 ( ∂ x E y + K z )
∂ t K z + Γ m K z = μ 0 ω pm 2 H z
∂ t E y = 1 ε 0 [ ( ∂ z H x − ∂ x H z ) − J y ]
∂ t J y + Γ e J y = ε 0 ω pe 2 E y
∂ t H x = + 1 μ ∂ z E y
∂ t H z = − 1 μ ∂ x E y
∂ t E y = 1 ε ( ∂ z H x − ∂ x H z )
f ( t ) = { 0 for t < 0 g on ( t ) sin ⁡ ( ω t ) for 0 < t < m T p sin ⁡ ( ω t ) for m T p < t < ( m + n ) T p g off ( t ) sin ⁡ ( ω t ) for ( m + n ) T p < t < ( m + n + m ) T p 0 for ( m + n + m ) T p < t
g on ( t ) = 10 x on 3 ( t ) − 15 x on 4 ( t ) + 6 x on 5 ( t )
g off ( t ) = 1 − [ 10 x off 3 ( t ) − 15 x off 4 ( t ) + 6 x off 5 ( t ) ]
E y x z = R ( K x 0 ) e i k x 0 Φ ' ( k x 0 ) E y , inc ( x − Φ ' ( k x 0 ) , z )
R ( k x ) = exp [ − i Φ ( k x ) ]

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