Abstract

The surface plasmon polaritons (SPPs) of four-layered structures composed of four kinds of materials—left-handed material, negative dielectric permittivity material, negative magnetic permeability material, and dielectrics—are investigated. The existence regions, dispersion relations, and excitation of the p and s polarized SPPs in several types of four-layered structures are studied in detail and it is shown that the properties of SPPs in different frequency regions are strongly dependent on the composite materials and their sequencing of the four-layered structures. The possibility of exciting and observing SPPs by the attenuated total reflection technique is also discussed.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values ε and μ,” Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
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  6. R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.
  7. F. Martín, F. Falcone, R. Marqués, J. Bonache, and M. Sorolla, “Transmission characteristics in split ring resonator based left-handed coplanar waveguides,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 293.
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  22. I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617 (2004).
    [CrossRef]
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    [CrossRef]
  24. S. A. Darmanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004).
    [CrossRef]
  25. H. F. Zhang, Q. Wang, N. H. Shen, R. Li, J. Chen, J. P. Ding, and H. T. Wang, “Surface plasmon polaritons at interfaces associated with artificial composite materials” J. Opt. Soc. Am. B 22, 2686-2696 (2005).
    [CrossRef]

2007 (2)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

C. Rockstuhl, T. Zentgraf, E. Pshenay-Severin, J. Petschulat, A. Chipouline, J. Kuhl, T. Pertsch, H. Giessen, and F. Lederer, “The origin of magnetic polarizability in metamaterials at optical frequencies--an electrodynamic approach,” Opt. Express 15, 8871-8883 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (3)

H. F. Zhang, Q. Wang, N. H. Shen, R. Li, J. Chen, J. P. Ding, and H. T. Wang, “Surface plasmon polaritons at interfaces associated with artificial composite materials” J. Opt. Soc. Am. B 22, 2686-2696 (2005).
[CrossRef]

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131-314 (2005).
[CrossRef]

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

2004 (3)

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

S. A. Darmanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617 (2004).
[CrossRef]

2003 (3)

J. A. Gaspar-Armenta and F. Villa, “Photonic surface-wave excitation: photonic crystal-metal interface,” J. Opt. Soc. Am. B 20, 2349-2354 (2003).
[CrossRef]

S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225, 233-240 (2003).
[CrossRef]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2002 (1)

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901 (2002).
[CrossRef] [PubMed]

2001 (2)

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys.:Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

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

2000 (2)

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

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

1999 (1)

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

1993 (1)

J. S. Nkoma, “Surface modes of a composite medium,” Solid State Commun. 87, 241-244 (1993).
[CrossRef]

1968 (1)

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

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Alù, A.

Baena, J. D.

J. Martel, R. Marqués, J. D. Baena, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Application of modified split-ring resonators to the design of small microstrip and CPW filters,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 194.

R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Basov, D. N.

Bonache, J.

F. Martín, F. Falcone, R. Marqués, J. Bonache, and M. Sorolla, “Transmission characteristics in split ring resonator based left-handed coplanar waveguides,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 293.

Chen, J.

Chipouline, A.

Darmanyan, S. A.

S. A. Darmanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004).
[CrossRef]

S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225, 233-240 (2003).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Derov, J. S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Ding, J. P.

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Engheta, N.

Falcone, F.

F. Martín, F. Falcone, R. Marqués, J. Bonache, and M. Sorolla, “Transmission characteristics in split ring resonator based left-handed coplanar waveguides,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 293.

R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.

J. Martel, R. Marqués, J. D. Baena, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Application of modified split-ring resonators to the design of small microstrip and CPW filters,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 194.

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Gaspar-Armenta, J. A.

Giessen, H.

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Holden, A. J.

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

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Ishikawa, A.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

Kawata, S.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

Kivshar, Y. S.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Kuhl, J.

Lederer, F.

Li, R.

Lu, W. T.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Maradudin, A. A.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Marqués, R.

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901 (2002).
[CrossRef] [PubMed]

F. Martín, F. Falcone, R. Marqués, J. Bonache, and M. Sorolla, “Transmission characteristics in split ring resonator based left-handed coplanar waveguides,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 293.

R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.

J. Martel, R. Marqués, J. D. Baena, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Application of modified split-ring resonators to the design of small microstrip and CPW filters,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 194.

Martel, J.

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901 (2002).
[CrossRef] [PubMed]

R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.

J. Martel, R. Marqués, J. D. Baena, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Application of modified split-ring resonators to the design of small microstrip and CPW filters,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 194.

Martín, F.

J. Martel, R. Marqués, J. D. Baena, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Application of modified split-ring resonators to the design of small microstrip and CPW filters,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 194.

R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.

F. Martín, F. Falcone, R. Marqués, J. Bonache, and M. Sorolla, “Transmission characteristics in split ring resonator based left-handed coplanar waveguides,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 293.

Medina, F.

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901 (2002).
[CrossRef] [PubMed]

R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.

J. Martel, R. Marqués, J. D. Baena, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Application of modified split-ring resonators to the design of small microstrip and CPW filters,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 194.

Mesa, F.

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901 (2002).
[CrossRef] [PubMed]

Narimanov, E. E.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Nemat-Nasser, S. C.

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

Nevière, M.

S. A. Darmanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004).
[CrossRef]

S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225, 233-240 (2003).
[CrossRef]

Nkoma, J. S.

J. S. Nkoma, “Surface modes of a composite medium,” Solid State Commun. 87, 241-244 (1993).
[CrossRef]

Padilla, W. J.

W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23, 404-414 (2006).
[CrossRef]

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

Parimi, P. V.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Pendry, J. B.

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

Pertsch, T.

Petschulat, J.

Podolskiy, V. A.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Pshenay-Severin, E.

Robbins, D. J.

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

Rockstuhl, C.

Ruppin, R.

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys.:Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

Salandrino, A.

Schultz, S.

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

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

Shadrivov, I. V.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Shelby, R. A.

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

Shen, N. H.

Sivco, D. L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Smith, D. R.

W. J. Padilla, D. R. Smith, and D. N. Basov, “Spectroscopy of metamaterials from infrared to optical frequencies,” J. Opt. Soc. Am. B 23, 404-414 (2006).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative 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 simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Smolyaninov, I. I.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Sokoloff, J.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Sorolla, M.

F. Martín, F. Falcone, R. Marqués, J. Bonache, and M. Sorolla, “Transmission characteristics in split ring resonator based left-handed coplanar waveguides,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 293.

R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.

J. Martel, R. Marqués, J. D. Baena, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Application of modified split-ring resonators to the design of small microstrip and CPW filters,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 194.

Sridhar, S.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Stewart, W. J.

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

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Tanaka, T.

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values 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 simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Villa, F.

Vodo, P.

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

Wang, H. T.

Wang, Q.

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Zakhidov, A. A.

S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225, 233-240 (2003).
[CrossRef]

Zayats, A. V.

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131-314 (2005).
[CrossRef]

S. A. Darmanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004).
[CrossRef]

Zentgraf, T.

Zhang, H. F.

IEEE Trans. Microwave Theory Tech. (1)

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

J. Opt. Soc. Am. B (4)

J. Phys.:Condens. Matter (1)

R. Ruppin, “Surface polaritons of a left-handed material slab,” J. Phys.:Condens. Matter 13, 1811-1819 (2001).
[CrossRef]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Nature Mater. (1)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Opt. Commun. (1)

S. A. Darmanyan, M. Nevière, and A. A. Zakhidov, “Surface modes at the interface of conventional and left-handed media,” Opt. Commun. 225, 233-240 (2003).
[CrossRef]

Opt. Express (2)

Phys. Lett. A (1)

R. Ruppin, “Surface polaritons of a left-handed medium,” Phys. Lett. A 277, 61-64 (2000).
[CrossRef]

Phys. Rep. (1)

A. V. Zayats, I. I. Smolyaninov, and A. A. Maradudin, “Nano-optics of surface plasmon polaritons,” Phys. Rep. 408, 131-314 (2005).
[CrossRef]

Phys. Rev. B (1)

S. A. Darmanyan, M. Nevière, and A. V. Zayats, “Analytical theory of optical transmission through periodically structured metal films via tunnel-coupled surface polariton modes,” Phys. Rev. B 70, 075103 (2004).
[CrossRef]

Phys. Rev. E (1)

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E 69, 016617 (2004).
[CrossRef]

Phys. Rev. Lett. (4)

P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004).
[CrossRef] [PubMed]

A. Ishikawa, T. Tanaka, and S. Kawata, “Negative magnetic permeability in the visible light region,” Phys. Rev. Lett. 95, 237401 (2005).
[CrossRef] [PubMed]

R. Marqués, J. Martel, F. Mesa, and F. Medina, “Left-handed-media simulation and transmission of EM waves in subwavelength split-ring-resonator-loaded metallic waveguides,” Phys. Rev. Lett. 89, 183901 (2002).
[CrossRef] [PubMed]

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

Science (1)

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

Solid State Commun. (1)

J. S. Nkoma, “Surface modes of a composite medium,” Solid State Commun. 87, 241-244 (1993).
[CrossRef]

Sov. Phys. Usp. (1)

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

Other (3)

J. Martel, R. Marqués, J. D. Baena, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Application of modified split-ring resonators to the design of small microstrip and CPW filters,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 194.

R. Marqués, J. D. Baena, J. Martel, F. Medina, F. Falcone, M. Sorolla, and F. Martín, “Novel small resonant electromagnetic particles for metamaterial and filter design,” in Proceedings of the International Conference on Electromagnetics in Advanced Applications (International Conference on Electromagnetics in Advanced Applications, 2003), pp. 439-443.

F. Martín, F. Falcone, R. Marqués, J. Bonache, and M. Sorolla, “Transmission characteristics in split ring resonator based left-handed coplanar waveguides,” in Progress in Electromagnetics Research Symposium (Progress in Electromagnetics Research, 2003), p. 293.

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Figures (8)

Fig. 1
Fig. 1

Geometry of the four-layered structures and the coordinate system.

Fig. 2
Fig. 2

Existence regions and dispersion relation curves of SPPs on the plane ( h h 0 , ω ) in two typical A B C A structures with the thickness of media 2 and 3 being h 0 d 1 = h 0 d 2 = 0.5 . (a) The interfaces of dielectric–NDPM–LHM–dielectric. Line (i) is h = ( ε 1 μ 1 ) 1 2 ( ω c ) , line (ii) is h = ( ε 0 μ 0 ) 1 2 ( ω c ) , and line (iii) is h = ( ε 3 μ 3 ) 1 2 ( ω c ) . (b) The interfaces of NDPM–NMPM–LHM–NDPM. Line (i) is h = ( ε 1 μ 1 ) 1 2 ( ω c ) , line (ii) is h = ( ε 3 μ 3 ) 1 2 ( ω c ) , and line (iii) is h = ( ε 0 μ 0 ) 1 2 ( ω c ) .

Fig. 3
Fig. 3

Configuration of a dielectric prism for the ATR spectra study.

Fig. 4
Fig. 4

ATR spectra for exciting and observing SPPs in the frequency regime for two typical A B C A structures, i.e., dielectric–NDPM–LHM–dielectric (solid curves) and NDPM–NMPM–LHM–NDPM (dashed curves), and the coupling prism used has ε 0 = 3.0 , μ 0 = 1.0 . (a) The p-polarization case. (b) The s-polarization case. The thicknesses of media 1, 2, and 3 are a = 5 mm , h 0 d 1 = 0.5 , and h 0 d 2 = 0.5 , respectively, and the incident angle is θ = 45 ° .

Fig. 5
Fig. 5

Existence regions and dispersion relation curves of SPPs on the plane ( h h 0 , ω ) in two typical A B A B structures with the thickness of media 2 and 3 being h 0 d 1 = h 0 d 2 = 0.5 . (a) The interfaces of dielectric–LHM–dielectric–LHM. Line (i) is h = ( ε 1 μ 1 ) 1 2 ( ω c ) , line (ii) is h = ( ε 2 μ 2 ) 1 2 ( ω c ) , and line (iii) is h = ( ε 0 μ 0 ) 1 2 ( ω c ) . (b) The interfaces of NDPM–LHM–NDPM–LHM. Line (i) is h = ( ε 1 μ 1 ) 1 2 ( ω c ) , line (ii) is h = ( ε 2 μ 2 ) 1 2 ( ω c ) , and line (iii) is h = ( ε 0 μ 0 ) 1 2 ( ω c ) .

Fig. 6
Fig. 6

ATR spectra for exciting and observing SPPs in the frequency regime for two typical A B A B structures, i.e., dielectric–LHM–dielectric–LHM (solid curves) and NDPM–LHM–NDPM–LHM (dashed curves), and the coupling prism used has ε 0 = 3.0 , μ 0 = 1.0 . (a) The p-polarization case. (b) The s-polarization case. The other parameters used are same as those in Fig. 4.

Fig. 7
Fig. 7

Existence regions and dispersion relation curves of SPPs on the plane ( h h 0 , ω ) in two typical A B C D structures with the thickness of media 2 and 3 being h 0 d 1 = h 0 d 2 = 0.5 . (a) The interfaces of dielectric–LHM–NDPM––NMPM. Line (i) is h = ( ε 3 μ 3 ) 1 2 ( ω c ) , line (ii) is h = ( ε 2 μ 2 ) 1 2 ( ω c ) , and line (iii) is h = ( ε 0 μ 0 ) 1 2 ( ω c ) . (b) The interfaces of NDPM–dielectric–LHM–NMPM. Line (i) is h = ( ε 2 μ 2 ) 1 2 ( ω c ) , line (ii) is h = ( ε 3 μ 3 ) 1 2 ( ω c ) , and line (iii) is h = ( ε 0 μ 0 ) 1 2 ( ω c ) .

Fig. 8
Fig. 8

ATR spectra for exciting and observing SPPs in the frequency regime for two typical A B C D structures, i.e., dielectric–LHM–NDPM–NMPM (solid curves) and NDPM–dielectric–LHM–NMPM (dashed curves), and the coupling prism used has ε 0 = 3.0 , μ 0 = 1.0 . (a) The p-polarization case. (b) The s-polarization case. The other parameters used are same as those in Fig. 4.

Equations (20)

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H 1 = a y A e k 1 x e i h z ,
E 1 = c ω ε 1 A ( h a x + i k 1 a z ) e k 1 x e i h z .
H 2 = a y ( B e k 2 x + C e k 2 x ) e i h z ,
E 2 = c ω ε 2 [ B ( h a x i k 2 a z ) e k 2 x + C ( h a x + i k 2 a z ) e k 2 x ] e i h z .
H 3 = a y ( D e k 3 x + E e k 3 x ) e i h z ,
E 3 = c ω ε 3 [ D ( h a x i k 3 a z ) e k 3 x + E ( h a x + i k 3 a z ) e k 3 x ] e i h z .
H 4 = a y F e k 4 x e i h z ,
E 4 = c ω ε 4 F ( h a x i k 4 a z ) e k 4 x e i h z .
k 1 , 2 , 3 , 4 2 = h 2 ε 1 , 2 , 3 , 4 μ 1 , 2 , 3 , 4 ( ω c ) 2 ,
h 2 > max [ ε 1 μ 1 ( ω c ) 2 , ε 2 μ 2 ( ω c ) 2 , ε 3 μ 3 ( ω c ) 2 , ε 4 μ 4 ( ω c ) 2 ] .
e 2 k 3 d 2 = ( k 1 ε 1 + k 2 ε 2 ) ( k 2 ε 2 k 3 ε 3 ) ( k 4 ε 4 k 3 ε 3 ) e 2 k 2 d 1 ( k 2 ε 2 k 1 ε 1 ) ( k 2 ε 2 + k 3 ε 3 ) ( k 4 ε 4 k 3 ε 3 ) ( k 1 ε 1 + k 2 ε 2 ) ( k 2 ε 2 + k 3 ε 3 ) ( k 4 ε 4 + k 3 ε 3 ) e 2 k 2 d 1 + ( k 2 ε 2 k 1 ε 1 ) ( k 2 ε 2 k 3 ε 3 ) ( k 4 ε 4 + k 3 ε 3 ) .
e 2 k 3 d 2 = ( k 1 μ 1 + k 2 μ 2 ) ( k 2 μ 2 k 3 μ 3 ) ( k 4 μ 4 k 3 μ 3 ) e 2 k 2 d 1 ( k 2 μ 2 k 1 μ 1 ) ( k 2 μ 2 + k 3 μ 3 ) ( k 4 μ 4 k 3 μ 3 ) ( k 1 μ 1 + k 2 μ 2 ) ( k 2 μ 2 + k 3 μ 3 ) ( k 4 μ 4 + k 3 μ 3 ) e 2 k 2 d 1 + ( k 2 μ 2 k 1 μ 1 ) ( k 2 μ 2 k 3 μ 3 ) ( k 4 μ 4 + k 3 μ 3 ) .
ε LHM ( ω ) = 1 ω p 2 ω ( ω + i γ ) ,
μ LHM ( ω ) = 1 F 1 ω 2 ω 2 ω 0 2 + i Γ 1 ω ,
ε NDPM ( ω ) = 1 ω a 2 ω ( ω + i γ a ) ,
μ NMPM ( ω ) = 1 F 2 ω 2 ω 2 ω 0 2 + i Γ 2 ω ,
R 4 = r 01 + R 3 e 2 k 1 a 1 + r 01 R 3 e 2 k 1 a .
R 3 = r 12 + R 2 e 2 k 2 d 1 1 + r 12 R 2 e 2 k 2 d 1 .
R 2 = r 23 + r 34 e 2 k 3 d 2 1 + r 23 r 34 e 2 k 3 d 2 ,
r j k = ε k k j ε j k k ε k k j + ε j k k ,

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