Abstract

Following our recent theoretical development of the concepts of nanoinductors, nanocapacitors, and nanoresistors at optical frequencies and the possibility of synthesizing more complex nanoscale circuits, we theoretically investigate in detail the problem of optical nanotransmission lines (NTLs) that can be envisioned by properly joining together arrays of these basic nanoscale circuit elements. We show how, in the limit in which these basic circuit elements are closely packed together, NTLs can be regarded as stacks of plasmonic and nonplasmonic planar slabs, which may be designed to effectively exhibit the properties of planar metamaterials with forward (right-handed) or backward (left-handed) operation. With the proper design, negative refraction and left-handed propagation are shown to be possible in these planar plasmonic guided-wave structures, providing possibilities for subwavelength focusing and imaging in planar optics and laterally confined waveguiding at IR and visible frequencies. The effective material parameters for such NTLs are derived, and the connection and analogy between these optical NTLs and the double-negative and double-positive metamaterials are also explored. Physical insights and justification for the results are also presented.

© 2006 Optical Society of America

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    [CrossRef]
  2. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  5. A. Alù and N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004).
    [CrossRef]
  6. A. Alù and N. Engheta, "An overview of salient properties of planar guided-wave structures with double-negative (DNG) and single-negative (SNG) layers," in Negative Refraction Metamaterials: Fundamental Properties and Applications, G.V.Eleftheriades, and K.G.Balmain, eds. (IEEE; Wiley, 2005), pp. 339-380.
    [CrossRef]
  7. A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers," J. Appl. Phys. 97, 094310 (2005).
    [CrossRef]
  8. A. Alù and N. Engheta, "Can negative-parameter metamaterials provide high directivity for small apertures and antennas?" in Presented at the USNC/CNC/URSI National Radio Science Meeting, Washington, D.C., July 3-8, 2005.
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  12. S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic bandgaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
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  13. G. Shvets and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902 (2004).
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  14. M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
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  20. A. Alù and N. Engheta, "Sub-wavelength focusing and negative refraction along positive-index and negative-index plasmonic nano-transmission lines and nano-layers," in Proceedings of the 2005 IEEE Antennas and Propagation Society International Symposium, (IEEE, 2005), Vol. 1A, pp. 35-38.
  21. 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).
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  23. A. Alù and N. Engheta, "Mode excitation by a line source in a parallel-plate waveguide filled with a pair of parallel double-negative and double-positive slabs," in Proceedings of 2003 IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), Vol. 3, pp. 359-362.
  24. Note that the current distribution in a TL as in Figs. would indeed excite a magnetic field distribution with even distribution with respect to the transverse coordinate, thereby justifying the use of the even mode in the ENG-DPS-ENG waveguide (for RH behavior) and in the DPS-ENG-DPS waveguide (for LH behavior)
  25. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299-15302 (2000).
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    [CrossRef]
  28. S. A. Maier, M. L. Brongersma, and H. A. Atwater, "Electromagnetic energy transport along arrays of closely spaced metal rods as an analogue to plasmonic devices," Appl. Phys. Lett. 78, 16-18 (2001).
    [CrossRef]
  29. A. D. Yaghjian, "Scattering-matrix analysis of linear periodic arrays," IEEE Trans. Antennas Propag. 50, 1050-1064 (2002).
    [CrossRef]
  30. R. Shore and A. D. Yaghjian, "Traveling electromagnetic waves on linear metallic nanosphere arrays," presented at the 11th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM'05), Saint-Malò, France, June 15-17 2005.
  31. N. Engheta, A. Alù, A. Salandrino, and N. Blyzniuk, "Circuit element representation of optical energy transport along a chain of plasmonic nanoparticles," in Digest of the 2004 OSA Annual Meeting (Optical Society of America, 2004), p. FWH47.
  32. A. W. Lohmann, A. Peer, D. Wang, and A. Frisesem, "Flatland optics: fundamentals," J. Opt. Soc. Am. A 17, 1755-1762 (2000).
    [CrossRef]

2005

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nanoinductors, nanocapacitors and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers," J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

2004

A. Alù and N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004).
[CrossRef]

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic bandgaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

G. Shvets and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902 (2004).
[CrossRef]

2003

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

G. Shvets, "Photonic approach to making a material with a negative index of refraction," Phys. Rev. B 67, 035109 (2003).
[CrossRef]

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

2002

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

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]

L. Liu, C. Caloz, C.-C. Chang, and T. Itoh, "Forward coupling phenomena between artificial left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

A. D. Yaghjian, "Scattering-matrix analysis of linear periodic arrays," IEEE Trans. Antennas Propag. 50, 1050-1064 (2002).
[CrossRef]

2001

S. A. Maier, M. L. Brongersma, and H. A. Atwater, "Electromagnetic energy transport along arrays of closely spaced metal rods as an analogue to plasmonic devices," Appl. Phys. Lett. 78, 16-18 (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

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

S. A. Tretyakov and A. J. Vitanen, "Line of periodically arranged passive dipole scatters," Electr. Eng. 82, 353-361 (2000).
[CrossRef]

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

A. W. Lohmann, A. Peer, D. Wang, and A. Frisesem, "Flatland optics: fundamentals," J. Opt. Soc. Am. A 17, 1755-1762 (2000).
[CrossRef]

1998

1997

1968

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

Alù, A.

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nanoinductors, nanocapacitors and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers," J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

A. Alù and N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004).
[CrossRef]

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

A. Alù and N. Engheta, "Can negative-parameter metamaterials provide high directivity for small apertures and antennas?" in Presented at the USNC/CNC/URSI National Radio Science Meeting, Washington, D.C., July 3-8, 2005.

A. Alù and N. Engheta, "Mode excitation by a line source in a parallel-plate waveguide filled with a pair of parallel double-negative and double-positive slabs," in Proceedings of 2003 IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), Vol. 3, pp. 359-362.

A. Alù and N. Engheta, "Sub-wavelength focusing and negative refraction along positive-index and negative-index plasmonic nano-transmission lines and nano-layers," in Proceedings of the 2005 IEEE Antennas and Propagation Society International Symposium, (IEEE, 2005), Vol. 1A, pp. 35-38.

A. Alù and N. Engheta, "An overview of salient properties of planar guided-wave structures with double-negative (DNG) and single-negative (SNG) layers," in Negative Refraction Metamaterials: Fundamental Properties and Applications, G.V.Eleftheriades, and K.G.Balmain, eds. (IEEE; Wiley, 2005), pp. 339-380.
[CrossRef]

A. Alù and N. Engheta, "Anomalies in the surface wave propagation along double-negative and single-negative cylindrical shells," presented at the 2004 Progress in Electromagnetics Research Symposium (PIERS'04), Pisa, Italy, March 28-31, 2004, CD Digest.

A. Alù, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," online at http://arxiv.org/pdf/cond-mat/0412263.

N. Engheta, A. Alù, A. Salandrino, and N. Blyzniuk, "Circuit element representation of optical energy transport along a chain of plasmonic nanoparticles," in Digest of the 2004 OSA Annual Meeting (Optical Society of America, 2004), p. FWH47.

Atwater, H. A.

S. A. Maier, M. L. Brongersma, and H. A. Atwater, "Electromagnetic energy transport along arrays of closely spaced metal rods as an analogue to plasmonic devices," Appl. Phys. Lett. 78, 16-18 (2001).
[CrossRef]

Aussenegg, F. R.

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Blyzniuk, N.

N. Engheta, A. Alù, A. Salandrino, and N. Blyzniuk, "Circuit element representation of optical energy transport along a chain of plasmonic nanoparticles," in Digest of the 2004 OSA Annual Meeting (Optical Society of America, 2004), p. FWH47.

Brongersma, M. L.

S. A. Maier, M. L. Brongersma, and H. A. Atwater, "Electromagnetic energy transport along arrays of closely spaced metal rods as an analogue to plasmonic devices," Appl. Phys. Lett. 78, 16-18 (2001).
[CrossRef]

Caloz, C.

L. Liu, C. Caloz, C.-C. Chang, and T. Itoh, "Forward coupling phenomena between artificial left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

Chang, C.-C.

L. Liu, C. Caloz, C.-C. Chang, and T. Itoh, "Forward coupling phenomena between artificial left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[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]

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Engheta, N.

A. Alù and N. Engheta, "Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers," J. Appl. Phys. 97, 094310 (2005).
[CrossRef]

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nanoinductors, nanocapacitors and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

A. Alù and N. Engheta, "Guided modes in a waveguide filled with a pair of single-negative (SNG), double-negative (DNG), and/or double-positive (DPS) layers," IEEE Trans. Microwave Theory Tech. 52, 199-210 (2004).
[CrossRef]

A. Alù and N. Engheta, "Pairing an epsilon-negative slab with a mu-negative slab: resonance, tunneling and transparency," IEEE Trans. Antennas Propag. 51, 2558-2570 (2003).
[CrossRef]

N. Engheta, "An idea for thin subwavelength cavity resonators using metamaterials with negative permittivity and permeability," IEEE Antennas Wireless Propag. Lett. 1, 10-13 (2002).
[CrossRef]

A. Alù and N. Engheta, "Mode excitation by a line source in a parallel-plate waveguide filled with a pair of parallel double-negative and double-positive slabs," in Proceedings of 2003 IEEE Antennas and Propagation Society International Symposium (IEEE, 2003), Vol. 3, pp. 359-362.

A. Alù and N. Engheta, "Can negative-parameter metamaterials provide high directivity for small apertures and antennas?" in Presented at the USNC/CNC/URSI National Radio Science Meeting, Washington, D.C., July 3-8, 2005.

A. Alù and N. Engheta, "Sub-wavelength focusing and negative refraction along positive-index and negative-index plasmonic nano-transmission lines and nano-layers," in Proceedings of the 2005 IEEE Antennas and Propagation Society International Symposium, (IEEE, 2005), Vol. 1A, pp. 35-38.

A. Alù and N. Engheta, "An overview of salient properties of planar guided-wave structures with double-negative (DNG) and single-negative (SNG) layers," in Negative Refraction Metamaterials: Fundamental Properties and Applications, G.V.Eleftheriades, and K.G.Balmain, eds. (IEEE; Wiley, 2005), pp. 339-380.
[CrossRef]

A. Alù and N. Engheta, "Anomalies in the surface wave propagation along double-negative and single-negative cylindrical shells," presented at the 2004 Progress in Electromagnetics Research Symposium (PIERS'04), Pisa, Italy, March 28-31, 2004, CD Digest.

A. Alù, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," online at http://arxiv.org/pdf/cond-mat/0412263.

N. Engheta, A. Alù, A. Salandrino, and N. Blyzniuk, "Circuit element representation of optical energy transport along a chain of plasmonic nanoparticles," in Digest of the 2004 OSA Annual Meeting (Optical Society of America, 2004), p. FWH47.

Frisesem, A.

Ho, K. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Itoh, T.

L. Liu, C. Caloz, C.-C. Chang, and T. Itoh, "Forward coupling phenomena between artificial left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[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.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

Johnson, S. G.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

Kobayashi, T.

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]

Krenn, J. R.

Landau, L.

L. Landau and E. M. Lifschitz, Electrodynamics of Continuous Media (Elsevier, 1984).

Leitner, A.

Lifschitz, E. M.

L. Landau and E. M. Lifschitz, Electrodynamics of Continuous Media (Elsevier, 1984).

Liu, L.

L. Liu, C. Caloz, C.-C. Chang, and T. Itoh, "Forward coupling phenomena between artificial left-handed transmission lines," J. Appl. Phys. 92, 5560-5565 (2002).
[CrossRef]

Lohmann, A. W.

Maier, S. A.

S. A. Maier, M. L. Brongersma, and H. A. Atwater, "Electromagnetic energy transport along arrays of closely spaced metal rods as an analogue to plasmonic devices," Appl. Phys. Lett. 78, 16-18 (2001).
[CrossRef]

McPeake, D.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic bandgaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Morimoto, A.

O'Brien, S.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic bandgaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Peer, A.

Pendry, J. B.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic bandgaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

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

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals," Appl. Phys. Lett. 82, 1069-1071 (2003).
[CrossRef]

Quinten, M.

Ramakrishna, S. A.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic bandgaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101 (2004).
[CrossRef]

Salandrino, A.

N. Engheta, A. Salandrino, and A. Alù, "Circuit elements at optical frequencies: nanoinductors, nanocapacitors and nanoresistors," Phys. Rev. Lett. 95, 095504 (2005).
[CrossRef] [PubMed]

N. Engheta, A. Alù, A. Salandrino, and N. Blyzniuk, "Circuit element representation of optical energy transport along a chain of plasmonic nanoparticles," in Digest of the 2004 OSA Annual Meeting (Optical Society of America, 2004), p. FWH47.

A. Alù, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," online at http://arxiv.org/pdf/cond-mat/0412263.

Sarychev, A. K.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Schultz, S.

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

Shalaev, V. M.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[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]

Shore, R.

R. Shore and A. D. Yaghjian, "Traveling electromagnetic waves on linear metallic nanosphere arrays," presented at the 11th International Symposium on Antenna Technology and Applied Electromagnetics (ANTEM'05), Saint-Malò, France, June 15-17 2005.

Shvets, G.

G. Shvets and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902 (2004).
[CrossRef]

G. Shvets, "Photonic approach to making a material with a negative index of refraction," Phys. Rev. B 67, 035109 (2003).
[CrossRef]

Sigalas, M. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Smith, D. R.

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

Soukoulis, C. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, "Metallic photonic crystals at optical wavelengths," Phys. Rev. B 62, 15299-15302 (2000).
[CrossRef]

Takahara, J.

Taki, H.

Tretyakov, S. A.

S. A. Tretyakov and A. J. Vitanen, "Line of periodically arranged passive dipole scatters," Electr. Eng. 82, 353-361 (2000).
[CrossRef]

Urzhumov, Y. A.

G. Shvets and Y. A. Urzhumov, "Engineering electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902 (2004).
[CrossRef]

Veselago, V. G.

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

Vitanen, A. J.

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Note that the current distribution in a TL as in Figs. would indeed excite a magnetic field distribution with even distribution with respect to the transverse coordinate, thereby justifying the use of the even mode in the ENG-DPS-ENG waveguide (for RH behavior) and in the DPS-ENG-DPS waveguide (for LH behavior)

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Figures (12)

Fig. 1
Fig. 1

(Color online) Conceptual synthesis of RH and LH NTLs at optical frequencies. (top row) Conventional circuit models of RH and LH lines using distributed inductors and capacitors. (middle row) Plasmonic and nonplasmonic nanoparticles may play the role of nanoinductors and nanocapacitors, following Ref. [19]. (bottom row) Closely packed nanoparticles, in the limit, become plasmonic and dielectric layers, which may be employed in a similar way in a NTL. A sketch of the voltage ( V ) and current ( I ) symbols along the lines is also depicted.

Fig. 2
Fig. 2

Geometry of the 2-D NTL analyzed here: a core slab with permittivity ϵ in and thickness d sandwiched between two half-spaces with permittivity ϵ out .

Fig. 3
Fig. 3

Dispersion properties of the odd and even guided modes supported by the structure of Fig. 2 with (a) ϵ in = 5 ϵ 0 , ϵ out = ϵ 0 (odd mode) and reversal of the two materials (even mode) and (b) ϵ out = ϵ 0 , ϵ out = ϵ 0 5 (odd mode) and reversal of the two materials (even mode), following the exact Eqs. (3) and the approximate Eqs. (4) valid for electrically thin layers and assuming no materials loss. The guided-wave number β increases hyperbolically when the thickness decreases, leading to a concentration of the guided mode around the two interfaces for subwavelength slabs. In the figure axes, k 0 = ω ϵ 0 μ 0 is the free-space wavenumber and λ 0 = 2 π k 0 is the corresponding free-space wavelength.

Fig. 4
Fig. 4

Field distributions for the dominant TM even modes in the two cases of RH and LH NTLs (cross section is shown here). The parameters have been chosen to have the same core thickness d = λ 0 50 ) and similar field distributions, and in the two cases β RH = 29.5 ω ϵ 0 μ 0 , β LH = 28.95 ω ϵ 0 μ 0 . The P net vector indicates the direction of net-power propagation, whereas the β vector refers to the phase flow.

Fig. 5
Fig. 5

Dispersion plots for the geometry envisioned in Fig. 2 taking into account the Drude model for silver (including loss). (a) The positive slope confirms a forward behavior for the RH NTL [even mode for the structure of Fig. 1a] and for the dual geometry and the odd mode. (b) The negative slope indicates the LH (i.e., backward) operation of these structures. The variation of permittivity for the ENG material is indicated in the figure at selected frequencies.

Fig. 6
Fig. 6

Damping factors ( Im β ) for the dispersion plots of Fig. 5, due to the presence of ohmic losses. Note how the damping factor has different signs in the two cases, due to the backwardness of the structures in (b). Real and imaginary parts of the silver permittivity are reported in the figure at certain selected frequencies.

Fig. 7
Fig. 7

Effective material parameters for the NTL considered in Figs. 5, 6: (a) ENG–air–ENG waveguide as a RH NTL and (b) air–ENG–air waveguide as a LH NTL. Note how an effectively positive or negative permeability is achieved, even when realistic material losses are assumed (as in Figs. 5, 6), and the materials are all nonmagnetic.

Fig. 8
Fig. 8

(Color online) Interface between the RH and the LH NTLs of Fig. 4: (a) top view of the contour plot of the phase distribution and (b) 3-D plot of the instantaneous electric field distribution at the x z plane). Note the nearly complete transmission; the low reflection and clearly evident negative refraction at the interface, which underlines the negative refraction (i.e., left-handedness) of the second NTL; and the good matching between the two structures.

Fig. 9
Fig. 9

Transmission coefficient at the interface between the RH and the LH NTLs of Fig. 4, as a function of the transverse β z [where sin 1 ( β z β ) represents the angle of incidence of the impinging mode]. Note the growing transmission coefficient in the evanescent region, connected to the growing exponential and subwavelength focusing phenomenon (e.g., Refs. [1, 2]).

Fig. 10
Fig. 10

(Color online) Same as in Fig. 8, but for a small localized source in the RH NTL. The subwavelength focusing and image reconstruction on the other side of the interface can be clearly seen.

Fig. 11
Fig. 11

(Color online) Analysis of imaging features due to the RH–LH interface described in the previous figures. Subwavelength resolution is clearly noticeable in this analysis. More details are given in the text.

Fig. 12
Fig. 12

Sketch of a proposed planar setup as a subwavelength imaging system, which consists of a LH NTL sandwiched between two RH NTLs, for operation in the IR and visible domains.

Tables (1)

Tables Icon

Table 1 Effective Parameters for the NTLs of Fig. 4

Equations (20)

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Z = ( i ω ϵ π a ) 1 .
H even odd = z ̂ H 0 exp ( i β x ) { sinh ( β 2 ω 2 ϵ out μ 0 d 2 ) exp [ β 2 ω 2 ϵ out μ 0 ( y d 2 ) ] y > d 2 cosh sinh ( y β 2 ω 2 ϵ in μ 0 ) y < d 2 ± sinh ( β 2 ω 2 ϵ out μ 0 d 2 ) exp [ β 2 ω 2 ϵ out μ 0 ( y + d 2 ) ] y < d 2 } ,
even : tanh ( β 2 ω 2 ϵ in μ 0 d 2 ) = ϵ in ϵ out β 2 ω 2 ϵ out μ 0 β 2 ω 2 ϵ in μ 0 ,
odd : coth ( β 2 ω 2 ϵ in μ 0 d 2 ) = ϵ in ϵ out β 2 ω 2 ϵ out μ 0 β 2 ω 2 ϵ in μ 0 .
d min ( 2 π ω ϵ in μ 0 , 2 π ω ϵ out μ 0 ) ,
even : β = 2 d tanh 1 ϵ in ϵ out ,
odd : β = 2 d coth 1 ϵ in ϵ out ,
P out even odd = β H 0 2 4 ω ϵ out cosh 2 sinh 2 ( β 2 ω 2 ϵ in μ 0 d 2 ) β 2 ω 2 ϵ out μ 0 ,
P in = β H 0 2 4 ω ϵ in [ sinh ( β 2 ω 2 ϵ in μ 0 d ) β 2 ω 2 ϵ in μ 0 d ] .
β ω = 1 v g = 2 ϵ 0 d ( ϵ ENG 2 ϵ 0 2 ) d ϵ ENG d ω ,
I = 0 i ω ϵ E x d y = 0 H z y d y = H z ( y = 0 ) .
V = E y ( y = 0 ) .
d I d x = H z x y = 0 = ω ϵ in E y y = 0 = i ω ϵ in V = i ω ϵ eff even V ,
d V d x = E y x y = 0 = E x y y = 0 i ω μ 0 H z y = 0 = i ω μ eff even I ,
ϵ eff even ϵ in ,
μ eff even μ 0 + E x y y = 0 i ω H z y = 0 .
β 2 = ω 2 ϵ eff μ eff .
Z c I 2 2 = Re ( S x ) y = 0 .
ϵ eff odd = 0 ϵ E y d y 0 E y d y ,
μ eff odd = μ 0 E x y = 0 i ω 0 H z d y .

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