Abstract

An optical metamaterial characterized simultaneously by negative permittivity and permeability, viz. doubly negative metamaterial (DNM), that comprises deeply subwavelength unit cells is introduced. The DNM can operate in the near infrared and visible spectra and can be manufactured using standard nanofabrication methods with compatible materials. The DNM”s unit cell comprise a continuous optically thin metal film sandwiched between two identical optically thin metal strips separated by a small distance form the film. The incorporation of the middle thin metal film avoids limitations of metamaterials comprised of arrays of paired wires/strips/patches to operate for large wavelength / unit cell ratios. A cavity model, which is a modification of the conventional patch antenna cavity model, is developed to elucidate the structure”s electromagnetic properties. A novel procedure for extracting the effective permittivity and permeability is developed for an arbitrary incident angle and those parameters were shown to be nearly angle-independent. Extensions of the presented two dimensional structure to three dimensions by using square patches are straightforward and will enable more isotropic DNMs.

© 2006 Optical Society of America

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2006 (6)

Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, "Experimental demonstration of negative index of refraction," Appl. Phys. Lett. 88, 221103-221101 (2006).
[CrossRef]

G. Shvets and Y. Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A 8, S122 (2006).
[CrossRef]

A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557 (2006).
[CrossRef] [PubMed]

A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036609 (2006).
[CrossRef]

W.J. Padilla, D.R. Smith, and D.N. Basov, "Spectroscopy of metamaterials from infrared to optical frequencies," J. Opt. Society America B 23, 404 (2006).
[CrossRef]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

2005 (7)

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, "Electrostatic (plasmon) resonances in nanoparticles," Phys. Rev. B 72, 155412 (2005).
[CrossRef]

Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, C. Wenshan, U. K. Chettiar, Y. Hsiao-Kuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005).
[CrossRef]

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
[CrossRef]

Y. Horii, C. Caloz, and T. Itoh, "Super-compact multilayered left-handed transmission line and diplexer application," IEEE Trans. Microwave Theory Tech. 53, 1527-1534 (2005).
[CrossRef]

2004 (4)

A. Alu 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]

N. M. Lawandy, "Localized surface plasmon singularities in amplifying media," Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

G. Shvets and Y. A. Urzhumov, "Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902-243901 (2004).
[CrossRef]

2003 (1)

P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, (2003).
[CrossRef] [PubMed]

2002 (1)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative 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, 056625-056621 (2001).
[CrossRef]

2000 (1)

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

1997 (2)

P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997).
[CrossRef]

F. Hide, B. J. Schwartz, M. A. Diaz-Garcia, and A. J. Heeger, "Conjugated polymers as solid state laser materials," Synth. Met. 91, 35 (1997).
[CrossRef]

1995 (1)

1992 (1)

D. J. Bergman and D. Stroud, ``Properties of Macroscopically Inhomogeneous Media,' Solid State Phys. 46, 147 (1992).
[CrossRef]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and &mu," Soviet Physics - Uspekhi 10, 509-514 (1968).
[CrossRef]

Alu, A.

A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557 (2006).
[CrossRef] [PubMed]

A. Alu 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]

Basov, D.N.

W.J. Padilla, D.R. Smith, and D.N. Basov, "Spectroscopy of metamaterials from infrared to optical frequencies," J. Opt. Society America B 23, 404 (2006).
[CrossRef]

Bergman, D. J.

D. J. Bergman and D. Stroud, ``Properties of Macroscopically Inhomogeneous Media,' Solid State Phys. 46, 147 (1992).
[CrossRef]

Brueck, S. R. J.

Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005).
[CrossRef]

Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005).
[CrossRef]

Caloz, C.

Y. Horii, C. Caloz, and T. Itoh, "Super-compact multilayered left-handed transmission line and diplexer application," IEEE Trans. Microwave Theory Tech. 53, 1527-1534 (2005).
[CrossRef]

Chettiar, U. K.

Diaz-Garcia, M. A.

F. Hide, B. J. Schwartz, M. A. Diaz-Garcia, and A. J. Heeger, "Conjugated polymers as solid state laser materials," Synth. Met. 91, 35 (1997).
[CrossRef]

Dolling, G.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Drachev, V. P.

Economou, E. N.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005).
[CrossRef] [PubMed]

Engheta, N.

A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557 (2006).
[CrossRef] [PubMed]

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
[CrossRef]

A. Alu 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]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Frauenglass, A.

Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005).
[CrossRef]

Fredkin, D. R.

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, "Electrostatic (plasmon) resonances in nanoparticles," Phys. Rev. B 72, 155412 (2005).
[CrossRef]

Gaylord, T. K.

Grann, E. B.

Heeger, A. J.

F. Hide, B. J. Schwartz, M. A. Diaz-Garcia, and A. J. Heeger, "Conjugated polymers as solid state laser materials," Synth. Met. 91, 35 (1997).
[CrossRef]

Heyman, E.

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625-056621 (2001).
[CrossRef]

Hide, F.

F. Hide, B. J. Schwartz, M. A. Diaz-Garcia, and A. J. Heeger, "Conjugated polymers as solid state laser materials," Synth. Met. 91, 35 (1997).
[CrossRef]

Horii, Y.

Y. Horii, C. Caloz, and T. Itoh, "Super-compact multilayered left-handed transmission line and diplexer application," IEEE Trans. Microwave Theory Tech. 53, 1527-1534 (2005).
[CrossRef]

Hsiao-Kuan, Y.

Itoh, T.

Y. Horii, C. Caloz, and T. Itoh, "Super-compact multilayered left-handed transmission line and diplexer application," IEEE Trans. Microwave Theory Tech. 53, 1527-1534 (2005).
[CrossRef]

Jiangfeng, Z.

Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, "Experimental demonstration of negative index of refraction," Appl. Phys. Lett. 88, 221103-221101 (2006).
[CrossRef]

Kafesaki, M.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005).
[CrossRef] [PubMed]

Kildishev, A. V.

Kolinko, P.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, (2003).
[CrossRef] [PubMed]

Koschny, T.

Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, "Experimental demonstration of negative index of refraction," Appl. Phys. Lett. 88, 221103-221101 (2006).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005).
[CrossRef] [PubMed]

Lalanne, P.

Lawandy, N. M.

N. M. Lawandy, "Localized surface plasmon singularities in amplifying media," Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

Lei, Z.

Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, "Experimental demonstration of negative index of refraction," Appl. Phys. Lett. 88, 221103-221101 (2006).
[CrossRef]

Linden, S.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Malloy, K. J.

Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005).
[CrossRef]

Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005).
[CrossRef]

Markoš, P.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Mayergoyz, I. D.

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, "Electrostatic (plasmon) resonances in nanoparticles," Phys. Rev. B 72, 155412 (2005).
[CrossRef]

Minhas, B. K.

Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005).
[CrossRef]

Mock, J. J.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

Moharam, M. G.

Osgood, R. M.

Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005).
[CrossRef]

Padilla, W.J.

W.J. Padilla, D.R. Smith, and D.N. Basov, "Spectroscopy of metamaterials from infrared to optical frequencies," J. Opt. Society America B 23, 404 (2006).
[CrossRef]

Panoiu, N. C.

Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005).
[CrossRef]

Pendry, J. B.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005).
[CrossRef] [PubMed]

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

Pommet, D. A.

Rye, P.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

Salandrino, A.

Sarychev, A. K.

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[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]

Schurig, D.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

Schwartz, B. J.

F. Hide, B. J. Schwartz, M. A. Diaz-Garcia, and A. J. Heeger, "Conjugated polymers as solid state laser materials," Synth. Met. 91, 35 (1997).
[CrossRef]

Shalaev, V. M.

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]

Shuang, Z.

Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005).
[CrossRef]

Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005).
[CrossRef]

Shvets, G.

A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036609 (2006).
[CrossRef]

G. Shvets and Y. Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A 8, S122 (2006).
[CrossRef]

G. Shvets and Y. A. Urzhumov, "Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902-243901 (2004).
[CrossRef]

Smith, D. R.

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, (2003).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[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]

Smith, D.R.

W.J. Padilla, D.R. Smith, and D.N. Basov, "Spectroscopy of metamaterials from infrared to optical frequencies," J. Opt. Society America B 23, 404 (2006).
[CrossRef]

Soukoulis, C. M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, "Experimental demonstration of negative index of refraction," Appl. Phys. Lett. 88, 221103-221101 (2006).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Stroud, D.

D. J. Bergman and D. Stroud, ``Properties of Macroscopically Inhomogeneous Media,' Solid State Phys. 46, 147 (1992).
[CrossRef]

Tuttle, G.

Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, "Experimental demonstration of negative index of refraction," Appl. Phys. Lett. 88, 221103-221101 (2006).
[CrossRef]

Urzhumov, Y.

G. Shvets and Y. Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A 8, S122 (2006).
[CrossRef]

Urzhumov, Y. A.

G. Shvets and Y. A. Urzhumov, "Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902-243901 (2004).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and &mu," Soviet Physics - Uspekhi 10, 509-514 (1968).
[CrossRef]

Wegener, M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

Wenjun, F.

Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005).
[CrossRef]

Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005).
[CrossRef]

Wenshan, C.

Zhang, Z.

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, "Electrostatic (plasmon) resonances in nanoparticles," Phys. Rev. B 72, 155412 (2005).
[CrossRef]

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005).
[CrossRef] [PubMed]

Ziolkowski, R. W.

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
[CrossRef]

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625-056621 (2001).
[CrossRef]

Appl. Phys. Lett. (3)

D. R. Smith, D. Schurig, J. J. Mock, P. Kolinko, and P. Rye, "Partial focusing of radiation by a slab of indefinite media," Appl. Phys. Lett. 84, 2244-2246 (2004).
[CrossRef]

Z. Jiangfeng, T. Koschny, Z. Lei, G. Tuttle, and C. M. Soukoulis, "Experimental demonstration of negative index of refraction," Appl. Phys. Lett. 88, 221103-221101 (2006).
[CrossRef]

N. M. Lawandy, "Localized surface plasmon singularities in amplifying media," Appl. Phys. Lett. 85, 5040 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (3)

Y. Horii, C. Caloz, and T. Itoh, "Super-compact multilayered left-handed transmission line and diplexer application," IEEE Trans. Microwave Theory Tech. 53, 1527-1534 (2005).
[CrossRef]

A. Alu 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]

N. Engheta and R. W. Ziolkowski, "A positive future for double-negative metamaterials," IEEE Trans. Microwave Theory Tech. 53, 1535-1556 (2005).
[CrossRef]

J. Opt. A (1)

G. Shvets and Y. Urzhumov, "Negative index meta-materials based on two-dimensional metallic structures," J. Opt. A 8, S122 (2006).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Society America B (1)

W.J. Padilla, D.R. Smith, and D.N. Basov, "Spectroscopy of metamaterials from infrared to optical frequencies," J. Opt. Society America B 23, 404 (2006).
[CrossRef]

Opt. Express (2)

A. Alu, A. Salandrino, and N. Engheta, "Negative effective permeability and left-handed materials at optical frequencies," Opt. Express 14, 1557 (2006).
[CrossRef] [PubMed]

P. Kolinko and D. R. Smith, "Numerical study of electromagnetic waves interacting with negative index materials," Opt. Express 11, (2003).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. B (2)

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

I. D. Mayergoyz, D. R. Fredkin, and Z. Zhang, "Electrostatic (plasmon) resonances in nanoparticles," Phys. Rev. B 72, 155412 (2005).
[CrossRef]

Phys. Rev. E (2)

A. K. Sarychev, G. Shvets, and V. M. Shalaev, "Magnetic Plasmon Resonance," Phys. Rev. E 73, 036609 (2006).
[CrossRef]

R. W. Ziolkowski and E. Heyman, "Wave propagation in media having negative permittivity and permeability," Phys. Rev. E 64, 056625-056621 (2001).
[CrossRef]

Phys. Rev. Lett. (5)

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

G. Shvets and Y. A. Urzhumov, "Engineering the electromagnetic properties of periodic nanostructures using electrostatic resonances," Phys. Rev. Lett. 93, 243902-243901 (2004).
[CrossRef]

Z. Shuang, F. Wenjun, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137401 (2005).
[CrossRef]

Z. Shuang, F. Wenjun, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402-037401 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223901 (2005).
[CrossRef] [PubMed]

Science (2)

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Simultaneous negative phase and group velocity of light in a metamaterial," Science 312, 892-894 (2006).
[CrossRef] [PubMed]

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 Phys. (1)

D. J. Bergman and D. Stroud, ``Properties of Macroscopically Inhomogeneous Media,' Solid State Phys. 46, 147 (1992).
[CrossRef]

Soviet Physics - Uspekhi (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ϵ and &mu," Soviet Physics - Uspekhi 10, 509-514 (1968).
[CrossRef]

Synth. Met. (1)

F. Hide, B. J. Schwartz, M. A. Diaz-Garcia, and A. J. Heeger, "Conjugated polymers as solid state laser materials," Synth. Met. 91, 35 (1997).
[CrossRef]

Other (3)

J. Jin, The Finite Elements Method in Electromagnetics, Second Edition (Wiley, New York, 2002).

J. R. James and P. S. Hall, Handbook of Microstrip Antennas (1988).

C. A. Balanis, Antenna Theory: Analysis and Design, Third Edition ed. (John Wiley, 2005).

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Figures (9)

Fig. 1.
Fig. 1.

Structure’s unit cell

Fig. 2.
Fig. 2.

Equivalent modified cavity used to model the cavity in Fig. 1.

Fig. 3.
Fig. 3.

Dependence of the structures scattering coefficients and effective properties on the middle film thickness. The structure’s parameters are chosen as Lx =100nm, w=50nm, ds =15nm for three values of the strip-symmetry plane separation and film thickness being h=7nm and df =0 (Lz =44.5nm), h=10.25 nm and df =6.5nm (Lz =50.5nm), as well as h=11.25 nm and df =8.5nm (Lz =52.5nm). (a): magnitude of the zeroth order transmission coefficient |T 0|; (b): effective permeability µ eff; (c) effective permittivity ε eff. For df =0, i.e. in the absence of the middle film, only a single magnetic (longer wavelength) and electric (lower wavelength) resonances are obtained; the resonances manifest themselves as minima in the transmission coefficient magnitude dependence. For d ≠ ⁠0, i.e. in the presence of the middle film, one magnetic are obtained in the wavelength range between two electric resonances. Associated with the magnetic resonance and longer wavelength electric resonance are bands of negative Re{µ eff} and Re{ε eff}, respectively. The bands are more separated for df =6.5nm and overlap for df =8.5nm thus resulting in a DNM.

Fig. 4.
Fig. 4.

Electric field distribution corresponding to (a) magnetic resonance and (b) electric resonances. The field distribution was obtained assuming static approximation and assuming that SiO2 (εd =2.25) occupies the entire space.

Fig. 5.
Fig. 5.

Comparison between the quasi-static dielectric permittivity ε qs ( ω ) = 1 f 0 s i f i ( s s i ) (where s(ω)=(1-εm (ω)/εd )-1 and εm is the dielectric permittivity of gold) and the extracted from fully can electromagnetic simulations ε eff(ω) as described in Sec. 4.1.

Fig. 6.
Fig. 6.

Effective index of refraction neff for different sets of parameters for a single DNM layer.

Fig. 7.
Fig. 7.

The ratio Re{n eff}/Im{n eff} characterizing the losses in the system as a function of the gain (Im{εd }) in the dielectric layer for a single DNM layer. The structure parameters are chosen as Lx =100nm, Lz =51.5nm, w=50nm, ds =15nm, df =7.5nm, h=10.75nm. It is evident that the loss is not high without any gain and it further improves significantly by increasing the gain; the required values of gain correspond to practically achievable values.

Fig. 8.
Fig. 8.

The effective index of refraction for different number of layers ml . The structure parameters are chosen as Lx =100nm, Lz =102.5nm, w=50nm, ds =15nm, df =8.5nm, h=11.25nm. DNM operation with stable negative index in the range 640nm–680nm.

Fig. 9.
Fig. 9.

The real part of effective parameters µ eff and ε eff for different angles of incidence for a single DNM layer. The structure parameters are chosen as Lx =100nm, Lx =52.5nm, w=50nm, ds =15nm, df =8.5nm, h=11.25nm. DNM operation is obtained over a wide range of incident angles.

Equations (12)

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Y s strip + Y z ( 1 j cot k z h ) = 0 ,
f magn f p π q d s h ε d w 2 .
Y s strip + Y z + Y z Y s film + j 2 Y z tan k z h 2 Y z + j Y s film tan k z h = 0 .
μ eff , yy = μ 0 , eff , yy f p , magn , yy f f magn , ε eff , ii = ε 0 , eff , ii f p , elect , ii ( 1 ) f f elect ( 1 ) f p , elect , ii ( 2 ) f f elect ( 2 ) ,
T = ( cos ( k 0 n z , eff H ) + j 2 ( Z z , eff cos θ + cos θ Z z , eff ) sin ( k 0 n z , eff H ) ) 1 ,
R = j 2 ( Z z , eff cos θ + cos θ Z z , eff ) sin ( k 0 n z , eff H ) T ,
n z , eff = ( cos 1 ( 1 ( R 2 T 2 ) 2 T ) + 2 π l ) ( k 0 H ) 1 ,
Z z , eff = cos θ ( 1 R 2 ) T 2 ( 1 R 2 ) T 2 .
n z , eff = ( μ eff , yy ε eff , xx sin 2 θ ε eff , zz ) 1 2 ,
Z z , eff = n z , eff ε eff , xx ,
ε eff , xx = n z , eff Z z , eff ,
μ eff , yy = n z , eff Z z , eff + sin 2 θ ε eff , zz ,

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