Abstract

We study experimentally the dynamic tunability and self-induced nonlinearity of split-ring resonators incorporating variable capacitance diodes. We demonstrate that the eigenfrequencies of the resonators can be tuned over a wide frequency range, and significantly, we show that the self-induced nonlinear effects observed in the varactor-loaded split-ring resonator structures can appear at relatively low power levels.

© 2006 Optical Society of America

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  1. C. Soukoulis, "Bending back light: The science of negative index materials," Optics and Photonics News, Vol.  17, No. 6, pp. 18-21 (2006), and references therein.
    [CrossRef]
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76,4773-4776 (1996).
    [CrossRef] [PubMed]
  3. 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]
  4. P. Markos and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65,036622-8 (2002).
    [CrossRef]
  5. P. Markos and C. M. Soukoulis, "Transmission studies of left-handed materials," Phys. Rev. B 65,033401-4 (2002).
    [CrossRef]
  6. 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]
  7. M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81,120-122 (2002).
    [CrossRef]
  8. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90,107401-4 (2003).
    [CrossRef] [PubMed]
  9. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and mu," Usp. Fiz. Nauk 92,517-526 (1967) (in Russian) [English translation: Phys. Usp. 10, 509 (1968)].
  10. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
    [CrossRef] [PubMed]
  11. V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30,3356-3358 (2005).
    [CrossRef]
  12. A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91,037401-4 (2003).
    [CrossRef] [PubMed]
  13. M. Lapine, M. Gorkunov, and K. H. Ringhofer, "Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements," Phys. Rev. E 67,065601-4 (2003).
    [CrossRef]
  14. I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
    [CrossRef]
  15. V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69,165112-165117 (2004).
    [CrossRef]
  16. M. Lapine and M. Gorkunov, "Three-wave coupling of microwaves in metamaterial with nonlinear resonant conductive elements," Phys. Rev. E 70,66601-8 (2004).
    [CrossRef]
  17. A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87,091104-3 (2005).
    [CrossRef]
  18. N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction," Opt. Express 13,1291-1298 (2005).
    [CrossRef] [PubMed]
  19. I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, "Nonlinear left-handed metamaterials," Radio Science 40,RS3S90 (2005).
    [CrossRef]
  20. I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Second-harmonic generation in nonlinear left-handed metamaterials," J. Opt. Soc. Am. B(Optical Physics) 23,529-534 (2006).
    [CrossRef]
  21. M. V. Gorkunov, I. V. Shadrivov, and Yu. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88,71912-3 (2006).
    [CrossRef]
  22. K. Aydin, K. Guven, N. Katsarakis, C.M. Soukoulis, and E. Ozbay, "Effect of disorder on magnetic resonance band gap in split-ring resoanntor structures," Opt. Express 12, 5896-5901 (2004).
    [CrossRef] [PubMed]
  23. I. Gil, J. Garcia Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40,1347-1348 (2004).
    [CrossRef]
  24. I. Gil, J. Bonache, J. García-García, F. Martín, "Tunable metameterial transmission lines based on varactor-loaded split-ring resonantors," IEEE Trans. Microwave Theory Tech. 54, 2665 - 2674 (2004).
    [CrossRef]

2006 (3)

C. Soukoulis, "Bending back light: The science of negative index materials," Optics and Photonics News, Vol.  17, No. 6, pp. 18-21 (2006), and references therein.
[CrossRef]

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Second-harmonic generation in nonlinear left-handed metamaterials," J. Opt. Soc. Am. B(Optical Physics) 23,529-534 (2006).
[CrossRef]

M. V. Gorkunov, I. V. Shadrivov, and Yu. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88,71912-3 (2006).
[CrossRef]

2005 (4)

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30,3356-3358 (2005).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87,091104-3 (2005).
[CrossRef]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction," Opt. Express 13,1291-1298 (2005).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, "Nonlinear left-handed metamaterials," Radio Science 40,RS3S90 (2005).
[CrossRef]

2004 (7)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
[CrossRef]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69,165112-165117 (2004).
[CrossRef]

M. Lapine and M. Gorkunov, "Three-wave coupling of microwaves in metamaterial with nonlinear resonant conductive elements," Phys. Rev. E 70,66601-8 (2004).
[CrossRef]

K. Aydin, K. Guven, N. Katsarakis, C.M. Soukoulis, and E. Ozbay, "Effect of disorder on magnetic resonance band gap in split-ring resoanntor structures," Opt. Express 12, 5896-5901 (2004).
[CrossRef] [PubMed]

I. Gil, J. Garcia Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40,1347-1348 (2004).
[CrossRef]

I. Gil, J. Bonache, J. García-García, F. Martín, "Tunable metameterial transmission lines based on varactor-loaded split-ring resonantors," IEEE Trans. Microwave Theory Tech. 54, 2665 - 2674 (2004).
[CrossRef]

2003 (3)

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91,037401-4 (2003).
[CrossRef] [PubMed]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, "Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements," Phys. Rev. E 67,065601-4 (2003).
[CrossRef]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90,107401-4 (2003).
[CrossRef] [PubMed]

2002 (3)

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81,120-122 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65,036622-8 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, "Transmission studies of left-handed materials," Phys. Rev. B 65,033401-4 (2002).
[CrossRef]

2000 (1)

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]

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]

1996 (1)

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

1967 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and mu," Usp. Fiz. Nauk 92,517-526 (1967) (in Russian) [English translation: Phys. Usp. 10, 509 (1968)].

Agranovich, V. M.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69,165112-165117 (2004).
[CrossRef]

Aydin, K.

K. Aydin, K. Guven, N. Katsarakis, C.M. Soukoulis, and E. Ozbay, "Effect of disorder on magnetic resonance band gap in split-ring resoanntor structures," Opt. Express 12, 5896-5901 (2004).
[CrossRef] [PubMed]

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81,120-122 (2002).
[CrossRef]

Baughman, R. H.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69,165112-165117 (2004).
[CrossRef]

Bayindir, M.

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81,120-122 (2002).
[CrossRef]

Boardman, A. D.

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
[CrossRef]

Bonache, J.

I. Gil, J. Bonache, J. García-García, F. Martín, "Tunable metameterial transmission lines based on varactor-loaded split-ring resonantors," IEEE Trans. Microwave Theory Tech. 54, 2665 - 2674 (2004).
[CrossRef]

Cai, W.

Chettiar, U. K.

Drachev, V. P.

Egan, P.

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
[CrossRef] [PubMed]

García-García, J.

I. Gil, J. Bonache, J. García-García, F. Martín, "Tunable metameterial transmission lines based on varactor-loaded split-ring resonantors," IEEE Trans. Microwave Theory Tech. 54, 2665 - 2674 (2004).
[CrossRef]

Gil, I.

I. Gil, J. Garcia Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40,1347-1348 (2004).
[CrossRef]

I. Gil, J. Bonache, J. García-García, F. Martín, "Tunable metameterial transmission lines based on varactor-loaded split-ring resonantors," IEEE Trans. Microwave Theory Tech. 54, 2665 - 2674 (2004).
[CrossRef]

Gorkunov, M.

M. Lapine and M. Gorkunov, "Three-wave coupling of microwaves in metamaterial with nonlinear resonant conductive elements," Phys. Rev. E 70,66601-8 (2004).
[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, "Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements," Phys. Rev. E 67,065601-4 (2003).
[CrossRef]

Gorkunov, M. V.

M. V. Gorkunov, I. V. Shadrivov, and Yu. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88,71912-3 (2006).
[CrossRef]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90,107401-4 (2003).
[CrossRef] [PubMed]

Guven, K.

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]

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

Katsarakis, N.

Kildishev, A. V.

Kivshar, Yu. S.

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Second-harmonic generation in nonlinear left-handed metamaterials," J. Opt. Soc. Am. B(Optical Physics) 23,529-534 (2006).
[CrossRef]

M. V. Gorkunov, I. V. Shadrivov, and Yu. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88,71912-3 (2006).
[CrossRef]

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, "Nonlinear left-handed metamaterials," Radio Science 40,RS3S90 (2005).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87,091104-3 (2005).
[CrossRef]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction," Opt. Express 13,1291-1298 (2005).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91,037401-4 (2003).
[CrossRef] [PubMed]

Koltenbah, B. E. C.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90,107401-4 (2003).
[CrossRef] [PubMed]

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
[CrossRef] [PubMed]

Lapine, M.

M. Lapine and M. Gorkunov, "Three-wave coupling of microwaves in metamaterial with nonlinear resonant conductive elements," Phys. Rev. E 70,66601-8 (2004).
[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, "Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements," Phys. Rev. E 67,065601-4 (2003).
[CrossRef]

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90,107401-4 (2003).
[CrossRef] [PubMed]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
[CrossRef] [PubMed]

Markos, P.

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81,120-122 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65,036622-8 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, "Transmission studies of left-handed materials," Phys. Rev. B 65,033401-4 (2002).
[CrossRef]

Martín, F.

I. Gil, J. Bonache, J. García-García, F. Martín, "Tunable metameterial transmission lines based on varactor-loaded split-ring resonantors," IEEE Trans. Microwave Theory Tech. 54, 2665 - 2674 (2004).
[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]

Ozbay, E.

K. Aydin, K. Guven, N. Katsarakis, C.M. Soukoulis, and E. Ozbay, "Effect of disorder on magnetic resonance band gap in split-ring resoanntor structures," Opt. Express 12, 5896-5901 (2004).
[CrossRef] [PubMed]

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81,120-122 (2002).
[CrossRef]

Padilla, W. J.

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]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90,107401-4 (2003).
[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]

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

Ringhofer, K. H.

M. Lapine, M. Gorkunov, and K. H. Ringhofer, "Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements," Phys. Rev. E 67,065601-4 (2003).
[CrossRef]

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]

Sarychev, A. K.

Schultz, S.

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. Zharov, and Yu. S. Kivshar, "Second-harmonic generation in nonlinear left-handed metamaterials," J. Opt. Soc. Am. B(Optical Physics) 23,529-534 (2006).
[CrossRef]

M. V. Gorkunov, I. V. Shadrivov, and Yu. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88,71912-3 (2006).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87,091104-3 (2005).
[CrossRef]

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, "Nonlinear left-handed metamaterials," Radio Science 40,RS3S90 (2005).
[CrossRef]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction," Opt. Express 13,1291-1298 (2005).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91,037401-4 (2003).
[CrossRef] [PubMed]

Shalaev, V. M.

Shen, Y. R.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69,165112-165117 (2004).
[CrossRef]

Smith, D. R.

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]

Soukoulis, C.

C. Soukoulis, "Bending back light: The science of negative index materials," Optics and Photonics News, Vol.  17, No. 6, pp. 18-21 (2006), and references therein.
[CrossRef]

Soukoulis, C. M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
[CrossRef] [PubMed]

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81,120-122 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65,036622-8 (2002).
[CrossRef]

P. Markos and C. M. Soukoulis, "Transmission studies of left-handed materials," Phys. Rev. B 65,033401-4 (2002).
[CrossRef]

Soukoulis, C.M.

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]

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

Sukhorukov, A. A.

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
[CrossRef]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90,107401-4 (2003).
[CrossRef] [PubMed]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and mu," Usp. Fiz. Nauk 92,517-526 (1967) (in Russian) [English translation: Phys. Usp. 10, 509 (1968)].

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]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
[CrossRef] [PubMed]

Youngs, I.

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

Yuan, H. K.

Zakhidov, A. A.

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69,165112-165117 (2004).
[CrossRef]

Zharov, A. A.

I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Second-harmonic generation in nonlinear left-handed metamaterials," J. Opt. Soc. Am. B(Optical Physics) 23,529-534 (2006).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87,091104-3 (2005).
[CrossRef]

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction," Opt. Express 13,1291-1298 (2005).
[CrossRef] [PubMed]

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, "Nonlinear left-handed metamaterials," Radio Science 40,RS3S90 (2005).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
[CrossRef]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91,037401-4 (2003).
[CrossRef] [PubMed]

Zharov, N. A.

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, "Nonlinear left-handed metamaterials," Radio Science 40,RS3S90 (2005).
[CrossRef]

Zharova, N. A.

N. A. Zharova, I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Nonlinear transmission and spatiotemporal solitons in metamaterials with negative refraction," Opt. Express 13,1291-1298 (2005).
[CrossRef] [PubMed]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87,091104-3 (2005).
[CrossRef]

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

M. Bayindir, K. Aydin, E. Ozbay, P. Markos, and C. M. Soukoulis, "Transmission properties of composite metamaterials in free space," Appl. Phys. Lett. 81,120-122 (2002).
[CrossRef]

A. A. Zharov, N. A. Zharova, I. V. Shadrivov, and Yu. S. Kivshar, "Subwavelength imaging with opaque nonlinear left-handed lenses," Appl. Phys. Lett. 87,091104-3 (2005).
[CrossRef]

M. V. Gorkunov, I. V. Shadrivov, and Yu. S. Kivshar, "Enhanced parametric processes in binary metamaterials," Appl. Phys. Lett. 88,71912-3 (2006).
[CrossRef]

Electron. Lett. (1)

I. Gil, J. Garcia Garcia, J. Bonache, F. Martin, M. Sorolla, and R. Marques, "Varactor-loaded split ring resonators for tunable notch filters at microwave frequencies," Electron. Lett. 40,1347-1348 (2004).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (2)

I. Gil, J. Bonache, J. García-García, F. Martín, "Tunable metameterial transmission lines based on varactor-loaded split-ring resonantors," IEEE Trans. Microwave Theory Tech. 54, 2665 - 2674 (2004).
[CrossRef]

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 (1)

Opt. Express (2)

Opt. Lett. (1)

Optics and Photonics News (1)

C. Soukoulis, "Bending back light: The science of negative index materials," Optics and Photonics News, Vol.  17, No. 6, pp. 18-21 (2006), and references therein.
[CrossRef]

Phys. Rev. B (2)

P. Markos and C. M. Soukoulis, "Transmission studies of left-handed materials," Phys. Rev. B 65,033401-4 (2002).
[CrossRef]

V. M. Agranovich, Y. R. Shen, R. H. Baughman, and A. A. Zakhidov, "Linear and nonlinear wave propagation in negative refraction metamaterials," Phys. Rev. B 69,165112-165117 (2004).
[CrossRef]

Phys. Rev. E (4)

M. Lapine and M. Gorkunov, "Three-wave coupling of microwaves in metamaterial with nonlinear resonant conductive elements," Phys. Rev. E 70,66601-8 (2004).
[CrossRef]

M. Lapine, M. Gorkunov, and K. H. Ringhofer, "Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements," Phys. Rev. E 67,065601-4 (2003).
[CrossRef]

I. V. Shadrivov, A. A. Sukhorukov, Yu. S. Kivshar, A. A. Zharov, A. D. Boardman, and P. Egan, "Nonlinear surface waves in left-handed materials," Phys. Rev. E 69,16617-9 (2004).
[CrossRef]

P. Markos and C. M. Soukoulis, "Numerical studies of left-handed materials and arrays of split ring resonators," Phys. Rev. E 65,036622-8 (2002).
[CrossRef]

Phys. Rev. Lett. (4)

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

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]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell’s law," Phys. Rev. Lett. 90,107401-4 (2003).
[CrossRef] [PubMed]

A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, "Nonlinear properties of left-handed metamaterials," Phys. Rev. Lett. 91,037401-4 (2003).
[CrossRef] [PubMed]

Radio Science (1)

I. V. Shadrivov, A. A. Zharov, N. A. Zharov, and Yu. S. Kivshar, "Nonlinear left-handed metamaterials," Radio Science 40,RS3S90 (2005).
[CrossRef]

Science (1)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100-terahertz," Science 306,1351-1353 (2004).
[CrossRef] [PubMed]

Usp. Fiz. Nauk (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsilon and mu," Usp. Fiz. Nauk 92,517-526 (1967) (in Russian) [English translation: Phys. Usp. 10, 509 (1968)].

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Figures (4)

Fig. 1.
Fig. 1.

Experimental structure used to study tunability and nonlinearity of a varactor-loaded split-ring resonator system. (a) Photography showing the fabricated SRR and biasing circuitry used for direct voltage tuning of the resonant frequency. (b) Top: electromagnetic representation of the SRR-diode structure; bottom: schematic of the biasing circuit.

Fig. 2.
Fig. 2.

(a) Experimental and (b) numerical results for the modulus of the reflection coefficient (S11) as a function of frequency for the SRR without the diode circuit, and with the diode circuit under both positive and negative biasing conditions.

Fig. 3.
Fig. 3.

Experimentally measured modulus of the SRR reflection coefficient (S 11) as a function of frequency and applied input power from the vector network analyzer. Power levels at the diode are significantly lower due to input coupling (see text).

Fig. 4.
Fig. 4.

Experimentally measured modulus of the reflection coefficient (S 11) as a function of the output power of vector network analyzer; (a) at several frequencies for zero voltage bias, and (b) -7 V (reverse) bias voltage. Power levels at the diode are significantly lower due to input coupling (see details in the text).

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