Abstract

In this letter, the properties of split-ring resonators (SRRs) loaded with high-Q capacitors and nonlinear varactors are theoretically analyzed and experimentally measured. We demonstrate that the resonance frequency fm of the nonlinear SRRs can be tuned by increasing the incident power. fm moves to lower and higher frequencies for the SRR loaded with one varactor and two back-to-back varactors, respectively. For high incident powers, we observe bistable tunable metamaterials and hysteresis effects. Moreover, the coupling between two nonlinear SRRs is also discussed.

© 2008 Optical Society of America

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  1. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
    [CrossRef] [PubMed]
  2. C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
    [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, andW. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave.Theory Technol. 47, 2075-2084 (1999).
    [CrossRef]
  4. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ε and μ," Sov. Phys. Usp. 10, 509-514 (1968)
    [CrossRef]
  5. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  6. 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).
  7. R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2002).
    [CrossRef]
  8. A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear Properties of Left-handed Materials," Phys. Rev. Lett. 91, 037401-4 (2003).
    [CrossRef] [PubMed]
  9. I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, "Tunable split-ring resonators for nonlinear negative-index metamaterials," Opt. Express 14, 9344-9349 (2006).
    [CrossRef] [PubMed]
  10. D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).
    [CrossRef]
  11. I. Gil, J. Bonache, J. Garcia-Garcia, and F. Martin, "Tunable metamaterial transmission lines based on varactor loaded split-ring resonators," IEEE Trans. Microwave Theory Tech 54, 2665-2674 (2007).
    [CrossRef]
  12. D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, "Multistability in nonlinear left-handed transmission lines," Appl. Phys. Lett. 92, 264104 (2008).
    [CrossRef]
  13. E. Ozbay, K. Aydin, S. Butun, K. Kolodziejak, and D. Pawlak, "Ferroelectric based tuneable SRR based metamaterial for microwave applications," in Proceedings of the 37th European Microwave Conference, 497-9 (2007).
  14. A. Degiron, J. J. Mock, and D. R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007).
    [CrossRef] [PubMed]
  15. L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonators and ferrite rods," Opt. Express 16, 8825-8834 (2008).
    [CrossRef] [PubMed]
  16. D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
    [CrossRef]
  17. J. Carbonell, V. E. Boria, and D. Lippens, "Nonlinear effects in split-ring resonators loaded with heterostructure barrier varactors," Microwave Opt. Technol. Lett. 50, 474-479 (2008).
    [CrossRef]
  18. K. Aydin and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
    [CrossRef]
  19. L. D. Landau and E. M. Lifshitz, Mechanics, 3rd Edition (Course of Theoretical Physics Vol. 1).

2008 (3)

D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, "Multistability in nonlinear left-handed transmission lines," Appl. Phys. Lett. 92, 264104 (2008).
[CrossRef]

L. Kang, Q. Zhao, H. Zhao, and J. Zhou, "Magnetically tunable negative permeability metamaterial composed by split ring resonators and ferrite rods," Opt. Express 16, 8825-8834 (2008).
[CrossRef] [PubMed]

J. Carbonell, V. E. Boria, and D. Lippens, "Nonlinear effects in split-ring resonators loaded with heterostructure barrier varactors," Microwave Opt. Technol. Lett. 50, 474-479 (2008).
[CrossRef]

2007 (6)

K. Aydin and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
[CrossRef]

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
[CrossRef]

A. Degiron, J. J. Mock, and D. R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007).
[CrossRef] [PubMed]

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

I. Gil, J. Bonache, J. Garcia-Garcia, and F. Martin, "Tunable metamaterial transmission lines based on varactor loaded split-ring resonators," IEEE Trans. Microwave Theory Tech 54, 2665-2674 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

2006 (1)

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

2003 (1)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear Properties of Left-handed Materials," Phys. Rev. Lett. 91, 037401-4 (2003).
[CrossRef] [PubMed]

2002 (2)

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).

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2002).
[CrossRef]

2000 (1)

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

1999 (1)

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

1968 (1)

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

Aydin, K.

K. Aydin and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
[CrossRef]

Bonache, J.

I. Gil, J. Bonache, J. Garcia-Garcia, and F. Martin, "Tunable metamaterial transmission lines based on varactor loaded split-ring resonators," IEEE Trans. Microwave Theory Tech 54, 2665-2674 (2007).
[CrossRef]

Boria, V. E.

J. Carbonell, V. E. Boria, and D. Lippens, "Nonlinear effects in split-ring resonators loaded with heterostructure barrier varactors," Microwave Opt. Technol. Lett. 50, 474-479 (2008).
[CrossRef]

Carbonell, J.

J. Carbonell, V. E. Boria, and D. Lippens, "Nonlinear effects in split-ring resonators loaded with heterostructure barrier varactors," Microwave Opt. Technol. Lett. 50, 474-479 (2008).
[CrossRef]

Chen, H.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
[CrossRef]

Degiron, A.

Garcia-Garcia, J.

I. Gil, J. Bonache, J. Garcia-Garcia, and F. Martin, "Tunable metamaterial transmission lines based on varactor loaded split-ring resonators," IEEE Trans. Microwave Theory Tech 54, 2665-2674 (2007).
[CrossRef]

Gil, I.

I. Gil, J. Bonache, J. Garcia-Garcia, and F. Martin, "Tunable metamaterial transmission lines based on varactor loaded split-ring resonators," IEEE Trans. Microwave Theory Tech 54, 2665-2674 (2007).
[CrossRef]

Gorkunov, M. V.

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

Holden, A. J.

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

Kang, L.

Kivshar, Y. S.

D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, "Multistability in nonlinear left-handed transmission lines," Appl. Phys. Lett. 92, 264104 (2008).
[CrossRef]

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, "Tunable split-ring resonators for nonlinear negative-index metamaterials," Opt. Express 14, 9344-9349 (2006).
[CrossRef] [PubMed]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear Properties of Left-handed Materials," Phys. Rev. Lett. 91, 037401-4 (2003).
[CrossRef] [PubMed]

Kong, J. A.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
[CrossRef]

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Lippens, D.

J. Carbonell, V. E. Boria, and D. Lippens, "Nonlinear effects in split-ring resonators loaded with heterostructure barrier varactors," Microwave Opt. Technol. Lett. 50, 474-479 (2008).
[CrossRef]

Markos, P.

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).

Martin, F.

I. Gil, J. Bonache, J. Garcia-Garcia, and F. Martin, "Tunable metamaterial transmission lines based on varactor loaded split-ring resonators," IEEE Trans. Microwave Theory Tech 54, 2665-2674 (2007).
[CrossRef]

Mock, J. J.

Morrison, S. K.

Mu, M.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
[CrossRef]

Ozbay, E.

K. Aydin and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
[CrossRef]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

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

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

Powell, D. A.

D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, "Multistability in nonlinear left-handed transmission lines," Appl. Phys. Lett. 92, 264104 (2008).
[CrossRef]

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

Ran, L.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
[CrossRef]

Robbins, D. J.

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

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2002).
[CrossRef]

Shadrivov, I. V.

D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, "Multistability in nonlinear left-handed transmission lines," Appl. Phys. Lett. 92, 264104 (2008).
[CrossRef]

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

I. V. Shadrivov, S. K. Morrison, and Y. S. Kivshar, "Tunable split-ring resonators for nonlinear negative-index metamaterials," Opt. Express 14, 9344-9349 (2006).
[CrossRef] [PubMed]

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear Properties of Left-handed Materials," Phys. Rev. Lett. 91, 037401-4 (2003).
[CrossRef] [PubMed]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2002).
[CrossRef]

Smith, D. R.

A. Degiron, J. J. Mock, and D. R. Smith, "Modulating and tuning the response of metamaterials at the unit cell level," Opt. Express 15, 1115-1127 (2007).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2002).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

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).

Veselago, V. G.

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

Wang, D.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
[CrossRef]

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Wu, B.

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
[CrossRef]

Zhao, H.

Zhao, Q.

Zharov, A. A.

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear Properties of Left-handed Materials," Phys. Rev. Lett. 91, 037401-4 (2003).
[CrossRef] [PubMed]

Zhou, J.

Appl. Phys. Lett. (3)

D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, "Self-tuning mechanisms of nonlinear split-ring resonators," Appl. Phys. Lett. 91, 144107 (2007).
[CrossRef]

D. A. Powell, I. V. Shadrivov, and Y. S. Kivshar, "Multistability in nonlinear left-handed transmission lines," Appl. Phys. Lett. 92, 264104 (2008).
[CrossRef]

D. Wang, L. Ran, H. Chen, M. Mu, J. A. Kong, and B. Wu, "Active left-handed material collaborated with microwave varactors," Appl. Phys. Lett. 91, 164101 (2007).
[CrossRef]

IEEE Trans. Microwave Theory Tech (1)

I. Gil, J. Bonache, J. Garcia-Garcia, and F. Martin, "Tunable metamaterial transmission lines based on varactor loaded split-ring resonators," IEEE Trans. Microwave Theory Tech 54, 2665-2674 (2007).
[CrossRef]

J. Appl. Phys. (1)

K. Aydin and E. Ozbay, "Capacitor-loaded split ring resonators as tunable metamaterial components," J. Appl. Phys. 101, 024911 (2007).
[CrossRef]

Microwave Opt. Technol. Lett. (1)

J. Carbonell, V. E. Boria, and D. Lippens, "Nonlinear effects in split-ring resonators loaded with heterostructure barrier varactors," Microwave Opt. Technol. Lett. 50, 474-479 (2008).
[CrossRef]

Opt. Express (3)

Phys. Rev. E (1)

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).

Phys. Rev. Lett. (2)

A. A. Zharov, I. V. Shadrivov, and Y. S. Kivshar, "Nonlinear Properties of Left-handed Materials," Phys. Rev. Lett. 91, 037401-4 (2003).
[CrossRef] [PubMed]

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

Science (3)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative Refractive Index at Optical Wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental Verification of a Negative Index of Refraction," Science 292, 77-79 (2002).
[CrossRef]

Sov. Phys. Usp. (1)

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

Theory Technol. (1)

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

Other (2)

E. Ozbay, K. Aydin, S. Butun, K. Kolodziejak, and D. Pawlak, "Ferroelectric based tuneable SRR based metamaterial for microwave applications," in Proceedings of the 37th European Microwave Conference, 497-9 (2007).

L. D. Landau and E. M. Lifshitz, Mechanics, 3rd Edition (Course of Theoretical Physics Vol. 1).

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Figures (5)

Fig. 1.
Fig. 1.

(a) The reflection of the SRR loaded with one varactor, measured by a loop antenna. The curves show the measurement results at input power from -15 dBm to 9 dBm in 3 dBm steps. The inset shows the picture of the loop antenna and the sample. (b) The hysteresis effect at high input power levels. The blue curves are measured for forward sweep (the source frequency of the network analyzer is scanned from low to high) and the red dashed curves are measured for reverse sweep (frequency is scanned from high to low).

Fig. 2.
Fig. 2.

The oscillation amplitude vs. source frequency calculated from the simplified nonlinear oscillator model. The curves from bottom to top correspond to excitation power from low to high. The blue arrow shows the jump for forward sweep of the top curve and the red arrow shows the jump for reverse sweep of the top curve.

Fig. 3.
Fig. 3.

The reflection of the SRR loaded with two back-to-back varactors, measured by a loop antenna. The curves show the measurement results at power levels from -14 dBm to 2 dBm, in 2 dBm steps. The inset shows the sample.

Fig. 4.
Fig. 4.

The reflection of (a) two linear SRRs and (b) two nonlinear SRRs at input power of -15 dBm. The legend shows the distance between the two SRRs. The distance between the first SRR and the antenna is fixed.

Fig. 5.
Fig. 5.

The 2d plot of the reflection of two coupled nonlinear SRRs. The x-axis shows the distance between the two SRRs and the y-axis shows the frequency. The four figures from left to right display the result at input power from -15 dBm to 0 dBm. The SRRs and the antenna are arranged such that they have the same axis and the planes of the rings are parallel to each other. The distance between the loop antenna and the first SRR is fixed and the second SRR is movable along its axis, as seen from the inset.

Metrics