## Nonlinear magnetic metamaterials

Optics Express, Vol. 16, Issue 25, pp. 20266-20271 (2008)

http://dx.doi.org/10.1364/OE.16.020266

Acrobat PDF (311 KB)

### Abstract

We study experimentally nonlinear tunable magnetic metamaterials operating at microwave frequencies. We fabricate the nonlinear metamaterial composed of double split-ring resonators where a varactor diode is introduced into each resonator so that the magnetic resonance can be tuned dynamically by varying the input power. We demonstrate that at higher powers the transmission of the metamaterial becomes power-dependent and, as a result, such metamaterial can demonstrate various nonlinear properties. In particular, we study experimentally the power-dependent shift of the transmission band and demonstrate nonlinearity-induced enhancement (or suppression) of wave transmission.

© 2008 Optical Society of America

1. C. M. Soukoulis, “Bending back light: The science of negative index materials,” Opt. Photon. News **17**, 16–21 (2006). [CrossRef]

*µ*. By designing the individual unit cells of metamaterials, one may construct composites with effective properties not occurring in nature.

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

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]

4. M. Gorkunov and M. Lapine, “Tuning of a nonlinear metamaterial band gap by an external magnetic field,” Phys. Rev. B **70**, 235109–9 (2004). [CrossRef]

5. 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]

6. S. Lim, C. Caloz, and T. Itoh, “Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth,” IEEE Trans. Microwave Theory Tech. **52**, 2678–2690 (2004). [CrossRef]

7. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature (London) **444**, 597–600 (2006). [CrossRef]

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

10. 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]

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

11. 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]

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]

12. M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. **85**, 1451–1453 (2004). [CrossRef]

13. 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]

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

15. A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. **31**, 2169–2171 (2006). [CrossRef] [PubMed]

16. S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E **73**, 36617 (2006). [CrossRef]

17. N. Lazarides, M. Eleftheriou, and G. P. Tsironis, “Discrete Breathers in Nonlinear Magnetic Metamaterials,” Phys. Rev. Lett. **97**, 157406–4 (2006). [CrossRef] [PubMed]

18. Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Sub-wavelength Discrete Solitons in Nonlinear Metamaterials,” Phys. Rev. Lett. **99**, 153901–4 (2007). [CrossRef] [PubMed]

19. S. Feng and K. Halterman, “Parametrically Shielding Electromagnetic Fields by Nonlinear Metamaterials,” Phys. Rev. Lett. **100**, 63901–4 (2008). [CrossRef]

20. A.B. Kozyrev, H. Kim, A. Karbassi, and D. W. van der Weide, “Wave propagation in nonlinear left-handed transmission line media,” Appl. Phys. Lett. **87**, 121109–3 (2005). [CrossRef]

21. A. B. Kozyrev, H. Kim, and D. W. van der Weide, “Parametric amplification in left-handed transmission line media,” Appl. Phys. Lett. **88**, 264101–3 (2006). [CrossRef]

22. A. B. Kozyrev and D. W. van der Weide, “Trains of envelope solitons in nonlinear left-handed transmission line media,” Appl. Phys. Lett. **91**, 254111–3 (2007). [CrossRef]

*magnetic metamaterial*operating at microwave frequencies. Such metamaterials are fabricated by modifying the properties of SRRs and introducing varactor diodes in each SRR element of the composite structure [9

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

11. 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]

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]

11. 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]

**91**, 037401–4 (2003). [CrossRef] [PubMed]

*S*

_{21}between the input of the source and output of the receiver antenna. The measured transmission parameter

*S*

_{21}characterizes local electric field in the vicinity of the receiver antenna. Due to the two-dimensional nature of the parallel plate waveguide, as well as symmetry of our sample, the electric field in the scanned area is expected to remain polarized mainly perpendicular to the plane of the plates. Due to the polarization selection imposed to the waveguide, we are not able to observe any polarization-conversion effects in our setup, and further experiments with free-space measurements could expose new polarization effects, as was already indicated in [23

23. M.W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express **15**, 5238–5247 (2007) [CrossRef] [PubMed]

**14**, 9344–9349 (2006). [CrossRef] [PubMed]

**91**, 144107 (2007). [CrossRef]

**91**, 037401–4 (2003). [CrossRef] [PubMed]

24. 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]

## Acknowledgment

## References and links

1. | C. M. Soukoulis, “Bending back light: The science of negative index materials,” Opt. Photon. News |

2. | D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. |

3. | A. A. Zharov, I. V. Shadrivov, and Yu. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett. |

4. | M. Gorkunov and M. Lapine, “Tuning of a nonlinear metamaterial band gap by an external magnetic field,” Phys. Rev. B |

5. | M. Lapine, M. Gorkunov, and K. H. Ringhofer, “Nonlinearity of a metamaterial arising from diode insertions into resonant conductive elements,” Phys. Rev. E |

6. | S. Lim, C. Caloz, and T. Itoh, “Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth,” IEEE Trans. Microwave Theory Tech. |

7. | H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz metamaterial devices,” Nature (London) |

8. | I. V. Shadrivov and Yu. S. Kivshar, “Nonlinear Effects in Left-Handed Metamaterials,” in |

9. | I. V. Shadrivov, S. K. Morrison, and Yu. S. Kivshar, “Tunable split-ring resonators for nonlinear negative-index metamaterials,” Opt. Express |

10. | A. Degiron, J. J. Mock, and D. R. Smith, “Modulating and tuning the response of metamaterials at the unit cell level,” Opt. Express |

11. | D. A. Powell, I. V. Shadrivov, Y. S. Kivshar, and M. V. Gorkunov, “Self-tuning mechanisms of nonlinear split-ring resonators,” Appl. Phys. Lett. |

12. | M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, “Tunable transmission and bistability in left-handed band-gap structures,” Appl. Phys. Lett. |

13. | 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 |

14. | I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, “Second-harmonic generation in nonlinear left-handed metamaterials,” J. Opt. Soc. Am. B |

15. | A. K. Popov and V. M. Shalaev, “Compensating losses in negative-index metamaterials by optical parametric amplification,” Opt. Lett. |

16. | S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, “Modulation instability in nonlinear negative-index material,” Phys. Rev. E |

17. | N. Lazarides, M. Eleftheriou, and G. P. Tsironis, “Discrete Breathers in Nonlinear Magnetic Metamaterials,” Phys. Rev. Lett. |

18. | Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, “Sub-wavelength Discrete Solitons in Nonlinear Metamaterials,” Phys. Rev. Lett. |

19. | S. Feng and K. Halterman, “Parametrically Shielding Electromagnetic Fields by Nonlinear Metamaterials,” Phys. Rev. Lett. |

20. | A.B. Kozyrev, H. Kim, A. Karbassi, and D. W. van der Weide, “Wave propagation in nonlinear left-handed transmission line media,” Appl. Phys. Lett. |

21. | A. B. Kozyrev, H. Kim, and D. W. van der Weide, “Parametric amplification in left-handed transmission line media,” Appl. Phys. Lett. |

22. | A. B. Kozyrev and D. W. van der Weide, “Trains of envelope solitons in nonlinear left-handed transmission line media,” Appl. Phys. Lett. |

23. | M.W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express |

24. | 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 |

**OCIS Codes**

(350.4010) Other areas of optics : Microwaves

(160.3918) Materials : Metamaterials

**ToC Category:**

Metamaterials

**History**

Original Manuscript: September 17, 2008

Revised Manuscript: November 16, 2008

Manuscript Accepted: November 21, 2008

Published: November 24, 2008

**Citation**

Ilya V. Shadrivov, Alexander B. Kozyrev, Daniel W. van der Weide, and Yuri S. Kivshar, "Nonlinear magnetic metamaterials," Opt. Express **16**, 20266-20271 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-25-20266

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### References

- C. M. Soukoulis, "Bending back light: The science of negative index materials," Opt. Photon. News 17, 16-21 (2006). [CrossRef]
- D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000). [CrossRef] [PubMed]
- 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. Gorkunov and M. Lapine, "Tuning of a nonlinear metamaterial band gap by an external magnetic field," Phys. Rev. B 70, 235109-9 (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]
- S. Lim, C. Caloz, and T. Itoh, "Metamaterial-based electronically controlled transmission-line structure as a novel leaky-wave antenna with tunable radiation angle and beamwidth," IEEE Trans. Microwave Theory Tech. 52, 2678-2690 (2004). [CrossRef]
- H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature (London) 444,597-600 (2006). [CrossRef]
- I. V. Shadrivov and Yu. S. Kivshar, "Nonlinear Effects in Left-Handed Metamaterials," in Physics of Negative refraction and Negative Index Materials, Vol. 98 of Springer Series in Materials Science, C. M. Krowne and Y. Zhang, eds., (Springer-Verlag, Berlin, 2007), pp. 331-371.
- I. V. Shadrivov, S. K. Morrison, and Yu. S. Kivshar, "Tunable split-ring resonators for nonlinear negative-index metamaterials," Opt. Express 14, 9344-9349 (2006). [CrossRef] [PubMed]
- 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]
- M. W. Feise, I. V. Shadrivov, and Yu. S. Kivshar, "Tunable transmission and bistability in left-handed band-gap structures," Appl. Phys. Lett. 85, 1451-1453 (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]
- I. V. Shadrivov, A. A. Zharov, and Yu. S. Kivshar, "Second-harmonic generation in nonlinear left-handed metamaterials," J. Opt. Soc. Am. B 23, 529-534 (2006). [CrossRef]
- A. K. Popov and V. M. Shalaev, "Compensating losses in negative-index metamaterials by optical parametric amplification," Opt. Lett. 31, 2169-2171 (2006). [CrossRef] [PubMed]
- S. Wen, Y. Wang, W. Su, Y. Xiang, X. Fu, and D. Fan, "Modulation instability in nonlinear negative-index material," Phys. Rev. E 73, 36617 (2006). [CrossRef]
- N. Lazarides, M. Eleftheriou, and G. P. Tsironis, "Discrete Breathers in Nonlinear Magnetic Metamaterials," Phys. Rev. Lett. 97, 157406-4 (2006). [CrossRef] [PubMed]
- Y. Liu, G. Bartal, D. A. Genov, and X. Zhang, "Subwavelength Discrete Solitons in Nonlinear Metamaterials," Phys. Rev. Lett. 99, 153901-4 (2007). [CrossRef] [PubMed]
- S. Feng and K. Halterman, "Parametrically Shielding Electromagnetic Fields by Nonlinear Metamaterials," Phys. Rev. Lett. 100, 63901-4 (2008). [CrossRef]
- A.B. Kozyrev, H. Kim, A. Karbassi, and D. W. van der Weide, "Wave propagation in nonlinear left-handed transmission line media," Appl. Phys. Lett. 87, 121109-3 (2005). [CrossRef]
- A. B. Kozyrev, H. Kim, and D. W. van der Weide, "Parametric amplification in left-handed transmission line media," Appl. Phys. Lett. 88, 264101-3 (2006). [CrossRef]
- A. B. Kozyrev and D. W. van der Weide, "Trains of envelope solitons in nonlinear left-handed transmission line media," Appl. Phys. Lett. 91, 254111-3 (2007). [CrossRef]
- M.W. Klein, M. Wegener, N. Feth, and S. Linden, "Experiments on second- and third-harmonic generation from magnetic metamaterials," Opt. Express 15, 5238-5247 (2007) [CrossRef] [PubMed]
- 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]

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