## Excitation of dark plasmonic modes in symmetry broken terahertz metamaterials |

Optics Express, Vol. 22, Issue 16, pp. 19401-19410 (2014)

http://dx.doi.org/10.1364/OE.22.019401

Acrobat PDF (405 KB)

### Abstract

Plasmonic structures with high symmetry, such as double-identical gap split ring resonators, possess dark eigenmodes. These dark eigenmodes are dominated by magnetic dipole and/or higher-order multi-poles such as electric quadrapoles. Consequently these dark modes interact very weakly with the surrounding environment, and can have very high quality factors (*Q*). In this work, we have studied, experimentally as well as theoretically, these dark eigenmodes in terahertz metamaterials. Theoretical investigations with the help of classical perturbation theory clearly indicate the existence of these dark modes in symmetric plasmonic metamaterials. However, these dark modes can be excited experimentally by breaking the symmetry within the constituting metamaterial resonators cell, resulting in high quality factor resonance mode. The symmetry broken metamaterials with such high quality factor can pave the way in realizing high sensitivity sensors, in addition to other applications.

© 2014 Optical Society of America

## 1. Introduction

1. V. G. Vaselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Sov. Phys. Usp. **10**, 509–514 (1968). [CrossRef]

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

7. 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 (2000). [CrossRef] [PubMed]

9. C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science **315**, 47–49 (2007). [CrossRef] [PubMed]

10. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. **85**, 3966 (2000). [CrossRef] [PubMed]

11. A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. **92**, 117403 (2004). [CrossRef] [PubMed]

12. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. smith, “Broadband ground-plane cloak,” Science **323**, 366–369 (2006). [CrossRef]

13. N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. **84**, 2943 (2004). [CrossRef]

15. D. R. Chowdhury, R. Singh, J. F. O’Hara, H. T. Chen, A. J. Taylor, and A. K. Azad, “Dynamically reconfigurable terahertz metamaterials through photo doped semiconductors,” Appl. Phys. Lett. **99**, 231101 (2011). [CrossRef]

16. H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for terahertz regime: Design fabrication and characterization,” Opt. Express **16**, 7181–7188 (2008). [CrossRef] [PubMed]

17. J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express **16**, 1786–1795 (2008). [CrossRef] [PubMed]

18. I. A. I. Naib, C. Jansen, and M. Koch, “Thin film sensing with planar asymetric metamaterial resonators,” Appl. Phys. Lett. **93**, 083507 (2008). [CrossRef]

19. P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. **4**, 795–808 (2010). [CrossRef]

20. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a brocken structural symmetry,” Phys. Rev. Lett. **99**, 147401 (2007). [CrossRef]

24. W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. **37**, 3366–3368 (2012). [CrossRef]

25. C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymetric metamaterials for ultrasensitive spectroscopy and identification of moleculer monolayers,” Nat. Mat. **11**, 69–75 (2012). [CrossRef]

26. D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. **11**, 2104–2108 (2011). [CrossRef] [PubMed]

## 2. Experiments

*n*m of titanium, followed by 200

*n*m of gold. Finally, the MM samples were realized through a typical lift off process leading to the formation of the metal SRRs.

*P*=

_{x}*P*= 88

_{y}*μ*m. The fabricated metamaterials samples were characterized using terahertz time domain spectroscopy (THz-TDS) [27

27. D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with tera-hertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B **7**, 2006–2015 (1990). [CrossRef]

*S*

_{21}) normalized to the bare GaAs substrate were obtained for all the samples.

*Q*factor for the resonances appearing nearing 0.7 THz are measured as ∼ 6 for all three samples. The low frequency dark resonance is experimentally inaccessible in MM1 because of the high structural symmetry. However, by introducing asymmetry one can experimentally access this asymmetric dark resonance mode, which usually offers a high

*Q*factor. The measured

*Q*factor of the resonance at 0.446 THz for MM3 is ∼ 10.2, much larger than observed for the resonance at 0.7 THz.

## 3. Simulations and discussion

29. Y. Zeng, D. A. R. Dalvit, J. O’Hara, and S. A. Trugman, “A modal analysis method to describe weak nonlinear effects in metamaterials,” Phys. Rev. B **85**, 125107 (2012). [CrossRef]

30. A. Raman and S. Fan, “Photonic band structure of dispersive meta-materials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. **104**, 087401 (2010). [CrossRef]

**u**= (

**H**,

**E**,

**P**,

**J**)

^{T}, and

*ℒ*is a non-Hermitian differential operator. As a consequence, the eigenvalues are in general complex, and the corresponding eigenvectors are not orthogonal to each other [31, 32]. However, the eigenvectors are

*bi-orthogonal*to the eigenvectors of the corresponding adjoint equation, From the theory of non-self-adjoint differential equations, one knows that the eigenvalues and eigenvectors of the two mutually adjoint equations can be ordered in such a way that

*d*

^{3}

**r**...). Also, it is possible to associate the same eigenvalue

*ω*with one eigenvector of (1) and with one eigenvector of the adjoint equation (2), i.e.,

_{m}*ω*↔

_{m}**u**

*,*

_{m}**u**

*and*

_{m}*y*= 0 mirror symmetry as well as

*x*= 0 mirror symmetry, its eigenmodes can be divided into four groups in terms of the

*x*component of the electric field. The first group

**u**

*is even in terms of*

_{n,ee}*x*= 0 mirror plane, and also even in terms of

*y*= 0 mirror plane, such that: The second group

**u**

*is even in terms of*

_{n,eo}*x*= 0 mirror plane, while odd in terms of

*y*= 0 mirror plane, such that: The third group

**u**

*is odd in terms of*

_{n,oe}*x*= 0 mirror plane, while even in terms of

*y*= 0 mirror plane, such that: The fourth group

**u**

*is odd in terms of*

_{n,oo}*x*= 0 mirror plane, while odd in terms of

*y*= 0 mirror plane, such that: Due to these symmetry, an

*x*-polarized incident plane wave can only excite the

**u**

*modes, while*

_{n,ee}*y*-polarized incident plane wave can only excite the

**u**

*modes. The*

_{n,oo}**u**

*and*

_{n,eo}**u**

*can not be excited at all, baring the characters of dark modes [33*

_{n,oe}33. D. E. Gomez, Z. Q. Teo, M. Altissimo, T. J. Davis, S. Earl, and A. Roberts, “The drak side of plasmonics,” Nano Lett. **13**, 3722–3728 (2013). [CrossRef]

*n*= 1) should look like: where the arrows indicate the current direction. Based on the current distribution, one may derive that the eigen frequencies of the first order modes may satisfy the following relations: (1) the

*eo*mode has the smallest frequency, and (2)

*Re*[

*ω*

_{1,oo}] ≃ 2

*Re*[

*ω*

_{1,eo}],

*Re*[

*ω*

_{1,oe}] ≃ 2

*Re*[

*ω*

_{1,ee}]. Through numerical simulation, three of these four eigenmodes are excited. It is found that the

*ee*mode is around 1.218 THz, the

*oo*mode is around 0.7246 THz and the

*eo*around 0.5739 THz. Furthermore, the corresponding eigenmode pattern are also calculated and plotted in Figs. 3, 4, and 5, and are found to perfectly agree with our analytical prediction.

*𝒳*corresponding the additional asymmetric part. For the structure we considered,

*𝒳*(

*x*,

*y*,

*z*) =

*𝒳*(

*x*, −

*y*,

*z*). Consequently, its eigenmodes can be divided into two groups in terms of the

*x*component of the electric field. The first group,

**v**

*, is odd in terms of*

_{n,o}*y*= 0 mirror plane, such that: and the second group,

**v**

*, is even in terms of*

_{n,e}*y*= 0 mirror plane, such that:

**v**in terms of the original eigenmodes

**U**such that: In doing so, the equation (3) can be reexpressed in terms of matrix:

**X**is defined as

*𝒳*can only couple an

*ee*mode to

*ee*and

*oe*mode, or an

*oo*mode to

*eo*and

*oo*mode. In other words, the new eigenmode can be written as Moreover, the corresponding eigenvalue Ω

*will be different to the original*

_{m}*ω*. In other words, the resonance location of the symmetric SRR systems will be changed by the degree of asymmetry.

_{m}**S**represents excitation sources or the incident wave. The total field

**V**can now be expanded in terms of the eigenvectors

**v**

*of the source-free problem, namely where Ω*

_{m}*are the corresponding complex eigenvalues of the source-free problem. Under a normal*

_{m}*x*-polarized incidence, the total field can be written as Similar equation can be obtained for the

*y*-polarized incidence

*x*-polarized incidence, the asymmetrical structure will present two valleys, around

*ω*

_{1,ee}and

*ω*

_{1,oe}. Under a

*y*-polarized incidence, the asymmetrical structure also will present two valleys, around

*ω*

_{1,eo}and

*ω*

_{1,oo}. Because of the fact that

*Re*[

*ω*

_{1,oe}] ≃ 2

*Re*[

*ω*

_{1,ee}], the first order

*oe*mode should be around 2.4 THz. It therefore can be excited but cannot be observed in the frequency regime our measurement system operates. It should be pointed out that the first grating mode of the array, has a frequency of 0.9472 THz, which is much smaller than the frequency of the first order

*oe*mode.

34. Y. Zeng, Y. Fu, M. Bengtsson, X. S. Chen, W. Lu, and H. Ågren, “Finite-difference time-domain simulations of exciton-polariton resonances in quantum-dot arrays,” Opt. Express **16**, 4507–4519 (2008). [CrossRef] [PubMed]

*μ*m. In order to compare the experiment directly, same geometry parameters are employed. The gold is treated as perfect conductor, which is a reasonable approximation in THz region. Moreover, it is assumed that the GaAs substrate has a semi-infinite thickness, with a permittivity of 12.56. All the MM samples were simulated under both orientations of electric field polarization. The simulated transmission amplitude reproduces the experimental results reasonably well. Experimental and numerical data are compared in Figs. 2 and 3, respectively for both the polarization of excitation beam. Experimental and simulated resonance frequencies are shifted slightly because of fabrication uncertainties. In these simulations we have considered the nominal parameters as used for the sample design. In the case of the electric field of polarization perpendicular to the split gap, the quality factor of the higher frequency resonance appearing near 0.7 THz is simulated to be 6.0 (approximately), matching well with the experimental value. The sharp resonance feature arising at lower frequency possesses much higher quality factor. The simulated quality factors for MM2 and MM3 are 35.8 and 35.2, respectively. The deviations in the amplitudes and line widths between simulations and measurements are due to the longer time scan of the measured and simulated pulses [35

35. M. T. Reiten, D. Roy Chowdhury, J. Zhou, A. J. Taylor, J. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. **98**, 131105 (2011). [CrossRef]

*x*polarization of excitation (electric field parallel to the split gap),

*x*- component (

**E**

*) and*

_{x}*y*- component (

**E**

*) of induced electric fields at the resonances are shown in Fig. 3. At the resonance, the computed electric field distributions for all the samples, asymmetrical as well as the symmetrical structure, demonstrate similar characteristics of the*

_{y}*ee*eigenmodes predicted theoretically (see, Fig. 3(a) and

**u**

_{1,ee}). Under

*y*-polarized excitation (electric field perpendicular to split gap), electric field distributions are computed at the higher-frequency (0.7 THz) resonance. The field distributions for all the MM samples resemble the

*oo*eigenmode (see Fig. 4 and

**u**

_{1,oo}). We have further simulated the

*x*- and

*y*- components of the induced electric field distributions at the theoretically predicted frequencies for

*eo*eigenmodes in Fig. 5. The

*eo*eigenmodes are supposed to be excited at 0.57 THz, 0.51 THz and 0.47 THz for MM1, MM2 and MM3, respectively. We note that for MM2 and MM3, the sharp resonance appears near the predicted frequencies although we do not see any resonance for MM1 in the measurements. Although the

*eo*eigenmode exists for MM1, it cannot be excited with a plane wave excitation. The

*eo*eigenmode for the symmetric structure (MM1) is excited numerically using a few random electric dipoles but bears the same character as predicted theoretically (see Fig. 5(a) and

**u**

_{1,eo}). This mode is generally not possible to excite for symmetric structure irrespective of polarization of probing beam. Interestingly, this

*eo*eigenmode (

**u**

_{1,eo}) is capable of holding the EM energy for longer time period, hence low in radiative resistance. Such low-loss radiation mode is associated with the enhanced quality factor of the

*eo*mode. The measured and simulated quality factors of this mode are observed to be as high as 10.2 and 35.8 in this symmetry broken plasmonic MM. It should be mentioned that this perturbed dark mode has been observed in asymmetrical microwave metamaterial in [20

20. V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a brocken structural symmetry,” Phys. Rev. Lett. **99**, 147401 (2007). [CrossRef]

36. B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mat. **9**, 707–715 (2010). [CrossRef]

37. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. **82**, 2257 (2010). [CrossRef]

## 4. Conclusion

## Acknowledgments

## References and links

1. | V. G. Vaselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Sov. Phys. Usp. |

2. | 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. |

3. | S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 Terahertz,” Science |

4. | O. Sydoruk, E. Tarartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys. |

5. | R. Singh, C. Rocksuhl, F. Lederer, and W. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B. |

6. | H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz meta-material devices,” Nature |

7. | 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. |

8. | R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative refraction of refraction,” Science |

9. | C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science |

10. | J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. |

11. | A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett. |

12. | R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. smith, “Broadband ground-plane cloak,” Science |

13. | N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett. |

14. | C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuehl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express |

15. | D. R. Chowdhury, R. Singh, J. F. O’Hara, H. T. Chen, A. J. Taylor, and A. K. Azad, “Dynamically reconfigurable terahertz metamaterials through photo doped semiconductors,” Appl. Phys. Lett. |

16. | H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for terahertz regime: Design fabrication and characterization,” Opt. Express |

17. | J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express |

18. | I. A. I. Naib, C. Jansen, and M. Koch, “Thin film sensing with planar asymetric metamaterial resonators,” Appl. Phys. Lett. |

19. | P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photon. Rev. |

20. | V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a brocken structural symmetry,” Phys. Rev. Lett. |

21. | E. Plum, V. A. Fedotov, and N. I. Zheludev, “Planar metamaterial with transmission and reflection that depend on the direction of incidence,” Appl. Phys. Lett. |

22. | I. Al-Naib, R. Singh, C. Rockstuhl, F. Lederer, S. Delprat, D. Rocheleau, M. Chaker, T. Ozaki, and R. Morandotti, “Excitation of a high Q subradiant resonance mode in mirrored single-gap asymmetric split ring resonator terahertz metamaterials,” Appl. Phy. Lett. |

23. | R. Singh, I. A. I. Al-Naib, Y. Yang, D. R. Chowdhury, W. Cao, C. Rockstuhl, T. Ozaki, R. Morandotti, and W. Zhang, “Observing metamaterial induced transparency in individual Fano resonators with broken symmetry,” Appl. Phy. Lett. |

24. | W. Cao, R. Singh, I. A. I. Al-Naib, M. He, A. J. Taylor, and W. Zhang, “Low-loss ultra-high-Q dark mode plasmonic Fano metamaterials,” Opt. Lett. |

25. | C. Wu, A. B. Khanikaev, R. Adato, N. Arju, A. A. Yanik, H. Altug, and G. Shvets, “Fano-resonant asymetric metamaterials for ultrasensitive spectroscopy and identification of moleculer monolayers,” Nat. Mat. |

26. | D. J. Shelton, I. Brener, J. C. Ginn, M. B. Sinclair, D. W. Peters, K. R. Coffey, and G. D. Boreman, “Strong coupling between nanoscale metamaterials and phonons,” Nano Lett. |

27. | D. Grischkowsky, S. Keiding, M. van Exter, and C. Fattinger, “Far-infrared time-domain spectroscopy with tera-hertz beams of dielectrics and semiconductors,” J. Opt. Soc. Am. B |

28. | R. D. Averitt and A. J. Taylor, “Ultrafast optical and far infra-red quasiparticle dynamics in correlated electron materials,” J. Phys.: Cond. Matter. |

29. | Y. Zeng, D. A. R. Dalvit, J. O’Hara, and S. A. Trugman, “A modal analysis method to describe weak nonlinear effects in metamaterials,” Phys. Rev. B |

30. | A. Raman and S. Fan, “Photonic band structure of dispersive meta-materials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. |

31. | R. Cole, |

32. | M. Naimark, |

33. | D. E. Gomez, Z. Q. Teo, M. Altissimo, T. J. Davis, S. Earl, and A. Roberts, “The drak side of plasmonics,” Nano Lett. |

34. | Y. Zeng, Y. Fu, M. Bengtsson, X. S. Chen, W. Lu, and H. Ågren, “Finite-difference time-domain simulations of exciton-polariton resonances in quantum-dot arrays,” Opt. Express |

35. | M. T. Reiten, D. Roy Chowdhury, J. Zhou, A. J. Taylor, J. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. |

36. | B. Luk’yanchuk, N. I. Zheludev, S. A. Maier, N. J. Halas, P. Nordlander, H. Giessen, and C. T. Chong, “The Fano resonance in plasmonic nanostructures and metamaterials,” Nat. Mat. |

37. | A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. |

**OCIS Codes**

(260.5740) Physical optics : Resonance

(160.3918) Materials : Metamaterials

**ToC Category:**

Plasmonics

**History**

Original Manuscript: May 16, 2014

Revised Manuscript: July 14, 2014

Manuscript Accepted: July 16, 2014

Published: August 4, 2014

**Citation**

Dibakar Roy Chowdhury, Xiaofang Su, Yong Zeng, Xiaoshuang Chen, Antoinette J. Taylor, and Abul Azad, "Excitation of dark plasmonic modes in symmetry broken terahertz metamaterials," Opt. Express **22**, 19401-19410 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-16-19401

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### References

- V. G. Vaselago, “The electrodynamics of substances with simultaneously negative values of epsilon and mu,” Sov. Phys. Usp.10, 509–514 (1968). [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]
- S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 Terahertz,” Science306, 1351–1353 (2004). [CrossRef] [PubMed]
- O. Sydoruk, E. Tarartschuk, E. Shamonina, and L. Solymar, “Analytical formulation for the resonant frequency of split rings,” J. Appl. Phys.105, 014903 (2009). [CrossRef]
- R. Singh, C. Rocksuhl, F. Lederer, and W. Zhang, “Coupling between a dark and a bright eigenmode in a terahertz metamaterial,” Phys. Rev. B.79, 085111 (2008). [CrossRef]
- H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, “Active terahertz meta-material devices,” Nature444, 597–600 (2006). [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 (2000). [CrossRef] [PubMed]
- R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative refraction of refraction,” Science292, 77–79 (2001). [CrossRef] [PubMed]
- C. M. Soukoulis, S. Linden, and M. Wegener, “Negative refractive index at optical wavelengths,” Science315, 47–49 (2007). [CrossRef] [PubMed]
- J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett.85, 3966 (2000). [CrossRef] [PubMed]
- A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett.92, 117403 (2004). [CrossRef] [PubMed]
- R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. smith, “Broadband ground-plane cloak,” Science323, 366–369 (2006). [CrossRef]
- N. Katsarakis, T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Electric coupling to the magnetic resonance of split ring resonators,” Appl. Phys. Lett.84, 2943 (2004). [CrossRef]
- C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuehl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express14, 8827–8836 (2006). [CrossRef] [PubMed]
- D. R. Chowdhury, R. Singh, J. F. O’Hara, H. T. Chen, A. J. Taylor, and A. K. Azad, “Dynamically reconfigurable terahertz metamaterials through photo doped semiconductors,” Appl. Phys. Lett.99, 231101 (2011). [CrossRef]
- H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for terahertz regime: Design fabrication and characterization,” Opt. Express16, 7181–7188 (2008). [CrossRef] [PubMed]
- J. F. O’Hara, R. Singh, I. Brener, E. Smirnova, J. Han, A. J. Taylor, and W. Zhang, “Thin-film sensing with planar terahertz metamaterials: sensitivity and limitations,” Opt. Express16, 1786–1795 (2008). [CrossRef] [PubMed]
- I. A. I. Naib, C. Jansen, and M. Koch, “Thin film sensing with planar asymetric metamaterial resonators,” Appl. Phys. Lett.93, 083507 (2008). [CrossRef]
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