## Metal-dielectric metamaterials for guided wave silicon photonics |

Optics Express, Vol. 19, Issue 24, pp. 24746-24761 (2011)

http://dx.doi.org/10.1364/OE.19.024746

Acrobat PDF (818 KB)

### Abstract

The aim of the present paper is to investigate the potential of metallic metamaterials for building optical functions in guided wave optics at 1.5µm. A significant part of this work is focused on the optimization of the refractive index variation associated with localized plasmon resonances. The minimization of metal related losses is specifically addressed as well as the engineering of the resonance frequency of the localized plasmons. Our numerical modeling results show that a periodic chain of gold cut wires placed on the top of a 100nm silicon waveguide makes it possible to achieve a significant index variation in the vicinity of the metamaterial resonance and serve as building blocks for implementing optical functions. The considered solutions are compatible with current nano-fabrication technologies.

© 2011 OSA

## 1. Introduction

1. J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science **312**(5781), 1780–1782 (2006). [CrossRef] [PubMed]

2. U. Leonhardt, “Optical conformal mapping,” Science **312**(5781), 1777–1780 (2006). [CrossRef] [PubMed]

3. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science **314**(5801), 977–980 (2006). [CrossRef] [PubMed]

5. R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science **323**(5912), 366–369 (2009). [CrossRef] [PubMed]

6. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science **328**(5976), 337–339 (2010). [CrossRef] [PubMed]

8. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics **3**(8), 461–463 (2009). [CrossRef]

9. M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. **6**(1), 87–95 (2008). [CrossRef]

10. H. Y. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. **102**(18), 183903 (2009). [CrossRef] [PubMed]

11. A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. **99**(18), 183901 (2007). [CrossRef] [PubMed]

12. M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express **16**(15), 11555–11567 (2008). [CrossRef] [PubMed]

17. R. Ghasemi, P.-H. Tichit, A. Degiron, A. Lupu, and A. de Lustrac, “Efficient control of a 3D optical mode using a thin sheet of transformation optical medium,” Opt. Express **18**(19), 20305–20312 (2010). [CrossRef] [PubMed]

3. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science **314**(5801), 977–980 (2006). [CrossRef] [PubMed]

8. L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics **3**(8), 461–463 (2009). [CrossRef]

3. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science **314**(5801), 977–980 (2006). [CrossRef] [PubMed]

18. D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. **85**(14), 2933–2936 (2000). [CrossRef] [PubMed]

19. 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**(24), 3356–3358 (2005). [CrossRef] [PubMed]

24. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. **7**(1), 31–37 (2008). [CrossRef] [PubMed]

30. A. N. Lagarkov, V. N. Kisel, and A. K. Sarychev, “Loss and gain in metamaterials,” J. Opt. Soc. Am. B **27**(4), 648–659 (2010). [CrossRef]

*hybrid*photonic structures in which metallic parts are coupled with dielectric (and almost lossless) waveguides [31

31. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. **85**(24), 5833–5836 (2004). [CrossRef]

31. T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. **85**(24), 5833–5836 (2004). [CrossRef]

38. B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. **35**(9), 1320–1322 (2010). [CrossRef] [PubMed]

## 2. Permittivity engineering with a transverse periodic chain of cut wires

38. B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. **35**(9), 1320–1322 (2010). [CrossRef] [PubMed]

_{eff}and permeability µ

_{eff}from the complex reflection and transmission coefficients

**and**

*r***, respectively, of the slab loaded with a transverse cut wire chain, we use the retrieval method proposed by Smith et al. [41**

*t*41. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B **65**(19), 195104 (2002). [CrossRef]

_{eff}and permeability µ

_{eff}of a bulk metamaterial illuminated by a plane wave in free space but it can also be applied to a guided wave configuration provided that the mode has planar wavefronts. The extension to determine the effective complex refractive index

*n**of a planar waveguide loaded with a metamaterial is presented in Appendix A. The difference with respect to the formula provided by Smith et al. in [41*

_{eff}41. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B **65**(19), 195104 (2002). [CrossRef]

_{eff slab}, has to be introduced in the expression of the impedance z:which is used for calculating ε

_{eff}= n

_{eff}/z and µ

_{eff}= n

_{eff}·z .

^{’}

_{eff}and imaginary ε

^{”}

_{eff}components of the effective complex permittivity for the case of 100nm, 150nm and 200nm slab thickness are represented in Figs. 4(a) , 4(b) and 4(c), respectively. As it can be observed, between 100THz and 300THz there is a strong variation of the ε

^{”}

_{eff}with the frequency ν that can be approximated by a Lorentzian type dispersion formula.

42. M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science **332**(6030), 702–704 (2011). [CrossRef] [PubMed]

_{0}. To achieve a low loss operation at 200THz, corresponding to the 1.5µm telecommunication wavelength, the resonance frequency should be shifted out of this spectral domain by a few half-widths of the absorption line. For example, if we wish to attain a resonance frequency of 250THz on a silicon slab, one evident solution is to decrease the length of the cut wires. Setting the cut wire length to 100nm, while leaving the rest of the parameters unchanged, indeed allows one to shift the resonance frequency toward 250THz.

43. D. J. Shelton, D. W. Peters, M. B. Sinclair, I. Brener, L. K. Warne, L. I. Basilio, K. R. Coffey, and G. D. Boreman, “Effect of thin silicon dioxide layers on resonant frequency in infrared metamaterials,” Opt. Express **18**(2), 1085–1090 (2010). [CrossRef] [PubMed]

## 3. Array of coupled periodic chains of cut wires

- • Does a 2D array of cut wires on top of a Si waveguide behave like an effective dielectric slab?
- • Do the results related to the permittivity engineering for a single periodic chain remain essentially valid?
- • What are the main guidelines for an optimal design of a coupled wire assembly?

**between adjacent wires is increased to 100nm or 150nm, the coupling between them is decreased. This is manifested by a broadening and splitting of the resonance in the transmission and loss spectra. A maximum in reflection is progressively building in the vicinity of the resonance. The observed phenomena are more pronounced in the case of 100nm thick Si slab where the interaction with the chains of cut wires is stronger.**

*d*44. S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdré, and U. Oesterlé, “Miniband transmission in a photonic crystal coupled-resonator optical waveguide,” Opt. Lett. **26**(13), 1019–1021 (2001). [CrossRef] [PubMed]

## 4. Summary and conclusions

_{eff}and permeability µ

_{eff}of such a composite slab was determined using a variant of the retrieval method described in [41

41. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B **65**(19), 195104 (2002). [CrossRef]

## Apendix A: Generalization of the retrieval method

**65**(19), 195104 (2002). [CrossRef]

*n*and impedance

*z*.

*z*of a single layer in the most general case of oblique incidence and different input and output media. Incidentally this inversion will serve to derive Eq. (1) which is in fact just a particular case of the generalized retrieval solution.

*p*replaced by the characteristic impedance

*q*:

*p*and

_{1}*p*given by Eq. (A2) correspond accordingly to the first and last semi-infinite media. The reflectivity and transmissivity coefficients of the film for the intensity of TE polarized wave are, respectively:

_{l}*p*and

_{1}*p*by

_{l}*q*and

_{1}*q*given the Eq. A3.

_{l}*β*and

*z*we obtain:

*β*:where

*m*is an integer. The explanation about the proper choice of the sign and value of the integer coefficient

*m*can be found in [41

**65**(19), 195104 (2002). [CrossRef]

*p*by

*q*in the systems of Eqs. A(10) and (A11). It follows that:

## Acknowledgement

## References and links

1. | J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science |

2. | U. Leonhardt, “Optical conformal mapping,” Science |

3. | D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science |

4. | B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B |

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

6. | T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science |

7. | J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. |

8. | L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics |

9. | M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl. |

10. | H. Y. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett. |

11. | A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett. |

12. | M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express |

13. | M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett. |

14. | L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, “Design of electromagnetic refractor and phase transformer using coordinate transformation theory,” Opt. Express |

15. | J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys. |

16. | P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express |

17. | R. Ghasemi, P.-H. Tichit, A. Degiron, A. Lupu, and A. de Lustrac, “Efficient control of a 3D optical mode using a thin sheet of transformation optical medium,” Opt. Express |

18. | D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett. |

19. | 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. |

20. | J. Zhou, Th. 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. |

21. | S. Zhang, W. Fan, 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. |

22. | G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. |

23. | B. Kanté, A. de Lustrac, and J. M. Lourtioz, “In-plane coupling and field enhancement in infrared metamaterial surfaces,” Phys. Rev. B |

24. | N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. |

25. | E. Poutrina and D. R. Smith, “High-frequency active metamaterials,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper ITuD6. |

26. | S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature |

27. | A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B |

28. | A. Fang, Th. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt. |

29. | Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett. |

30. | A. N. Lagarkov, V. N. Kisel, and A. K. Sarychev, “Loss and gain in metamaterials,” J. Opt. Soc. Am. B |

31. | T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett. |

32. | A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 ° bends,” Opt. Lett. |

33. | R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature |

34. | D. Dai and S. He, “A silicon-based hybrid plasmonic waveguide with a metal cap for a nano-scale light confinement,” Opt. Express |

35. | J. T. Kim, S. Park, J. J. Ju, S. Lee, and S. Kim, “Low bending loss characteristics of hybrid plasmonic waveguide for flexible optical interconnect,” Opt. Express |

36. | M. Wu, Z. Han, and V. Van, “Conductor-gap-silicon plasmonic waveguides and passive components at subwavelength scale,” Opt. Express |

37. | M. Fevrier, P. Gogol, A. Aassime, R. Megy, A. Bondi, J. M. Lourtioz, and B. Dagens, “Localized surface plasmon excitation through evanescent coupling from dielectric or SOI waveguide at telecom wavelength,” presented at the CLEO/QELS 2011, paper EJ1.1, Germany, Munich, 22–25 May 2011. |

38. | B. Reinhard, O. Paul, R. Beigang, and M. Rahm, “Experimental and numerical studies of terahertz surface waves on a thin metamaterial film,” Opt. Lett. |

39. | |

40. | E. D. Palik, |

41. | D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B |

42. | M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science |

43. | D. J. Shelton, D. W. Peters, M. B. Sinclair, I. Brener, L. K. Warne, L. I. Basilio, K. R. Coffey, and G. D. Boreman, “Effect of thin silicon dioxide layers on resonant frequency in infrared metamaterials,” Opt. Express |

44. | S. Olivier, C. Smith, M. Rattier, H. Benisty, C. Weisbuch, T. Krauss, R. Houdré, and U. Oesterlé, “Miniband transmission in a photonic crystal coupled-resonator optical waveguide,” Opt. Lett. |

45. | M. Born and E. Wolf, |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(160.1190) Materials : Anisotropic optical materials

(160.4760) Materials : Optical properties

(240.6680) Optics at surfaces : Surface plasmons

(260.5740) Physical optics : Resonance

(160.3918) Materials : Metamaterials

(350.4238) Other areas of optics : Nanophotonics and photonic crystals

**ToC Category:**

Metamaterials

**History**

Original Manuscript: September 19, 2011

Revised Manuscript: October 17, 2011

Manuscript Accepted: October 18, 2011

Published: November 17, 2011

**Citation**

A. Lupu, N. Dubrovina, R. Ghasemi, A. Degiron, and A. de Lustrac, "Metal-dielectric metamaterials for guided wave silicon photonics," Opt. Express **19**, 24746-24761 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-24-24746

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### References

- J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,” Science312(5781), 1780–1782 (2006). [CrossRef] [PubMed]
- U. Leonhardt, “Optical conformal mapping,” Science312(5781), 1777–1780 (2006). [CrossRef] [PubMed]
- D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Science314(5801), 977–980 (2006). [CrossRef] [PubMed]
- B. Kanté, D. Germain, and A. de Lustrac, “Experimental demonstration of a nonmagnetic metamaterial cloak at microwave frequencies,” Phys. Rev. B80(20), 201104 (2009). [CrossRef]
- R. Liu, C. Ji, J. J. Mock, J. Y. Chin, T. J. Cui, and D. R. Smith, “Broadband ground-plane cloak,” Science323(5912), 366–369 (2009). [CrossRef] [PubMed]
- T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328(5976), 337–339 (2010). [CrossRef] [PubMed]
- J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater.8(7), 568–571 (2009). [CrossRef] [PubMed]
- L. H. Gabrielli, J. Cardenas, C. B. Poitras, and M. Lipson, “Silicon nanostructure cloak operating at optical frequencies,” Nat. Photonics3(8), 461–463 (2009). [CrossRef]
- M. Rahm, D. Schurig, D. A. Roberts, S. A. Cummer, D. R. Smith, and J. B. Pendry, “Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations,” Photon. Nanostruct.: Fundam. Appl.6(1), 87–95 (2008). [CrossRef]
- H. Y. Chen, B. Hou, S. Chen, X. Ao, W. Wen, and C. T. Chan, “Design and experimental realization of a broadband transformation media field rotator at microwave frequencies,” Phys. Rev. Lett.102(18), 183903 (2009). [CrossRef] [PubMed]
- A. Greenleaf, Y. Kurylev, M. Lassas, and G. Uhlmann, “Electromagnetic wormholes and virtual magnetic monopoles from metamaterials,” Phys. Rev. Lett.99(18), 183901 (2007). [CrossRef] [PubMed]
- M. Rahm, D. A. Roberts, J. B. Pendry, and D. R. Smith, “Transformation-optical design of adaptive beam bends and beam expanders,” Opt. Express16(15), 11555–11567 (2008). [CrossRef] [PubMed]
- M. Rahm, S. A. Cummer, D. Schurig, J. B. Pendry, and D. R. Smith, “Optical design of reflectionless complex media by finite embedded coordinate transformations,” Phys. Rev. Lett.100(6), 063903 (2008). [CrossRef] [PubMed]
- L. Lin, W. Wang, J. Cui, C. Du, and X. Luo, “Design of electromagnetic refractor and phase transformer using coordinate transformation theory,” Opt. Express16(10), 6815–6821 (2008). [CrossRef] [PubMed]
- J. Huangfu, S. Xi, F. Kong, J. Zhang, H. Chen, D. Wang, B.-I. Wu, L. Ran, and J. A. Kong, “Application of coordinate transformation in bent waveguides,” J. Appl. Phys.104(1), 014502 (2008). [CrossRef]
- P. H. Tichit, S. N. Burokur, and A. de Lustrac, “Waveguide taper engineering using coordinate transformation technology,” Opt. Express18(2), 767–772 (2010). [CrossRef] [PubMed]
- R. Ghasemi, P.-H. Tichit, A. Degiron, A. Lupu, and A. de Lustrac, “Efficient control of a 3D optical mode using a thin sheet of transformation optical medium,” Opt. Express18(19), 20305–20312 (2010). [CrossRef] [PubMed]
- D. R. Smith and N. Kroll, “Negative refractive index in left-handed materials,” Phys. Rev. Lett.85(14), 2933–2936 (2000). [CrossRef] [PubMed]
- 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(24), 3356–3358 (2005). [CrossRef] [PubMed]
- J. Zhou, Th. 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(22), 223902 (2005). [CrossRef] [PubMed]
- S. Zhang, W. Fan, 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(13), 137404 (2005). [CrossRef] [PubMed]
- G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett.31(12), 1800–1802 (2006). [CrossRef] [PubMed]
- B. Kanté, A. de Lustrac, and J. M. Lourtioz, “In-plane coupling and field enhancement in infrared metamaterial surfaces,” Phys. Rev. B80(3), 035108 (2009). [CrossRef]
- N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater.7(1), 31–37 (2008). [CrossRef] [PubMed]
- E. Poutrina and D. R. Smith, “High-frequency active metamaterials,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper ITuD6.
- S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H.-K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials,” Nature466(7307), 735–738 (2010). [CrossRef] [PubMed]
- A. Fang, Th. Koschny, M. Wegener, and C. M. Soukoulis, “Self-consistent calculation of metamaterials with gain,” Phys. Rev. B79(24), 241104 (2009). [CrossRef]
- A. Fang, Th. Koschny, and C. M. Soukoulis, “Lasing in metamaterial nanostructures,” J. Opt.12(2), 024013 (2010). [CrossRef]
- Z. G. Dong, H. Liu, T. Li, Z. H. Zhu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Optical loss compensation in a bulk left-handed metamaterial by the gain in quantum dots,” Appl. Phys. Lett.96(4), 044104 (2010). [CrossRef]
- A. N. Lagarkov, V. N. Kisel, and A. K. Sarychev, “Loss and gain in metamaterials,” J. Opt. Soc. Am. B27(4), 648–659 (2010). [CrossRef]
- T. Nikolajsen, K. Leosson, and S. I. Bozhevolnyi, “Surface plasmon polariton based modulators and switches operating at telecom wavelengths,” Appl. Phys. Lett.85(24), 5833–5836 (2004). [CrossRef]
- A. Degiron, C. Dellagiacoma, J. G. McIlhargey, G. Shvets, O. J. F. Martin, and D. R. Smith, “Simulations of hybrid long-range plasmon modes with application to 90 ° bends,” Opt. Lett.32(16), 2354–2356 (2007). [CrossRef] [PubMed]
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