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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 8 — Apr. 13, 2009
  • pp: 6026–6031
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Negative refractive index metamaterials aided by extraordinary optical transmission

C. García-Meca, R. Ortuño, F.J. Rodríguez-Fortuño, J. Martí, and A. Martínez  »View Author Affiliations


Optics Express, Vol. 17, Issue 8, pp. 6026-6031 (2009)
http://dx.doi.org/10.1364/OE.17.006026


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Abstract

We study under which conditions extraordinary optical transmission (EOT) structures can be used to build negative refractive index media. As a result, we present a metamaterial with superimposed EOT and negative index at visible wavelengths. The tailoring process starting from a simple hole array until achieving the negative index is detailed. We also discuss the so-called fishnet metamaterial (previously linked to EOT) under the same prism. Using the ideas put forward in this work, other structures with negative index could be engineered in the optical or visible spectrum.

© 2009 Optical Society of America

1. Introduction

2. Theoretical remarks

Let us begin with some considerations on EOT so as to motivate our exposition. First, in order to unify criterions, we will consider (as usual) that EOT takes place when the normalized transmission Tn exceeds unity, being Tn defined as Tn = (Pout/Pin)(Aucell/Ahole) = T(Aucell/Ahole), where Aucell is the area of the unit cell, Ahole is the area of a single hole and Pin and Pout are, respectively, the input and output electromagnetic power. On the other hand, there exist a number of structures that lead to the EOT phenomenon. They mainly differ in the shape of the holes and the type and thickness of the metal that constitutes the film in which they are pierced. However, if we regard an EOT structure as a homogeneous medium, we can model it with effective electric permittivity ε = ε′ + iε″ and magnetic permeability μ = μ′ + iμ″, whatever features it may have. We will limit ourselves to study normal incidence with the impinging wave oriented as in Figs.1and 3.Thus, despite the tensorial character of ε and μ, the retrieval of their relevant components for that direction can be considered as a scalar problem. Simple EOT structures (made up of one metal layer) normally act as a dilute metal and exhibit a weak magnetic response. This means that their permittivity is negative at frequencies below that of the first EOT peak (and possibly below other EOT peaks) and that their permeability is small and positive (unless otherwise stated, when talking about permittivity, permeability, impedance or refractive index we refer to their real part). For instance, in the structures analyzed below, μ′ is between 0.5 and 0.8 from DC to beyond the first EOT peak frequency. Nonetheless, when the transmission T (not normalized) is close to one, as it usually happens in EOT peaks, the equivalent medium must be impedance-matched to air, i.e., the real part of its equivalent characteristic impedance z = z′ + iz″ has to be z′ = Re{(μ/ε)1/2} ≈ 1. As a consequence, the resonances with high T tend to present positive values of ε′ similar to those of μ′ (provided that ε″ and μ″ are negligible). In other words, the metal film, which has a highly negative ε′ in bulk, exhibits positive ε′ frequency regions when drilled, where the transmission is enhanced. In order to achieve a low-loss NIM, it is necessary to have ε′ < 0 and μ′ < 0 [7

7. R. A. Depine and A. Lakhtakia, “A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microwave Opt. Technol. Lett. 41, 315–316 (2004). [CrossRef]

]. Owing to the continuity of the constitutive parameters, ε′ takes small negative values and crosses zero at frequencies right below the resonance because it is negative at lower frequencies as we mentioned above. Hence, we already have the first condition (ε′ < 0) below the EOT peak spectral location. We are interested in this moderately negative ε′ region with the aim of obtaining an impedance-matched NIM band, since the negative values of μ′ that can be typically achievable artificially are small, especially in the visible regime. Finally, if we could insert a magnetic resonance in this region with μ′ taking negative values, we would fulfill the second condition. Our argument can be summarized as follows: pick an EOT structure and modify it in order to introduce a magnetic resonance at a frequency slightly lower than that of the EOT peak, where ε′ is still negative. Of course, this modification must not significantly alter the electric response of the medium in the working region. A priori, it may seem complex to do this, but next, we present a couple examples.

3. NEOT structures

Fig. 1. (a) Silver periodic hole array exhibiting EOT. (b) NEOT structure resulting from adding slits to the structure in (a).

Fig. 2. (a) Normalized transmission of the structures depicted in Fig. 1(a) (blue) and Fig. 1(b) (magenta). (b) Real part of z for both structures (correspondence by color). (c) Comparison of effective ε′ for the hole array with (dashed purple) and without slits (solid blue). Retrieved μ′ (magenta) and n′ (grey) of the hole array with slits [NEOT structure in Fig 1(b)].
Fig. 3. (a) 3-layer metamaterial. (b) Normalized transmission with M2 = MgF2 (purple) and M2 = Ag (blue). NEOT region in grey. (c) Fishnet ε′ (magenta). ε′ of structure in (a) with M2 = Ag and fishnet dimensions (grey) and with b=600 nm, i.e., only horizontal strips (red). Fishnet μ′ (purple) and n′ (blue).

4. Conclusion

In summary, we have shown that EOT structures allow for the creation of negative refractive index composites by taking advantage of high transmission peaks, as long as it is possible to modify the structure in order to create magnetic activity at frequencies slightly lower than those of the peaks. This is the case of the fishnet metamaterial, in which a magnetic resonance exhibiting negative permeability is generated in the proximity of a high T localized resonance. In addition, we have presented a structure with superimposed extraordinary transmission and negative index of refraction at visible frequencies. Although based on the same ideas, the physical origin of EOT and the magnetic activity in the proposed structure is different from the fishnet one, supporting the generality of the described procedure, which opens up the way for building new NEOT structures at optical wavelengths.

Acknowledgments

Financial support by the Spanish MCyT and EU-FEDER under contract TEC2005-06923-C03-03 is gratefully acknowledged. C. García-Meca, R. Ortuño and F.J. Rodriguez-Fortuño also acknowledge financial support from grants FPU of MICINN, FPI of Universidad Politécnica de Valencia, and from a grant of La Caixa, respectively.

References and links

1.

F. J. García de Abajo, “Colloquium: Light scattering by particle and hole arrays,” Rev. Mod. Phys. 79, 1267–1290 (2007). [CrossRef]

2.

C. Genet and T.W. Ebbesen, “Light in tiny holes,” Nature 445, 39–46 (2007). [CrossRef] [PubMed]

3.

V. M. Shalaev, “Optical negative-index metamaterials,” Nature Photon. 1, 41–48 (2006). [CrossRef]

4.

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

5.

M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, “Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays,” Opt. Express 15, 1107–1114 (2007). [CrossRef] [PubMed]

6.

A. Mary, S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett. 101, 103902 (2008). [CrossRef] [PubMed]

7.

R. A. Depine and A. Lakhtakia, “A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microwave Opt. Technol. Lett. 41, 315–316 (2004). [CrossRef]

8.

V. P. Drachev, U. K. Chettiar, A. V. Kildishev, Y. Hsiao-Kuan, W. Cai, and V. M. Shalaev, “The Ag dielectric function in plasmonic metamaterials,” Opt. Express 16, 1186–1195 (2008). [CrossRef] [PubMed]

9.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972). [CrossRef]

10.

X. Chen, T. M. Grzegorczyk, B. Wu, J. Pacheco Jr., and J. A. Kong , “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E 70, 016608–016614 (2004). [CrossRef]

11.

L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, “Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays,” Phys. Rev. Lett. 86, 1114 (2001). [CrossRef] [PubMed]

12.

C. García-Meca, R. Ortuño, R. Salvador, A. Martínez, and J. Martí, “Low-loss single-layer metamaterial with negative index of refraction at visible wavelengths,” Opt. Express 15, 9320–9325 (2007). [CrossRef] [PubMed]

13.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31, 1800–1802 (2006). [CrossRef] [PubMed]

14.

R. Ortuño, C. García-Meca, F.J. Rodríguez-Fortuño, J. Martí, and A. Martínez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B 79, 075425 (2009). [CrossRef]

OCIS Codes
(240.5420) Optics at surfaces : Polaritons
(240.6680) Optics at surfaces : Surface plasmons
(350.3618) Other areas of optics : Left-handed materials
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: October 30, 2008
Revised Manuscript: January 15, 2009
Manuscript Accepted: January 27, 2009
Published: March 31, 2009

Citation
C. García-Meca, R. Ortuño, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, "Negative refractive index metamaterials aided by extraordinary optical transmission," Opt. Express 17, 6026-6031 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-8-6026


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References

  1. F. J. García de Abajo, "Colloquium: Light scattering by particle and hole arrays," Rev. Mod. Phys. 79, 1267-1290 (2007). [CrossRef]
  2. C. Genet and T. W. Ebbesen, "Light in tiny holes," Nature 445, 39-46 (2007). [CrossRef] [PubMed]
  3. V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2006). [CrossRef]
  4. C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007). [CrossRef] [PubMed]
  5. M. Beruete, M. Sorolla, M. Navarro-Cía, F. Falcone, I. Campillo, and V. Lomakin, "Extraordinary transmission and left-handed propagation in miniaturized stacks of doubly periodic subwavelength hole arrays," Opt. Express 15, 1107-1114 (2007). [CrossRef] [PubMed]
  6. A. Mary, S. G. Rodrigo, F. J. García-Vidal, and L. Martín-Moreno, "Theory of negative-refractive-index response of double-fishnet structures," Phys. Rev. Lett. 101, 103902 (2008). [CrossRef] [PubMed]
  7. R. A. Depine and A. Lakhtakia, "A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity," Microwave Opt. Technol. Lett. 41, 315-316 (2004). [CrossRef]
  8. V. P. Drachev, U. K. Chettiar, A. V. Kildishev, Y. Hsiao-Kuan, W. Cai, and V. M. Shalaev, "The Ag dielectric function in plasmonic metamaterials," Opt. Express 16, 1186-1195 (2008). [CrossRef] [PubMed]
  9. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972). [CrossRef]
  10. X. Chen, T. M. Grzegorczyk, B. Wu, J. Pacheco, Jr., and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Phys. Rev. E 70, 016608-016614 (2004). [CrossRef]
  11. L. Martín-Moreno, F. J. García-Vidal, H. J. Lezec, K. M. Pellerin, T. Thio, J. B. Pendry, and T. W. Ebbesen, "Theory of Extraordinary Optical Transmission through Subwavelength Hole Arrays," Phys. Rev. Lett. 86, 1114 (2001). [CrossRef] [PubMed]
  12. C. García-Meca, R. Ortuño, R. Salvador, A. Martínez, and J. Martí, "Low-loss single-layer metamaterial with negative index of refraction at visible wavelengths," Opt. Express 15, 9320-9325 (2007). [CrossRef] [PubMed]
  13. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Opt. Lett. 31, 1800-1802 (2006). [CrossRef] [PubMed]
  14. R. Ortuño, C. García-Meca, F. J. Rodríguez-Fortuño, J. Martí, and A. Martínez, "Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays," Phys. Rev. B (to be published). [CrossRef]

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