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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 2 — Jan. 28, 2013
  • pp: 1804–1811
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Universal scaling of plasmonic refractive index sensors

Yen-Kai Chang, Zong-Xing Lou, Kao-Der Chang, and Chih-Wei Chang  »View Author Affiliations


Optics Express, Vol. 21, Issue 2, pp. 1804-1811 (2013)
http://dx.doi.org/10.1364/OE.21.001804


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Abstract

We establish experimental and numerical evidence that the refractive index sensitivities of various subwavelength plasmonic sensors obey a simple universal scaling relation that the sensitivities linearly increase with λm/neff (where λm is the resonant wavelengths and neff is the effective refractive index of the environment) and exhibit a slope equal to 1 instead of 2 predicted theoretically. The universal scaling relation is independent of the geometrical structures or contributions of multipolar resonances of individual metal structures (i.e. plasmonic atoms). It is also independent of spatial distributions or field-enhancements of electromagnetic hot spots in coupled metal structures (i.e. plasmonic molecules). The universal scaling relation reveals the fundamental standing wave resonances for all plasmonic atoms and the predominant near-field electric couplings for most plasmonic molecules. The established universal relation also helps to exclude some magnetically coupled plasmonic molecules for practical applications due to their reduced sensitivities.

© 2013 OSA

1. Introduction

Plasmonic sensors are not limited to plasmonic atoms. Coupling two or more plasmonic atoms into plasmonic molecules can lead to rich phenomena, including nontrivial frequency shifts [10

10. Y. C. Chao, H. C. Tseng, K. D. Chang, and C. W. Chang, “Three types of couplings between asymmetric plasmonic dimers,” Opt. Express 20(3), 2887–2894 (2012). [CrossRef] [PubMed]

], redistributions of electromagnetic hot spots and the field-enhancements [11

11. H. C. Tseng and C. W. Chang, “High displacement sensitivity in asymmetric plasmonic nanostructures,” Opt. Express 18(17), 18360–18367 (2010). [CrossRef] [PubMed]

]. Although it has been known that the presence of the electromagnetic hot spots are necessary for enhancing Raman scatterings and fluorescence [12

12. A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009). [CrossRef]

, 13

13. E. C. Le Ru and P. G. Etchegoin, “Phenomenological local field enhancement factor distributions around electromagnetic hot spots,” J. Chem. Phys. 130(18), 181101 (2009). [CrossRef] [PubMed]

], their roles in sensing the environmental refractive index remain unclear. Unfortunately, comparing to the intensive studies on plasmonic atoms, much fewer works were done in plasmonic molecules [14

14. I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly Strained Compliant Optical Metamaterials with Large Frequency Tunability,” Nano Lett. 10(10), 4222–4227 (2010). [CrossRef] [PubMed]

16

16. N. Verellen, P. Van Dorpe, C. J. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon Line Shaping Using Nanocrosses for High Sensitivity Localized Surface Plasmon Resonance Sensing,” Nano Lett. 11(2), 391–397 (2011). [CrossRef] [PubMed]

]. Besides, it is not clear whether the refractive index sensitivities of plasmonic molecules would obey a universal relation similar to plasmonic atoms.

Because elucidating the universal phenomena of the plasmonic sensors with diverse geometries and couplings will be of fundamental importance for practical applications, here we provide key experimental and numerical evidence that the linear scaling relation is a universal property of surface plasmons. In fact, the universal scaling relation established in Fig. 1 is a direct result of the standing wave resonances of surface plasmons and is insensitive to geometrical variations of plasmonic atoms or couplings in most plasmonic molecules. Our experimental results show that it is also independent of the nature of dipolar or multipolar resonances, the distributions or field-enhancements of the electromagnetic hot spots. The established universal behavior also helps to exclude some unlikely theoretical or experimental results reported earlier.

We start the investigation on the simplest plasmonic atoms with geometries like a rod or a split-ring resonator (SRR). The resonant frequencies of a metal rod or a SRR can be characterized by the one-dimensional standing wave model of surface plasmons [17

17. C. Y. Chen, S. C. Wu, and T. J. Yen, “Experimental verification of standing-wave plasmonic resonances in split-ring resonators,” Appl. Phys. Lett. 93(3), 034110 (2008). [CrossRef]

]:
λm=2neff(Lm)λ0
(1)
where λm is the resonant wavelength of the m-th harmonic mode, L is the total length of the rod or the SRR, neff is the effective refractive index of the environment, and λ0 is a geometrically dependent offset. The standing wave model has been experimentally and numerically verified in rods and SRRs at the fundamental mode (m = 1) and at higher harmonic resonances (m > 1) as well [17

17. C. Y. Chen, S. C. Wu, and T. J. Yen, “Experimental verification of standing-wave plasmonic resonances in split-ring resonators,” Appl. Phys. Lett. 93(3), 034110 (2008). [CrossRef]

19

19. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006). [CrossRef]

]. Note that for m = 1, the resonances are dominated by electric/magnetic dipoles, whereas they contain significant contributions from multipolar modes when m > 1. From Eq. (1), we can easily obtain the refractive index sensitivities (m/dneff) of rods or SRRs:
dλmdneff=λ0neff+(λ0neffdλ0dneff)
(2)
Equation (2) shows that the refractive index sensitivities increase with λm/neff with a slope equal to 1 and an offset −250nm/RIU (obtained from the fit in Fig. 1). Importantly, the refractive index sensitivity is independent of the harmonic number m. Thus the presence of multipolar resonances does not affect the universal scaling relation. Finally, generalizing the result to two or three dimensions with complex structures will introduce a small geometrical correction factor to λ0 and will yield similar results like Eq. (2). We thus plot the prediction of Eq. (2) as the dashed line in Fig. 1. Note that neff = 1.33 for plasmonic atoms suspended in water. For those dispersed in glass slides, we have employed simulations to determine the neff (see supporting information). Clearly, the experimental data of most plasmonic atoms fall on the dashed line, suggesting that the standing wave model is applicable to diverse geometries and the geometrical corrections to the complex structures remain small. In addition, we have found that the anomalous deviations to the universal scaling relation in nanostars can be attributed to the inconsistencies of the experimental data [3

3. C. L. Nehl, H. W. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Nano Lett. 6(4), 683–688 (2006). [CrossRef] [PubMed]

]. Therefore, we conclude that the standing wave model explains the refractive index sensitivities of all plasmonic atoms known so far.

2. Methods

It will be interesting to see whether plasmonic molecules would follow identical universal scaling relation shown in Fig. 1. Naively, one may speculate that due to the strong near-field couplings, the enhanced multipolar contributions, the field-enhancements, and re-distributions of electromagnetic hot spots, deviations to the universal scaling relation may occur in plasmonic molecules. To investigate their effects on the refractive index sensitivities and the universal relation, we have designed and fabricated three kinds of plasmonic molecules with asymmetric structures (Fig. 2(a, b)
Fig. 2 (a, b) SEM images of the fabricated Molecules A and B with inter-molecular separation s = 20nm. (c, d) Electric field (hot spot) distributions of Molecules A and B at the respective antisymmetric resonant modes. (e, f) Electric field (hot spot) distributions of Molecules A and B at the respective symmetric resonant modes. The arrows denote the flows of the surface currents.
and Fig. 3(a, b)
Fig. 3 (a, b) SEM images of the fabricated Molecules C with inter-molecular separation s = 11nm and 20nm. (c, d) Electric field (hot spot) distributions at the respective antisymmetric resonant modes. (e, f) Electric field (hot spot) distributions at the respective symmetric resonant modes. The arrows denote the flows of the surface currents. Note that the field-enhancement is more pronounced for the symmetric mode at s = 11nm.
). Coupling two plasmonic atoms into a plasmonic molecule always leads to complex interactions between different resonant modes. Recently we have categorized the complex interactions into three types of couplings [10

10. Y. C. Chao, H. C. Tseng, K. D. Chang, and C. W. Chang, “Three types of couplings between asymmetric plasmonic dimers,” Opt. Express 20(3), 2887–2894 (2012). [CrossRef] [PubMed]

]. Among them, the Type III coupling that contains two redshifts in resonant wavelengths is particularly interesting because they do not have any mechanical analogies. The fabricated Molecules A, B, and C all belong to the Type III coupling. Moreover, the distances between of constituted elements can be artificially designed so that the coupling strength, the resonant frequencies, the multipolar contributions, the hot spot distributions, and the field-enhancements can be controlled via advanced electron beam lithography (Elionix ELS 7000). Experimentally, we fabricated arrays (40μm × 40μm) of plasmonic molecules by patterning 40nm thick Au films on quartz substrates. The inter-molecular separations (s) were varied from 11nm to 20nm and their refractive index sensitivities were characterized by measuring the transmitted spectra using an infrared spectrometer equipped with a broadband light source. We also employed finite difference time domain simulation using commercial software CST Microwave Studio to assist our analyses. The electrical conductivity of gold is described by the Drude model with plasmon frequency 2.175 × 1015 Hz and a practical damping rate 1.2 × 1014 Hz.

3. Results and discussions

Figures 2(c-f) show the simulated electric field and surface current distributions of the fabricated plasmonic molecules (Molecules A and B) with s = 20nm. The asymmetric structures of Molecules A and B allow both antisymmetric and symmetric resonant modes to be observed at the far field. Particularly, both the antisymmetric resonant modes of Molecules A and B exhibit antiparallel surface currents and thereby contain large contributions from electric quadrupoles. On the other hand, the symmetric modes are dominated by electric and magnetic dipolar resonances. Moreover, the hot spots appearing at the edges of the structures exhibit field-enhancements more than 25-fold and they are also dependent on the resonant modes. As shown in Figs. 2(c-f), the hot spots are much larger in the antisymmetric modes than those in the symmetric modes. Thus the design of Molecules A and B allows experimental investigations on the effects of different electric quadrupolar contributions as well as the hot spot distributions to the refractive index sensitivities.

Because the associated field-enhancements at the hot spots not only depend on the resonant modes but also strongly correlate with the inter-molecular interactions, we have also fabricated Molecule C with s varied from 20nm to 11nm. As shown in Figs. 3(a, b), the sharp edges persist during the experimental lift-off processes even though s is reduced to 11nm. For the symmetric mode, the field-enhancements shown in Figs. 3(e, f) are at least 30-fold for s = 20nm and can be more than 50-fold when s is reduced to 11nm. Thus the genuine effect of field-enhancements on the refractive index sensitivities can be investigated in the two Molecule C’s.

Figures 4(a-d)
Fig. 4 Experimental (solid curves) and simulated (dashed curves) transmission spectra of Molecules (a) A, (b) B, (c) C (s = 11nm), and (d) C (s = 20nm) before (blue curves) and after (red curves) dropping water refractive index tests.
show measured transmission spectra of Molecules A, B, and C (s = 20nm and 11nm). The refractive index sensitivities are tested using water (n = 1.33). The resonant wavelength redshifts (Δλm) is 191nm (antisymmetric mode) for Molecule A, Δλm = 160nm (symmetric mode) and 175nm (antisymmetric mode) for Molecule B. For the symmetric mode of Molecule C, we obtain Δλm = 178nm for s = 20nm and Δλm = 206nm for s = 11nm. The measured spectra are consistent with the simulation results.

To understand the universal scaling relation established for plasmonic molecules, we note that from dimensional analyses, coupling two or more plasmonic atoms into plasmonic molecules will result in new resonant frequencies expressed by the general formulation:
ω=ωa+Meε+μMm
(3)
where ωa is the resonant frequency of the uncoupled plasmonic atom, Me is a function independent of ε, and Mm is a function independent of ε and μ. The last two terms of Eq. (3) together represent the couplings. Experimentally, because no magnetic responses can be observed at optical frequencies, μ = 1 and dMe/dneff = dMm/dneff = 0. The slope of m/dneff vs. λm/neff of plasmonic molecules thus follows:
dλm/dneffλm/neff=dω/dneffω/neff=dωa/dneff+Me/neff2ωa/neff+Me/neff2+Mm/neff
(4)
Because plasmonic atoms follow (a/dneff)/(ωa/neff) = −1 and the coupling strengths (Me, Mm) are always smaller than the ωa, Eq. (4) can be approximated to
dλm/dneffλm/neff1O(Mmωa)
(5)
The last term denotes corrections to the order of Mma. Thus we learn that the slope will be close to 1 if the interactions of the plasmonic molecules are not dominated by magnetic interactions. The result is numerically confirmed in Fig. 5(b), in which the effects from the substrates are removed (i.e. neff = 1) by simulation. From Fig. 5(b), we learn that most plasmonic molecules studied so far follow the universal scaling relation, suggesting the predominant electric couplings. Experimentally, so far notable deviations to the universal scaling are found in complimentary plasmonic molecules only [21

21. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef] [PubMed]

]. However, the anomalous deviation is not confirmed by simulations. From an application’s point of view, we also learn that plasmonic molecules with strong magnetic interactions will not be suitable for practical applications due to their reduced refractive index sensitivities.

In summary, we established a universal scaling relation for refractive sensitivities of various plasmonic atoms and molecules operating in the visible or infrared ranges. In general, the refractive index sensitivities increase with respect to λm/neff and exhibit a slope equal to 1. The universal scaling is independent of the structures of the subwavelength metals, multipolar contributions, field-enhancements, hot spot distributions, or couplings in most cases. We find the universal scaling relation can be explained by the standing wave model of surface plasmons for all plasmonic atoms and the predominant electric couplings for most plasmonic molecules studied so far.

Acknowledgments

We thank Dr. Wei-Li Lee’s supports on nanofabrication. This work was supported by the National Science Council of Taiwan (NSC101-2112-M-002-014-MY3).

References and links

1.

K. M. Mayer and J. H. Hafner, “Localized Surface Plasmon Resonance Sensors,” Chem. Rev. 111(6), 3828–3857 (2011). [CrossRef] [PubMed]

2.

E. Petryayeva and U. J. Krull, “Localized surface plasmon resonance: Nanostructures, bioassays and biosensing--A review,” Anal. Chim. Acta 706(1), 8–24 (2011). [CrossRef] [PubMed]

3.

C. L. Nehl, H. W. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Nano Lett. 6(4), 683–688 (2006). [CrossRef] [PubMed]

4.

Y. G. Sun and Y. N. Xia, “Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes,” Anal. Chem. 74(20), 5297–5305 (2002). [CrossRef] [PubMed]

5.

H. J. Chen, X. S. Kou, Z. Yang, W. H. Ni, and J. F. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir 24(10), 5233–5237 (2008). [CrossRef] [PubMed]

6.

L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. N. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett. 5(10), 2034–2038 (2005). [CrossRef] [PubMed]

7.

L. J. Sherry, R. C. Jin, C. A. Mirkin, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver triangular nanoprisms,” Nano Lett. 6(9), 2060–2065 (2006). [CrossRef] [PubMed]

8.

C. Y. Tsai, S. P. Lu, J. W. Lin, and P. T. Lee, “High sensitivity plasmonic index sensor using slablike gold nanoring arrays,” Appl. Phys. Lett. 98(15), 153108 (2011). [CrossRef] [PubMed]

9.

M. M. Miller and A. A. Lazarides, “Sensitivity of metal nanoparticle surface plasmon resonance to the dielectric environment,” J. Phys. Chem. B 109(46), 21556–21565 (2005). [CrossRef] [PubMed]

10.

Y. C. Chao, H. C. Tseng, K. D. Chang, and C. W. Chang, “Three types of couplings between asymmetric plasmonic dimers,” Opt. Express 20(3), 2887–2894 (2012). [CrossRef] [PubMed]

11.

H. C. Tseng and C. W. Chang, “High displacement sensitivity in asymmetric plasmonic nanostructures,” Opt. Express 18(17), 18360–18367 (2010). [CrossRef] [PubMed]

12.

A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics 3(11), 654–657 (2009). [CrossRef]

13.

E. C. Le Ru and P. G. Etchegoin, “Phenomenological local field enhancement factor distributions around electromagnetic hot spots,” J. Chem. Phys. 130(18), 181101 (2009). [CrossRef] [PubMed]

14.

I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly Strained Compliant Optical Metamaterials with Large Frequency Tunability,” Nano Lett. 10(10), 4222–4227 (2010). [CrossRef] [PubMed]

15.

I. M. Pryce, Y. A. Kelaita, K. Aydin, and H. A. Atwater, “Compliant Metamaterials for Resonantly Enhanced Infrared Absorption Spectroscopy and Refractive Index Sensing,” ACS Nano 5(10), 8167–8174 (2011). [CrossRef] [PubMed]

16.

N. Verellen, P. Van Dorpe, C. J. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon Line Shaping Using Nanocrosses for High Sensitivity Localized Surface Plasmon Resonance Sensing,” Nano Lett. 11(2), 391–397 (2011). [CrossRef] [PubMed]

17.

C. Y. Chen, S. C. Wu, and T. J. Yen, “Experimental verification of standing-wave plasmonic resonances in split-ring resonators,” Appl. Phys. Lett. 93(3), 034110 (2008). [CrossRef]

18.

F. Neubrech, T. Kolb, R. Lovrincic, G. Fahsold, A. Pucci, J. Aizpurua, T. W. Cornelius, M. E. Toimil-Molares, R. Neumann, and S. Karim, “Resonances of individual metal nanowires in the infrared,” Appl. Phys. Lett. 89(25), 253104 (2006). [CrossRef]

19.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006). [CrossRef]

20.

M. Piliarik, P. Kvasnička, N. Galler, J. R. Krenn, and J. Homola, “Local refractive index sensitivity of plasmonic nanoparticles,” Opt. Express 19(10), 9213–9220 (2011). [CrossRef] [PubMed]

21.

N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing,” Nano Lett. 10(4), 1103–1107 (2010). [CrossRef] [PubMed]

OCIS Codes
(250.5403) Optoelectronics : Plasmonics
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Sensors

History
Original Manuscript: November 13, 2012
Revised Manuscript: January 8, 2013
Manuscript Accepted: January 9, 2013
Published: January 16, 2013

Citation
Yen-Kai Chang, Zong-Xing Lou, Kao-Der Chang, and Chih-Wei Chang, "Universal scaling of plasmonic refractive index sensors," Opt. Express 21, 1804-1811 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-2-1804


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References

  1. K. M. Mayer and J. H. Hafner, “Localized Surface Plasmon Resonance Sensors,” Chem. Rev.111(6), 3828–3857 (2011). [CrossRef] [PubMed]
  2. E. Petryayeva and U. J. Krull, “Localized surface plasmon resonance: Nanostructures, bioassays and biosensing--A review,” Anal. Chim. Acta706(1), 8–24 (2011). [CrossRef] [PubMed]
  3. C. L. Nehl, H. W. Liao, and J. H. Hafner, “Optical properties of star-shaped gold nanoparticles,” Nano Lett.6(4), 683–688 (2006). [CrossRef] [PubMed]
  4. Y. G. Sun and Y. N. Xia, “Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes,” Anal. Chem.74(20), 5297–5305 (2002). [CrossRef] [PubMed]
  5. H. J. Chen, X. S. Kou, Z. Yang, W. H. Ni, and J. F. Wang, “Shape- and size-dependent refractive index sensitivity of gold nanoparticles,” Langmuir24(10), 5233–5237 (2008). [CrossRef] [PubMed]
  6. L. J. Sherry, S. H. Chang, G. C. Schatz, R. P. Van Duyne, B. J. Wiley, and Y. N. Xia, “Localized surface plasmon resonance spectroscopy of single silver nanocubes,” Nano Lett.5(10), 2034–2038 (2005). [CrossRef] [PubMed]
  7. L. J. Sherry, R. C. Jin, C. A. Mirkin, G. C. Schatz, and R. P. Van Duyne, “Localized surface plasmon resonance spectroscopy of single silver triangular nanoprisms,” Nano Lett.6(9), 2060–2065 (2006). [CrossRef] [PubMed]
  8. C. Y. Tsai, S. P. Lu, J. W. Lin, and P. T. Lee, “High sensitivity plasmonic index sensor using slablike gold nanoring arrays,” Appl. Phys. Lett.98(15), 153108 (2011). [CrossRef] [PubMed]
  9. M. M. Miller and A. A. Lazarides, “Sensitivity of metal nanoparticle surface plasmon resonance to the dielectric environment,” J. Phys. Chem. B109(46), 21556–21565 (2005). [CrossRef] [PubMed]
  10. Y. C. Chao, H. C. Tseng, K. D. Chang, and C. W. Chang, “Three types of couplings between asymmetric plasmonic dimers,” Opt. Express20(3), 2887–2894 (2012). [CrossRef] [PubMed]
  11. H. C. Tseng and C. W. Chang, “High displacement sensitivity in asymmetric plasmonic nanostructures,” Opt. Express18(17), 18360–18367 (2010). [CrossRef] [PubMed]
  12. A. Kinkhabwala, Z. F. Yu, S. H. Fan, Y. Avlasevich, K. Mullen, and W. E. Moerner, “Large single-molecule fluorescence enhancements produced by a bowtie nanoantenna,” Nat. Photonics3(11), 654–657 (2009). [CrossRef]
  13. E. C. Le Ru and P. G. Etchegoin, “Phenomenological local field enhancement factor distributions around electromagnetic hot spots,” J. Chem. Phys.130(18), 181101 (2009). [CrossRef] [PubMed]
  14. I. M. Pryce, K. Aydin, Y. A. Kelaita, R. M. Briggs, and H. A. Atwater, “Highly Strained Compliant Optical Metamaterials with Large Frequency Tunability,” Nano Lett.10(10), 4222–4227 (2010). [CrossRef] [PubMed]
  15. I. M. Pryce, Y. A. Kelaita, K. Aydin, and H. A. Atwater, “Compliant Metamaterials for Resonantly Enhanced Infrared Absorption Spectroscopy and Refractive Index Sensing,” ACS Nano5(10), 8167–8174 (2011). [CrossRef] [PubMed]
  16. N. Verellen, P. Van Dorpe, C. J. Huang, K. Lodewijks, G. A. E. Vandenbosch, L. Lagae, and V. V. Moshchalkov, “Plasmon Line Shaping Using Nanocrosses for High Sensitivity Localized Surface Plasmon Resonance Sensing,” Nano Lett.11(2), 391–397 (2011). [CrossRef] [PubMed]
  17. C. Y. Chen, S. C. Wu, and T. J. Yen, “Experimental verification of standing-wave plasmonic resonances in split-ring resonators,” Appl. Phys. Lett.93(3), 034110 (2008). [CrossRef]
  18. F. Neubrech, T. Kolb, R. Lovrincic, G. Fahsold, A. Pucci, J. Aizpurua, T. W. Cornelius, M. E. Toimil-Molares, R. Neumann, and S. Karim, “Resonances of individual metal nanowires in the infrared,” Appl. Phys. Lett.89(25), 253104 (2006). [CrossRef]
  19. C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B84(1–2), 219–227 (2006). [CrossRef]
  20. M. Piliarik, P. Kvasnička, N. Galler, J. R. Krenn, and J. Homola, “Local refractive index sensitivity of plasmonic nanoparticles,” Opt. Express19(10), 9213–9220 (2011). [CrossRef] [PubMed]
  21. N. Liu, T. Weiss, M. Mesch, L. Langguth, U. Eigenthaler, M. Hirscher, C. Sönnichsen, and H. Giessen, “Planar Metamaterial Analogue of Electromagnetically Induced Transparency for Plasmonic Sensing,” Nano Lett.10(4), 1103–1107 (2010). [CrossRef] [PubMed]

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