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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 17 — Aug. 16, 2010
  • pp: 18360–18367
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High displacement sensitivity in asymmetric plasmonic nanostructures

Hsuan-Chi Tseng and Chih-Wei Chang  »View Author Affiliations


Optics Express, Vol. 18, Issue 17, pp. 18360-18367 (2010)
http://dx.doi.org/10.1364/OE.18.018360


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Abstract

The strong couplings between two asymmetric plasmonic nanostructures can lead to ultra-sensitive optical responses when their separation changes. We employ electromagnetic numerical simulations to study the displacement sensitivity of two kinds of plasmonic systems: (1) a split-ring resonator and a metal rod; (2) two metal rods of asymmetric lengths. Structural asymmetry makes antiparallel current interactions possible and greatly enhances the sensitivity to 5%/nm for normalized frequency changes and 29%/nm for normalized transmittance changes. These are the highest displacement sensitivity among all physical systems investigated so far. In addition, we also find that these systems display a universal scaling curve independent of their shapes or dimensions. These asymmetric plasmonic nanostructures will open widespread applications from strain mapping, surface wave or heat wave imaging, optomechanical sensing, to environmental detections.

© 2010 OSA

1. Introduction

Nanoscale metal structures enabling localized surface plasmon resonances have generated much excitement for their diverse applications in environmental sensing and chemical labeling [1

1. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]

,2

2. M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008). [CrossRef] [PubMed]

]. In these plasmonic systems, an external light drives the collective oscillation of the conduction electrons of a metal, which results in local-field enhancements and strong scatterings around the metal structures. Because the resonance frequency is highly sensitive to the environment, these metal structures have been extensively used for detecting molecules with zeptomole sensitivity [3

3. A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with zeptomole sensitivity,” Nano Lett. 3(8), 1057–1062 (2003). [CrossRef]

6

6. K. Zhang, Y. J. Xiang, X. C. Wu, L. L. Feng, W. W. He, J. B. Liu, W. Y. Zhou, and S. S. Xie, “Enhanced optical responses of Au@Pd core/shell nanobars,” Langmuir 25(2), 1162–1168 (2009). [CrossRef]

]. Furthermore, unlike organic fluorophores, these plasmonic sensors do not suffer from blinking or bleaching. Thus they can serve as nanoscale plasmonic rulers that make high-speed analyses of macromolecules possible [7

7. C. Sönnichsen, B. M. Reinhard, J. Liphardt, and A. P. Alivisatos, “A molecular ruler based on plasmon coupling of single gold and silver nanoparticles,” Nat. Biotechnol. 23(6), 741–745 (2005). [CrossRef] [PubMed]

,8

8. G. L. Liu, Y. D. Yin, S. Kunchakarra, B. Mukherjee, D. Gerion, S. D. Jett, D. G. Bear, J. W. Gray, A. P. Alivisatos, L. P. Lee, and F. F. Chen, “A nanoplasmonic molecular ruler for measuring nuclease activity and DNA footprinting,” Nat. Nanotechnol. 1(1), 47–52 (2006). [CrossRef]

]. In addition, due to deep subwavelength couplings between plasmonic elements, when integrating these structures with nanoelectromechanical systems (NEMS), they will enable sensitive optical detections of thermal or even quantum fluctuations. These features are believed to generate great impacts on the field of optomechanics and NEMS in the near future.

The unusual displacement sensitivity originates from the strong distance-dependent couplings between plasmonic nanostructures. Recently, intensive works have been devoted to studies of interactions between nanorods, nanospheres, nanoshells and nano-prisms etc. with symmetric structures [9

9. K. H. Su, Q. H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]

15

15. P. K. Jain and M. A. El-Sayed, “Plasmonic coupling in noble metal nanostructures,” Chem. Phys. Lett. 487(4-6), 153–164 (2010). [CrossRef]

]. In general, the effects can be qualitatively understood by a plasmon hybridization model which considers electric interactions between plasmonic metal structures similar to chemical bonding in natural molecules [16

16. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

]. The model depicts a universal scaling curve for normalized resonance frequency changes with respect to normalized distances [17

17. P. K. Jain, W. Y. Huang, and M. A. El-Sayed, “On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: A plasmon ruler equation,” Nano Lett. 7(7), 2080–2088 (2007). [CrossRef]

]. However, so far these investigations are limited to structurally symmetric systems and it is not known which kinds of systems would exhibit the highest sensitivity. Here we show that introducing structural asymmetry makes antiparallel current interactions possible and greatly enhances the displacement sensitivity in two kinds of plasmonic nanostructures. In fact, these two systems display the highest displacement sensitivity among all systems (including plasmonic or non-plasmonic systems) investigated so far. These structurally-asymmetric plasmonic systems, though they are fixed to a substrate, will have potential applications in strain mapping, surface wave or heat wave imaging, and thermal or quantum vibrational sensing when they are integrated with NEMS devices.

2. Methods

Figure 1
Fig. 1 Schematics of two asymmetric plasmonic nanostructures (a) a SRR and a metal rod (b) two metal rods of asymmetric lengths. An external light polarized along y-axis is incident normal to the two nanostructures. In the paper, thickness (t) = 30 nm and w = 50 nm unless otherwise mentioned.
illustrates the schematics of two kinds of asymmetric plasmonic nanostructures: one consisting of a split-ring resonator (SRR) and a metal rod (Fig. 1(a)) and the other one consisting of two metal rods of asymmetric lengths (Fig. 1(b)). Since both SRRs and metal rods are model plasmonic elements which exhibit strong electric dipolar resonances, we choose these two structures for studying the effects from structural asymmetry. When the two plasmonic elements are coupled, the resonant frequency changes in accord with the coupling strength. Introducing structural asymmetry makes the interactions between each element more intriguing and may bring more interesting phenomena. To explore their potential applications in displacement sensing, we have performed numerical simulations using software package CST Microwave Studio to study the optical transmission spectra when the separation between the elements changes. We have also systematically varied the dimensions of the elements so that the resonance frequencies are within infrared to visible range for practical applications. To avoid non-local effects at small distances, we have restricted the separation (s) to be larger than 2nm [18

18. F. J. García de Abajo, “Nonlocal Effects in the Plasmons of Strongly Interacting Nanoparticles, Dimers, and Waveguides,” J. Phys. Chem. C 112(46), 17983–17987 (2008). [CrossRef]

]. The substrate is either glass (refraction index = 1.5) or sapphire (refraction index = 1.7). The dimensions of the systems are subwavelength (~λ/4) and couplings between nearest neighbor elements can be neglected. The electrical conductivity of gold is described by the Drude model with plasmon frequency 1.37 × 1016 Hz. Importantly, in order to consider experimental implementations, we set the damping rate of gold to be 1.2 × 1014 Hz, which is three times higher than the bulk value and is a practical parameter for experiments utilizing ordinary fabrication techniques [9

9. K. H. Su, Q. H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]

,10

10. B. M. Reinhard, M. Siu, H. Agarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5(11), 2246–2252 (2005). [CrossRef] [PubMed]

,17

17. P. K. Jain, W. Y. Huang, and M. A. El-Sayed, “On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: A plasmon ruler equation,” Nano Lett. 7(7), 2080–2088 (2007). [CrossRef]

]. In the simulation, a transient pulse polarized along y-axis was incident to the system and then the transmittance of the wave was analyzed. Each mesh size was less than λ/2000 to ensure simulation accuracy.

3. Results and discussions

Figure 2(a)
Fig. 2 Simulated separation dependent transmittance of (a) a SRR and a metal rod with L SRR = L rod = 200 nm, t = 40 nm, and a glass substrate, in which two resonances (as marked by the shaded blue and pink colors) are found to red-shift when reducing the separation. The upper figures display the respective current flow distributions. (b) two metal rods with Llong = 250 nm, Lshort = 175 nm, and a sapphire substrate, in which two resonances (as marked by the shaded green and pink colors) are found to red-shift when reducing the separation. The upper figures display the respective current flow distributions.
shows the simulated transmittance spectra for the SRR-rod system shown in Fig. 1(a). In the frequency range of interests, the SRR exhibits an electric dipolar resonance at 391 THz (identified by the dip of the transmittance) and the metal rod exhibits an electric dipolar resonance at 310 THz. Due to the conservation of degrees of freedom and the structural asymmetry, coupling these two elements results in two resonances which are both optically bright modes as shown in Fig. 2(a). Interestingly, both resonances display red-shifts when the distance between the SRR and the metal rod decreases. We found the most dramatic changes to be the first resonance in the range of 180-330 THz. As shown in Fig. 2(a), the first resonance changes 68 THz when the separation slightly increases from 2 nm to 10 nm. In contrast, the second resonance (in the range of 381 THz to 385 THz) does not show such a dramatic effect. The origin of the difference can be understood from the current flow distributions for the two resonances. As shown in Fig. 2(a), the first resonance exhibits antiparallel current flows in the region of proximity. On the other hand, the second resonance, which displays small frequency changes, exhibits parallel current distributions in the region of proximity.

Similarly, coupling a long metal rod (resonance frequency = 237 THz) and a short metal rod (resonance frequency = 306 THz) results in two optically bright resonances. As shown in Fig. 2(b), the two resonances show red-shifts when the distance between the two metal rods decreases. The most dramatic change of the resonance frequency is again found in the first resonance (frequency changes 32 THz from 4 nm to 10 nm), in which the current flow shows antiparallel distributions. On the other hand, the second resonance, which exhibits parallel current distributions, only shows small changes.

On the other hand, parallel current interactions shown in the second resonance of the SRR-rod system or the asymmetric rod system do not exhibit comparable displacement sensitivities. As shown in Fig. 4
Fig. 4 Normalized frequency changes vs. normalized separations for various asymmetric nanostructures with parallel current interactions. Introducing more asymmetry into the systems shifts the curves upward but the displacement sensitivity remains low.
, increasing the asymmetry of the SRR-rod or the asymmetric-rod systems shifts the curves upward [26

26. Here for the SRR-rod system, the frequency change is normalized to the second resonance frequency of an individual SRR and the separation is normalized to Lrod. For the asymmetric-rod systems, the frequency change is normalized to the resonance frequency of the short, isolated metal rod and the separation is normalized to Llong. Again, due to the structural asymmetry, the choices of normalization parameters are a little arbitrary. But we have found that different combinations give similar results.

]. However, the displacement sensitivities remain at least three times lower than those shown in Fig. 3.

For the antisymmetric mode (antiparallel current distribution), the effect of the community inductance, the electric coupling, and the magnetic coupling contribute coherently to the large redshift. The deep subwavelength nature of these couplings, when combined with the large redshift, results in a much larger displacement sensitivity in the antiparallel current distributions than that in the parallel current distributions. The parameters for Fig. 2(b) shown above have also quantitatively explained the main features observed in the simulation.

Although the systems investigated so far are fixed to a substrate, they can be used for strain mapping when a stress is applied to the substrate. Besides, due to the broadband optical responses, they can be used for dynamical imaging of surface waves or heat currents that produce lattice compression or refraction index changes. Moreover, once they are integrated with NEMS devices, they are also capable of detecting tiny motions arising from thermal or quantum fluctuations. For comparison, so far the highest displacement sensitivity was reported in a micromechanical resonator which incorporates a very high finesse (F = 30000) Fabry-Perot cavity. The device had achieved quantum-limited sensitivity at the 10−19m/Hz level [29

29. O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97(13), 133601 (2006). [CrossRef] [PubMed]

]. Following 2πs/λ=2/F, a displacement of s = 2 nm in the microresonator would correspond to 50% change of the transmittance at λ = 1064 nm; or equivalently, an normalized transmittance change of 25%/nm. For our system, a monolayer of the asymmetric nanostructures can further enhance the normalized transmittance change to 29%/nm at λ = 1550 nm. We believe that once multilayers of such asymmetric nanostructures are fabricated, more improvements can be achieved. In addition, unlike a Fabry-Perot cavity that requires multi-wavelength engineering, the plasmonic systems can further reduce the size of a device to deep subwavelength. The structurally asymmetric plasmonic systems not only exhibit the highest displacement sensitivity among all plasmonic or non-plasmonic systems investigated so far, but also can generate great impacts on nanoscale optomechanical applications. Finally, it should be noted that other varieties of asymmetric plasmonic nanostructures could exhibit even higher sensitivities. The optimization of structural designs for achieving the highest displacement sensitivity is certainly worth future investigations.

In summary, we have investigated displacement sensitivities of two kinds of structurally asymmetric plasmonic systems. The structural asymmetry makes the antiparallel current interactions possible, which greatly enhances the displacement sensitivity to reach a normalized frequency change of 5%/nm or a normalized transmittance change of 29%/nm. These structurally asymmetric plasmonic systems constitute the highest displacement sensitivity investigated so far and will have widespread applications ranging from strain mapping, surface wave or heat wave imaging, to thermal or quantum motional sensing when integrated with NEMS devices.

Acknowledgments

The authors thank Prof. W. K. Hung and Wei-Chih Ho for their helps during the early stage of the work. C. W. Chang would like to thank supports from Golden-Jade fellow of Kenda Foundation, Taiwan. This work was supported by the National Science Council of Taiwan (NSC98-2112-M-002-021-MY3).

References and links

1.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]

2.

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008). [CrossRef] [PubMed]

3.

A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with zeptomole sensitivity,” Nano Lett. 3(8), 1057–1062 (2003). [CrossRef]

4.

G. Raschke, S. Brogl, A. S. Susha, A. L. Rogach, T. A. Klar, J. Feldmann, B. Fieres, N. Petkov, T. Bein, A. Nichtl, and K. Kurzinger, “Gold nanoshells improve single nanoparticle molecular sensors,” Nano Lett. 4(10), 1853–1857 (2004). [CrossRef]

5.

S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009). [CrossRef] [PubMed]

6.

K. Zhang, Y. J. Xiang, X. C. Wu, L. L. Feng, W. W. He, J. B. Liu, W. Y. Zhou, and S. S. Xie, “Enhanced optical responses of Au@Pd core/shell nanobars,” Langmuir 25(2), 1162–1168 (2009). [CrossRef]

7.

C. Sönnichsen, B. M. Reinhard, J. Liphardt, and A. P. Alivisatos, “A molecular ruler based on plasmon coupling of single gold and silver nanoparticles,” Nat. Biotechnol. 23(6), 741–745 (2005). [CrossRef] [PubMed]

8.

G. L. Liu, Y. D. Yin, S. Kunchakarra, B. Mukherjee, D. Gerion, S. D. Jett, D. G. Bear, J. W. Gray, A. P. Alivisatos, L. P. Lee, and F. F. Chen, “A nanoplasmonic molecular ruler for measuring nuclease activity and DNA footprinting,” Nat. Nanotechnol. 1(1), 47–52 (2006). [CrossRef]

9.

K. H. Su, Q. H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]

10.

B. M. Reinhard, M. Siu, H. Agarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5(11), 2246–2252 (2005). [CrossRef] [PubMed]

11.

P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110(37), 18243–18253 (2006). [CrossRef] [PubMed]

12.

O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Optical scattering resonances of single and coupled dimer plasmonic nanoantennas,” Opt. Express 15(26), 17736–17746 (2007). [CrossRef] [PubMed]

13.

P. K. Jain and M. A. El-Sayed, “Noble metal nanoparticle pairs: effect of medium for enhanced nanosensing,” Nano Lett. 8(12), 4347–4352 (2008). [CrossRef]

14.

A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon coupling of gold nanorods at short distances and in different geometries,” Nano Lett. 9(4), 1651–1658 (2009). [CrossRef] [PubMed]

15.

P. K. Jain and M. A. El-Sayed, “Plasmonic coupling in noble metal nanostructures,” Chem. Phys. Lett. 487(4-6), 153–164 (2010). [CrossRef]

16.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]

17.

P. K. Jain, W. Y. Huang, and M. A. El-Sayed, “On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: A plasmon ruler equation,” Nano Lett. 7(7), 2080–2088 (2007). [CrossRef]

18.

F. J. García de Abajo, “Nonlocal Effects in the Plasmons of Strongly Interacting Nanoparticles, Dimers, and Waveguides,” J. Phys. Chem. C 112(46), 17983–17987 (2008). [CrossRef]

19.

P. K. Jain and M. A. El-Sayed, “Universal scaling of plasmon coupling in metal nanostructures: extension from particle pairs to nanoshells,” Nano Lett. 7(9), 2854–2858 (2007). [CrossRef] [PubMed]

20.

C. Tabor, R. Murali, M. Mahmoud, and M. A. El-Sayed, “On the use of plasmonic nanoparticle pairs as a plasmon ruler: the dependence of the near-field dipole plasmon coupling on nanoparticle size and shape,” J. Phys. Chem. A 113(10), 1946–1953 (2009). [CrossRef]

21.

T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009). [CrossRef]

22.

Due to the asymmetric structures, the choice of D is a little arbitrary here. But the universal curve does not change much even if we choose D = Lrod for the SRR-rod systems or D = Llong for the asymmetric-rod system.

23.

P. K. Jain and M. A. El-Sayed, “Surface plasmon resonance sensitivity of metal nanostructures: Physical basis and universal scaling in metal nanoshells,” J. Phys. Chem. C 111(47), 17451–17454 (2007). [CrossRef]

24.

Even if we restrict s/D > 0.1 to exclude any numerical errors arising from possible nonlocal effects, we obtain A = 0.238 and τ = 0.065, which is still much more sensitive than previous results.

25.

P. K. Jain and M. A. El-Sayed, “Surface plasmon coupling and its universal size scaling in metal nanostructures of complex geometry: Elongated particle pairs and nanosphere trimers,” J. Phys. Chem. C 112(13), 4954–4960 (2008). [CrossRef]

26.

Here for the SRR-rod system, the frequency change is normalized to the second resonance frequency of an individual SRR and the separation is normalized to Lrod. For the asymmetric-rod systems, the frequency change is normalized to the resonance frequency of the short, isolated metal rod and the separation is normalized to Llong. Again, due to the structural asymmetry, the choices of normalization parameters are a little arbitrary. But we have found that different combinations give similar results.

27.

T. Li, R. X. Ye, C. Li, H. Liu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Structural-configurated magnetic plasmon bands in connected ring chains,” Opt. Express 17(14), 11486–11494 (2009). [CrossRef] [PubMed]

28.

H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97(24), 243902 (2006). [CrossRef]

29.

O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97(13), 133601 (2006). [CrossRef] [PubMed]

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

ToC Category:
Optics at Surfaces

History
Original Manuscript: July 21, 2010
Revised Manuscript: July 28, 2010
Manuscript Accepted: August 1, 2010
Published: August 12, 2010

Citation
Hsuan-Chi Tseng and Chih-Wei Chang, "High displacement sensitivity in asymmetric plasmonic nanostructures," Opt. Express 18, 18360-18367 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-18360


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References

  1. J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]
  2. M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008). [CrossRef] [PubMed]
  3. A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with zeptomole sensitivity,” Nano Lett. 3(8), 1057–1062 (2003). [CrossRef]
  4. G. Raschke, S. Brogl, A. S. Susha, A. L. Rogach, T. A. Klar, J. Feldmann, B. Fieres, N. Petkov, T. Bein, A. Nichtl, and K. Kurzinger, “Gold nanoshells improve single nanoparticle molecular sensors,” Nano Lett. 4(10), 1853–1857 (2004). [CrossRef]
  5. S. S. Aćimović, M. P. Kreuzer, M. U. González, and R. Quidant, “Plasmon near-field coupling in metal dimers as a step toward single-molecule sensing,” ACS Nano 3(5), 1231–1237 (2009). [CrossRef] [PubMed]
  6. K. Zhang, Y. J. Xiang, X. C. Wu, L. L. Feng, W. W. He, J. B. Liu, W. Y. Zhou, and S. S. Xie, “Enhanced optical responses of Au@Pd core/shell nanobars,” Langmuir 25(2), 1162–1168 (2009). [CrossRef]
  7. C. Sönnichsen, B. M. Reinhard, J. Liphardt, and A. P. Alivisatos, “A molecular ruler based on plasmon coupling of single gold and silver nanoparticles,” Nat. Biotechnol. 23(6), 741–745 (2005). [CrossRef] [PubMed]
  8. G. L. Liu, Y. D. Yin, S. Kunchakarra, B. Mukherjee, D. Gerion, S. D. Jett, D. G. Bear, J. W. Gray, A. P. Alivisatos, L. P. Lee, and F. F. Chen, “A nanoplasmonic molecular ruler for measuring nuclease activity and DNA footprinting,” Nat. Nanotechnol. 1(1), 47–52 (2006). [CrossRef]
  9. K. H. Su, Q. H. Wei, X. Zhang, J. J. Mock, D. R. Smith, and S. Schultz, “Interparticle coupling effects on plasmon resonances of nanogold particles,” Nano Lett. 3(8), 1087–1090 (2003). [CrossRef]
  10. B. M. Reinhard, M. Siu, H. Agarwal, A. P. Alivisatos, and J. Liphardt, “Calibration of dynamic molecular rulers based on plasmon coupling between gold nanoparticles,” Nano Lett. 5(11), 2246–2252 (2005). [CrossRef] [PubMed]
  11. P. K. Jain, S. Eustis, and M. A. El-Sayed, “Plasmon coupling in nanorod assemblies: optical absorption, discrete dipole approximation simulation, and exciton-coupling model,” J. Phys. Chem. B 110(37), 18243–18253 (2006). [CrossRef] [PubMed]
  12. O. L. Muskens, V. Giannini, J. A. Sánchez-Gil, and J. Gómez Rivas, “Optical scattering resonances of single and coupled dimer plasmonic nanoantennas,” Opt. Express 15(26), 17736–17746 (2007). [CrossRef] [PubMed]
  13. P. K. Jain and M. A. El-Sayed, “Noble metal nanoparticle pairs: effect of medium for enhanced nanosensing,” Nano Lett. 8(12), 4347–4352 (2008). [CrossRef]
  14. A. M. Funston, C. Novo, T. J. Davis, and P. Mulvaney, “Plasmon coupling of gold nanorods at short distances and in different geometries,” Nano Lett. 9(4), 1651–1658 (2009). [CrossRef] [PubMed]
  15. P. K. Jain and M. A. El-Sayed, “Plasmonic coupling in noble metal nanostructures,” Chem. Phys. Lett. 487(4-6), 153–164 (2010). [CrossRef]
  16. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302(5644), 419–422 (2003). [CrossRef] [PubMed]
  17. P. K. Jain, W. Y. Huang, and M. A. El-Sayed, “On the universal scaling behavior of the distance decay of plasmon coupling in metal nanoparticle pairs: A plasmon ruler equation,” Nano Lett. 7(7), 2080–2088 (2007). [CrossRef]
  18. F. J. García de Abajo, “Nonlocal Effects in the Plasmons of Strongly Interacting Nanoparticles, Dimers, and Waveguides,” J. Phys. Chem. C 112(46), 17983–17987 (2008). [CrossRef]
  19. P. K. Jain and M. A. El-Sayed, “Universal scaling of plasmon coupling in metal nanostructures: extension from particle pairs to nanoshells,” Nano Lett. 7(9), 2854–2858 (2007). [CrossRef] [PubMed]
  20. C. Tabor, R. Murali, M. Mahmoud, and M. A. El-Sayed, “On the use of plasmonic nanoparticle pairs as a plasmon ruler: the dependence of the near-field dipole plasmon coupling on nanoparticle size and shape,” J. Phys. Chem. A 113(10), 1946–1953 (2009). [CrossRef]
  21. T. J. Davis, K. C. Vernon, and D. E. Gomez, “Designing plasmonic systems using optical coupling between nanoparticles,” Phys. Rev. B 79(15), 155423 (2009). [CrossRef]
  22. Due to the asymmetric structures, the choice of D is a little arbitrary here. But the universal curve does not change much even if we choose D = Lrod for the SRR-rod systems or D = Llong for the asymmetric-rod system.
  23. P. K. Jain and M. A. El-Sayed, “Surface plasmon resonance sensitivity of metal nanostructures: Physical basis and universal scaling in metal nanoshells,” J. Phys. Chem. C 111(47), 17451–17454 (2007). [CrossRef]
  24. Even if we restrict s/D > 0.1 to exclude any numerical errors arising from possible nonlocal effects, we obtain A = 0.238 and τ = 0.065, which is still much more sensitive than previous results.
  25. P. K. Jain and M. A. El-Sayed, “Surface plasmon coupling and its universal size scaling in metal nanostructures of complex geometry: Elongated particle pairs and nanosphere trimers,” J. Phys. Chem. C 112(13), 4954–4960 (2008). [CrossRef]
  26. Here for the SRR-rod system, the frequency change is normalized to the second resonance frequency of an individual SRR and the separation is normalized to Lrod. For the asymmetric-rod systems, the frequency change is normalized to the resonance frequency of the short, isolated metal rod and the separation is normalized to Llong. Again, due to the structural asymmetry, the choices of normalization parameters are a little arbitrary. But we have found that different combinations give similar results.
  27. T. Li, R. X. Ye, C. Li, H. Liu, S. M. Wang, J. X. Cao, S. N. Zhu, and X. Zhang, “Structural-configurated magnetic plasmon bands in connected ring chains,” Opt. Express 17(14), 11486–11494 (2009). [CrossRef] [PubMed]
  28. H. Liu, D. A. Genov, D. M. Wu, Y. M. Liu, J. M. Steele, C. Sun, S. N. Zhu, and X. Zhang, “Magnetic plasmon propagation along a chain of connected subwavelength resonators at infrared frequencies,” Phys. Rev. Lett. 97(24), 243902 (2006). [CrossRef]
  29. O. Arcizet, P. F. Cohadon, T. Briant, M. Pinard, A. Heidmann, J. M. Mackowski, C. Michel, L. Pinard, O. Français, and L. Rousseau, “High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor,” Phys. Rev. Lett. 97(13), 133601 (2006). [CrossRef] [PubMed]

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