Abstract

The multipolar plasmon resonance and propagation of Au nanorings with symmetry broken were analyzed by using DDA and FDTD methods. Based on the multipolar plasmon resonance and propagation, we proposed ring-nanosensors with high sensitivities and optical ring-nanoantennas with large local field enhancements. We revealed that the refractive index sensitivities of split nanorings are about 100% larger than those of perfect nanorings with same size; the local field intensity enhancement of split nanoring with three gaps has increased by 37% than that of dipole antennas.

©2009 Optical Society of America

1. Introduction

Nanometer sized rings or ring-like structures have gained great interest for their promising properties. Several kinds of methods were developed to fabricate nanorings (NRs): lithography or etching [1–7], template method [8–17], molecular beam epitaxy [18–22], and polyol method [23, 24]. The properties and possible applications for porphyrin NRs [25], semiconductor NRs [26], magnetic NRs [27, 28], normal metal NRs [29–31], and noble metal NRs [32–54] have been well studied. Noble metal NRs or ring-like structures were proposed to be used for negative index of refraction [32, 33], wave guiding [34–36], miniature plasmonic wave plates [37], focusing of surface plasmons [38, 39], surface enhanced Raman scattering (SERS) [40–45], biosensors [46–50], and nanoantennas [51, 52]. Noble metal NRs are particularly attractive for sensing applications due to their large cavity volumes and uniform electric fields inside the ring [48]. And the refractive index sensitivities of NRs are substantially larger than those of nanodisks with similar diameters [47].

Recently, symmetry broken systems have been drawn much attentions [55–60]. It is found that Cu split rings have sharp trapped-mode resonances [61], and Ag split NRs can be used to term a “lasing spaser” [62]. Multipolar plasmons are excited in NRs with symmetry broken, and multipolar plasmon resonances (MPRs) have been found in the spectra [63–67]. Sheridan et al. argued that split NRs have MPRs [64–66]. While Hao et al. also found that under oblique incident excitations, MPRs appear in perfect NRs for retardation effects [67]. With multipolar plasmons excitations, the resonance frequencies are very easy to be modified to the visible and near-infrared ranges for large sized NRs.

Aizpurua et al. revealed that the resonances of perfect NRs are correlated to the aspect ratio of NRs, and an analytical model has been obtained [48]. Larsson et al. have shown the refractive index sensitivities of Au NRs are very large, a guideline for biosensors design have been given, i.e. minimize near field overlap with substrates [47], and Dmitriev et al. proved that a pillar can be used to reduce substrate effect [68]. By using the dyadic Green’s tensor approach and plasmon hybridization method, Mary et al. [69, 70] and Dutta et al. [71] showed the refractive index sensitivities are larger for NRs with small aspect ratio, and the resonances are correlated to ring circumference and surface plasmon (SP) wavelengths of the rod. This property can help to understand the mechanisms that cause the large refractive index sensitivities of NRs. When the environmental refractive index is changed, the resonance wavelength should be changed to keep SP wavelength a constant, and a small change of refractive index would lead to a large change of resonance wavelength. A nanodisk can be seen as a NR with inside radius equals to 0, and the variation of resonance wavelength is much smaller for NRs with large aspect ratio. On the other hand, it is concerned whether there is any way to improve the refractive index sensitivity furthermore for other structures. Au NRs were proposed to be used as nanoantennas [51, 52], but the local field enhancement is much weaker than that of dipole antennas [72].

In this paper, the spectra and near field distributions for NRs with symmetry broken have been calculated by discrete dipole approximation (DDA) [73] and finite difference time domain (FDTD) methods [74], respectively. The MPRs positions depend on the ring circumferences and SP wavelengths of the rod. Based on this property, we predict the refractive index sensitivities of split NRs are about 100% larger than those of perfect NRs with same size, and the mathematical simulation results are in good agreement with this prediction. Under oblique incident excitations, the energy is focusing to one side of the ring that induced by plasmons propagations. Gaps are introduced in NRs to increase SP interactions, and a strong local field enhancement that stronger than dipole antennas has been achieved.

2. Multipolar plasmon resonance and propagation in Au nanorings

NRs of circular are discussed at first for they are easier for theoretical studies than NRs of square. Figure 1(a) represents the cross section structures of perfect and split Au NRs, where the ring radius is R, r is the rod radius, d is the gap width for split NRs, and φ is the incident angle. Suppose n is the environmental refractive index, the light polarization is fixed along y-axis, and r = 25 nm in the following discussions.

 

Fig. 1. (a). Cross section structures of perfect and split Au NRs of circular, where R is ring radius, r is the rod radius, d = 30 nm is the gap width, and the light polarization is fixed along y-axis. (b). Extinction spectra for perfect NRs with different R, where the incident angle φ = 90°. (c). Extinction spectra for split NRs with different R, where φ = 0. (d). Field intensity I distributions for perfect Au NRs obtained at the cross section with R = 200 nm, where the excitation wavelengths are 1555, (e). 897, and (f). 666 nm, respectively. (g). I distributions for split Au NRs with R = 100nm, where the excitation wavelengths are 1626, and (h). 659 nm, respectively. The attached multimedia shows the time evolution processes of perfect NRs that under oblique incident excitations (Media 1).

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The extinction spectra for NRs with R = 100, 200, and 400 nm are shown in Fig. 1(b), where φ = 90°, n = 1, and Au electric permittivity is taken from [75]. MPRs have been found in the spectra, as so called dark plasmons are excited [67]. Figure 1(d)–1(f) give the near field intensity I = ∣E2 distributions obtained at the cross section for R = 200 nm under resonance excitations. SP wave packets have been found, indicating SP propagations might be involved in the multipolar plasmons excitations.

The fundamental mode of the longitudinal component of the SP wave vector k for nanorod with radius r satisfies the equation [76, 77],

k22k2J0'(k2R)J0(k2R)k12k1H0'(k1R)H0(k1R)=0

where ki = εi 1/2 k 0 is the wave vector in medium i, ki⊥ = (ki 2-k 2)1/2 is the transverse wave vector, J 0 and H 0 are Bessel and Hankel function of the first kind, respectively. Table 1 represents the resonance wavelengths λ RES as well as their corresponding SP wavelengths λ SP = 2π / Rek for perfect NRs. The ring circumference C and λ SP satisfy the following relationship at resonances,

CN×λSP/2(N=2,4,6……)

λ SP depends on r for a certain excitation wavelength, and there will be a resonance when C equals approximately to an integer times of the corresponding λ SP. Figure 1(d)–1(f) represent the MPRs modes N = 2, 4, and 6, respectively, and the distance between two SP wave packet peaks equals to half of λ SP.

Tables Icon

Table 1. The Resonance Wavelengths as Well as Their Corresponding λ SP that Shown in Fig. 1(b).

To understand the multipolar plasmons excitation processes more clearly, the field evolutions in time domain are also recorded in the calculations, and here is the field evolution processes: at first, the left side of NR is illuminated by light, and surface plasmon polaritons (SPPs) are excited, which propagate to the right side that forms SP waves; then, SP waves reach the right side, and significant reflection occurred that would cause standing SP wave formation; finally, after several periods of adjustment, field distributions reach the steady states. (For better understanding, please see Fig. 1 (Media 1), which shows the time evolution of field lg∣E∣/∣E Max∣.)

Sheridan et al. reported split NRs also have MPRs under normal incident excitations (φ = 0) [64–66], and we found the MPRs correlate to C and λ SP too. The gap is located as shown in Fig. 1(a), and Fig. 1(c) is the extinction spectra for split Au NRs with R = 100, 200, and 400 nm, where φ = 0, d = 30 nm, and n = 1. It is found C and λ SP satisfy the following relationship at resonances,

CM×λSP/2(M=1,3,5……)

Resonances appear when C equals approximately to a semi-integer times of the corresponding λ SP. Figure 1(g) and 1(h) are I distributions for R = 100 nm under the two resonance excitations shown in Fig. 1(c), which represent the two resonance modes M = 1 and 3.

The inside and outside circumferences are not equal to each other for NRs. SPPs are not only propagating along the outside surface, and the inside surface of NRs would affect field distributions. It is noted that the error of Eqs. (2) and (3) is larger for NRs with large aspect ratio r/R. Error corrections should be added to Eqs. (2) and (3) to gain the exact relationship between MPRs and NR structures, and the relationships between resonances and the aspect ratio of NRs were discussed in former works [48,69–71]. The gap size would also affect SP distributions, the larger gap size the larger error for Eq. (3). And Eq. (3) can be well satisfied for split nanorings when the gap size is less than 1/10 λ SP.

3. Refractive index sensitivities of Au ring-nanosensors

According to previous experimental and mathematical simulation results, the main resonance (N = 2) wavelength is unchanged with different incident angle for perfect NRs [67], which means Eq. (2) should be satisfied even with normal incident excitation, i.e. λ SP is a constant at main resonance. Since there have no SP propagation processes involved when φ = 0, the property of λ SP correlated resonances must be an inside mechanism for NR structures.

As for MPRs of perfect and split NRs with the same size, λ SP is a constant for sub-resonance mode, since C is a constant too, it can be predicted that the n sensitivities are proportional to their mode number’s reciprocal, i.e. 1/N or 1/M. And for the main resonance of split NRs (M = 1), the n sensitivity should be 100% larger than those of perfect NRs (N = 2).

 

Fig. 2. (a). Extinction spectra for perfect Au NRs of circular with different environmental refractive index n, where R = 100 nm, φ = 90°, and the thin solid line is the spectra for φ = 0 with n = 1.33. (b). Extinction spectra for the same sized split Au NRs of circular with different environmental n, where φ = 0°.

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Figure 2(a) is the extinction spectra for perfect NRs in different environmental index n, where R = 100 nm, and φ = 90°. The thin solid line is the spectra for φ = 0 in n = 1.33, there is only the main resonance, and the resonance peak position is unchanged compared with φ = 90° [67]. The spectra for the same sized split NRs with different index n are shown in Fig. 2(b), where φ = 0, and for the excitation wavelength that longer than 1900 nm, the material response of Au is modeled using plasma dispersion εP(ω)=-ωp 2/2πω(2πω+iΓ), the following parameters were employed, the plasma frequency ωp=1.35 × 1016 Hz, and the damping constant Γ= 1.3 1 × 1014 Hz.

 

Fig. 3. (a). λ RES shifts that related to the resonance position in n = 1.33 for different resonance modes. (b). λ SP versus excitation wavelength for a rod with r = 25 nm, and the average λ SP for different modes are labeled.

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When n = 1.33, the resonance wavelengths are 2144, 1018, 817 and 658 nm for resonance modes 1 to 4, respectively, and Fig. 3(a) represents λ RES shifts that related to the resonance position in n = 1.33. The slopes for different modes do proportional to their mode number’s reciprocal, and the slope for the mode M = 1 is about 100% larger than N = 2, indicating the refractive index sensitivity of the main resonance for split NRs has increased about one time compared to perfect NRs. Table 2 is the corresponding λ SP at resonances shown in the spectra. The variation of λ SP is within ±2 nm for a certain mode, and Eqs. (2) and (3) have been well satisfied. Figure 3(b) gives the relationship between excitation wavelength and λ SP for a rod with r = 25 nm in different n, and the average λ SP for different modes are labeled. The mathematical simulation results agree well with the predictions.

Tables Icon

Table 2. λ SP for Different Resonance Modes with Different Environmental Refractive Index n.

4. Local field enhancements of Au ring-nanoantennas

NRs of square have the same property as NRs of circular [67], and since NRs of square are easier to be fabricated, NRs of square will be discussed in this section. Figure 4(a) is the cross section structures of NRs of square, T and H are the thickness and height, respectively. In this section, the parameters are fixed at n = 1, T = 45 nm, H = 30 nm, and the excitation wavelength is 800 nm, where ε Au = -24+1.53i. Modify NR radius, I distributions that the local field enhancement reach the maximums for different modes are shown in Fig. 4(b)–4(g), where φ = 85°. The variance of C is about 500 nm for adjacent modes, while λ SP is measured about 520 nm according the images of field distribution, which means Eq. (2) is also satisfied by NRs of square.

 

Fig. 4. (a). Cross section structures of perfect and split Au NRs of square, where R is ring radius, T is the thickness, H is the height, d and w are the widths of middle and side gaps, respectively, and θ is the angle between the two side gaps. (b). I distributions obtained at the cross section for perfect Au NRs of square with R = 92nm, (c). 170 nm, (d). 250 nm, (e). 330 nm, (f) 406 nm, and (g) 482 nm, where T = 45 nm, H = 30 nm, the excitation wavelength is 800 nm, φ = 85°, and the local field enhancement has reach the maximum for different modes.

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I distributions of the sub-resonance mode N = 6 with different incident angles are shown in Fig. 5. When φ = 0, the NR reveals dipole mode but out of main resonance, and the local field enhancement is very weak. The multipolar plasmons are excited when φ ≠ 0, and the field enhancement is increasing with the increase of φ.

 

Fig. 5. (a). I distributions for perfect NR with φ = 0. (b) 30° and (c) 90°, where the excitation wavelength is 800 nm, R = 250 nm, T = 45 nm, and H = 30 nm.

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From the I distributions or field evolution in time domain, it is found that the field enhancement on the right side is much stronger than the left side for sub-resonances that under oblique incident excitations. It can be understood that there are SP propagation processes for φ > 0, and the energy is focusing to the right side. This property means NRs can be used as plasmonic lens, and the same property was also found in disk structures [78, 79]. It is well known that a small gap between two nanoparticles would lead to very strong SP interactions, and a so called “hot spot” would be formed in the gap. We will show that by using its energy focusing property, the local field enhancement for split NRs can be much stronger than dipole nanoantennas [72]. The gaps are addressed as shown in Fig. 4(a), where d and w are, respectively, the widths of the middle and side gaps. And θ is the angle between the two side gaps. The enhancement of four types of NRs will be discussed: type 1, w = d = 0, i.e. perfect NRs; type 2, w ≠ 0 and d = 0; type 3, w = 0 and d ≠ 0; and type 4, w ≠ 0 and d ≠ 0.

 

Fig. 6. (a). I distributions for perfect NR (type 1), (b) split NR with 2 gaps (type 2), (c) 1 gaps (type 3), and (d) 3 gaps (type 4). Where the excitation wavelength is 800 nm, φ = 85°, d = w = 30 nm, R = 250 nm for type 1 and 2, R = 275 nm for type 3 and 4, λ = 52° for type 2, and θ = 80° for type 4. (e) I distribution of dipole antennas, where the gap width is 30 nm, the length of a single rod is 142 nm, and the field enhancement has reached the maximum.

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The gaps of type 2 are located around the right two field packet peaks of perfect NRs. Modify w and θ, Fig. 6(b) shows the I distribution of type 2 for φ = 85°, where the local field enhancement on the right side has reach the maximum, R = 250 nm, w = 30 nm, and θ = 52°. And compared with perfect NR shown in Fig. 6(a), the local field on the right side has gained a great enhancement. In the calculations, it is found that w and θ should not be too large or too small to get a strong enhancement. Because for a long gap w, SP is not easy to transmit across the gap, and the energy can not focus to the right part; and for a short gap, SP can propagate to the right side very easily, but the energy is only propagate along the surface of the NR, and the SP interactions in the gaps are weak. As for a large θ, for example θ = 60°, the gaps are right addressed on the two field packet peaks, the energy can only transmit through the ring surface, and the SP interactions in the gaps are weak; the right piece of the NR can be seen as a single rod antennas, the rod is out of its resonance for a small θ, and the field enhancement is also weak. (Please see the Appendix for better understanding.)

Unlike a dimer, the SP interactions in the gaps are not so strong for type 2, so the ring structures are modified as type 3 and 4. For type 3, R is increased to 275 nm to gain the maximum local field enhancement for the mode M = 7. The corresponding I distribution is shown in Fig. 6(c), where d = 30 nm and φ = 85°. Strong SP interactions occurred in the gap, and there is a huge field enhancement. For the structure of type 4, two side gaps are introduced to increase SP interactions, and the field enhancement on the right side reaches the maximum when w = 30 nm, and θ = 80°. Figure 6(d) is the corresponding I distribution. Compared with Fig. 6(c), the field intensity in the middle gap has increased dramatically. It is also noted that for type 4, the sub field peaks enhancement around the ring is weaker than that of type 3, which means most of the energy has focused to the right side for type 4. And for the same reasons as type 2, w and θ should not be too large or too small to get the strongest enhancement. As a comparison, Fig. 6(e) shows the I distribution of dipole antennas with φ = 85°, where the gap width is 30 nm, the singe rod length is 142 nm, and the local field enhancement has reached the maximum. It can be seen the field enhancement of type 4 is much stronger than the dipole antennas too.

 

Fig. 7. Local field intensity enhancement versus φ for different structures.

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The relationships between local field enhancement and incident angle φ for different structures are displayed in Fig. 7, where local field intensity integrated in the middle gap I Int = ∫I ds has been calculated, and the integral area is about 45×30 nm2. The field enhancement for dipole antennas is a constant for different φ, while it is increasing with the increase of φ for split NRs. The field enhancement for split NR of type 4 is much stronger than that of type 3, it is even stronger than dipole antennas when φ > 60°, and the field intensity in the gap is increased by 37% than that of dipole antennas when φ = 90°.

5. Conclusion

In conclusion, MPRs that induced by multipolar plasmons excitation and propagation in Au NRs with symmetry broken are investigated. It is found that MPRs are correlated to ring circumference and suface plasmon wavelength of the rod. And for perfect NRs, there will be a resonance when the ring circumference is about an integer times of SP wavelength, while a semi-integer for split NRs with one gap. These relationships reveal that the refractive index sensitivities for MPRs are proportional to their mode number’s reciprocal. And the refractive index sensitivity of split NRs at main resonance is about 100% larger than those of perfect NRs with same size. For SPPs propagation processes that under oblique incident excitation, the energy is focusing to one side of the NRs, and NR can be used as plasmonic lens. The local field intensity enhancement of split NR with three gaps has increased about 37% than that of dipole antennas.

Appendix A: Local field enhancements versus different ring structures

For split NRs with two side gaps (type 2), when the gap width w = 30 nm, I distributions with θ = 48°, 52°, and 60° are displayed in Fig. 8(a)–8(c), respectively, where φ = 85 , R = 250 nm, the excitation wavelength is 800 nm. The plot on the right side of the ring is the brightest for θ = 52°, indicating it has the largest local field enhancement. When θ = 60°, the gaps are right addressed on the two field packet peaks, the energy can only transmit through the ring surface, the SP interactions in the gaps are weak, and the field enhancement on the right side is not strong. When θ = 48°, the right piece of the split ring is far out of resonance for its short length, and the field enhancement on the right side is also weak. To investigate the local field enhancement under different situations, local field intensity integrated I Int = ∫I ds has been calculated, where the integral area is about 142 × 274 nm2 around the right piece part of the split NRs. The circle points in Fig. 8(g) represent the relationship between I Int and θ when w = 30 nm, the filed intensity enhancement reaches the maximum when θ is about 52°.

 

Fig. 8. (a). I distributions for split NRs of type 2 with θ = 48°, (b) 52°, and (c) 60°, where w = 30 nm, φ = 85°, and R =250 nm. (d) I distributions with θ = 52° for w = 10 nm, (e) 26 nm, and (f) 44 nm. (g) The relationship between local field enhancement I Int and θ when w = 30 nm (circle point), as well as the relationship between I Int and w when θ = 52° (square point).

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When θ = 52°, Fig. 8(d)–(f) represent I distributions with w = 10, 26, and 44 nm, respectively. For this type NRs with two side gaps that under oblique incident excitations, the local field enhancements of smaller gap size ring have been calculated with different excitation wavelengths, and the changes of resonance wavelengths are within 10 nm. The main reason that causes the weaker enhancement for smaller gap size ring is that, on the two sides of one gap, the charge is the same according to the calculations of the charge distributions, and there are not strong SP interactions as dipole nanoantennas [72]. Like a perfect NR, SPPs are very easy to transmit through the narrow gaps when w = 10 nm, SP interactions in the gaps are weak, and the local filed enhancement on the right side is not so strong for small gaps. When w = 44 nm, the gap is too large for SP energy transmission, the right piece of the ring is nearly isolated, and the local field enhancement is also weak. The square points in Fig. 8(g) show the relationship between I Int and w when θ= 52°, the filed intensity enhancement reaches the maximum when w is about 30 nm. From 8(g), it is found the local field enhancement is the largest when w ≈ 30 nm and θ ≈ 52° for this sub-resonance mode (N = 6).

For split NRs with three gaps (type 4), Fig. 9(a)–9(b) represent / distributions for θ = 70°, 80 , and 96 , respectively, where w = 30 nm, and R = 275 nm. For the same reasons as split NRs with two gaps, the plot on the right side of the ring is the brightest for θ = 80°, indicating it has the largest local field enhancement. The circle points in Fig. 9(g) show the relationship between I Int and θ when w = 30 nm, where the integral area for I Int is about 45 × 30 nm2 that in the middle gap of the split NRs, and the filed intensity enhancement reaches the maximum when θ is about 80°.

 

Fig. 9. (a). I distributions for split NRs of type 4 with θ = 70°, (b) 80°, and (c) 96°, where w = 30 nm, φ = 85°, and R =275 nm. (d) I distributions with θ = 80° for w = 0, (e) 26 nm, and (f) 44 nm. (g) The relationship between local field enhancement I Int and θ when w = 30 nm (circle points), as well as the relationship between I Int and w when θ = 80° (square points).

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When θ = 80°, Fig. 9(d)–9(f) represent I distributions with w = 0, 26, and 44 nm, respectively. And θ is also should not be too large or too small to get the strongest local field enhancement. The square points in Fig. 9(g) display the relationship between IInt and w when θ = 80°, the filed intensity reaches the maximum when w is about 30 nm. From 9(g), it is found the local field enhancement is the largest when w ≈ 30 nm and θ ≈ 80° for this sub-resonance mode (M = 7).

Acknowledgments

This work was supported by the Natural Science Foundation of China (10534030, 10874134), the National Program on Key Science Research (2007CB935300) and Key Project of Ministry of Education (708063).

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31. K. A. Matveev, A. I. Larkin, and L. I. Glazman, “Persistent current in superconducting nanorings,” Phys. Rev. Lett. 89, 096802 (2002). [CrossRef]   [PubMed]  

32. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 Terahertz,” Science 306, 1351 (2004). [CrossRef]   [PubMed]  

33. S. Zou, “Light-driven circular plasmon current in a silver nanoring,” Opt. Lett. 33, 2113 (2008), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-18-2113. [CrossRef]   [PubMed]  

34. B. Wang and G. P. Wang, “Plasmonic waveguide ring resonator at terahertz frequencies,” Appl. Phys. Lett. 89, 133106 (2006). [CrossRef]  

35. S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508 (2006). [CrossRef]   [PubMed]  

36. K. Y. Jung, F. L. Teixeira, and R. M. Reano, “Au/SiO2 nanoring plasmon waveguides at optical communication band,” J. Lightwave Technol. 25, 2757 (2007). [CrossRef]  

37. A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101, 043902 (2008). [CrossRef]   [PubMed]  

38. J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, “Resonant and non-resonant generation and focusing of surface plasmons with circular gratings,” Opt. Express 14, 5664 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-12-5664. [CrossRef]   [PubMed]  

39. S. Seo, H. C. Kim, H. Ko, and M. Cheng, “Subwavelength proximity nanolithography using a plasmonic lens,” J. Vac. Sci. Technol. B 25, 2271 (2007). [CrossRef]  

40. G. Laurent, N. Félidj, J. Grand, J. Aubard, and G. Lévi, “Raman scattering images and spectra of gold ring arrays,” Phys. Rev. B 73, 245417 (2006). [CrossRef]  

41. S. Wang, D. F. P. Pile, C. Sun, and X. Zhang, “Nanopin plasmonic resonator array and its optical properties,” Nano Lett. 7, 1076 (2007). [CrossRef]   [PubMed]  

42. F. Hao, P. Nordlander, M. T. Burnett, and S. A. Maier, “Enhanced tenability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities,” Phys. Rev. B 76, 245417 (2007). [CrossRef]  

43. A. W. Clark, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Nanophotonic split-ring resonators as dichroics for molecular spectroscopy,” Appl. Phys. Lett. 93, 023121 (2008). [CrossRef]  

44. G. L. Liu, Y. Lu, J. Kim, J. C. Doll, and L. P. Lee, “Magnetic nanocrescents as controllable surface-enhanced Raman scattering nanoprobes for biomolecular imaging,” Adv. Mater. 17, 2683 (2005). [CrossRef]  

45. Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5, 119 (2005). [CrossRef]   [PubMed]  

46. S. Kim, J. M. Jung, D. G. Choi, H. T. Jung, and S. M. Yang, “Patterned arrays of Au rings for localized surface plasmon resonance,” Langmuir 22, 7109 (2006). [CrossRef]   [PubMed]  

47. E. M. Larsson, J. Alegret, M. Käll, and D. S. Sutherland, “Sensing characteristics of NIR localized surface plasmon resonances in gold nanorings for application as ultrasensitive biosensors,” Nano Lett. 7, 1256 (2007). [CrossRef]   [PubMed]  

48. J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003). [CrossRef]   [PubMed]  

49. 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, 494 (2008). [CrossRef]   [PubMed]  

50. J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transf. 89, 11 (2004). [CrossRef]  

51. T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, “Annular nanoantenna on fibre micro-axicon,” J. Microsc. 229, 354 (2007). [CrossRef]  

52. M. A. Suarez, T. Grosjean, D. Charraut, and D. Courjon, “Nanoring as a magnetic or electric field sensitive nano-antenna for near-field optics applications,” Opt. Commun. 270, 447 (2007). [CrossRef]  

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

54. Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101, 043903 (2008). [CrossRef]   [PubMed]  

55. A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171 (2008). [CrossRef]   [PubMed]  

56. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31 (2008). [CrossRef]  

57. S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, and B. A. Kalinikos, “Experimental observation of symmetry-breaking nonlinear modes in an active ring,” Nature 426, 159 (2003). [CrossRef]   [PubMed]  

58. H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and N. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. 103, 10856 (2006). [CrossRef]   [PubMed]  

59. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: Subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8, 3983 (2008). [CrossRef]   [PubMed]  

60. E. M. Larsson, F. Hao, L. Eurenius, E. Olsson, P. Nordlander, and D. S. Sutherland, “Plasmon hybridization in stacked double gold nanorings with reduced symmetry,” Small 4, 1630 (2008). [CrossRef]   [PubMed]  

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

62. N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351 (2008). [CrossRef]  

63. K. Li, L. Clime, L. Tay, B. Cui, M. Geissler, and T. Veres, “Multiple surface plasmon resonances and near-infrared field enhancement of gold nanowells,” Anal. Chem. 80, 4945 (2008). [CrossRef]   [PubMed]  

64. A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Multiple plasmon resonances from gold nanostructures,” Appl. Phys. Lett. 90, 143105 (2007). [CrossRef]  

65. A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonantors,” Appl. Phys. Lett. 91, 093109 (2007). [CrossRef]  

66. A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Fabrication and tuning of nanoscale metallic ring and split-ring arrays,” J. Vac. Sci. Technol. B 25, 2628 (2007). [CrossRef]  

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68. A. Dmitriev, C. Hägglund, S. Chen, H. Fredriksson, T. Pakizeh, M. Käll, and D. S. Sutherland, “Enhanced nanoplasmonic optical sensors with reduced substrate effect,” Nano Lett. 8, 3893 (2008). [CrossRef]   [PubMed]  

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77. S. D. Liu, M. T. Cheng, Z. J. Yang, and Q. Q. Wang, “Surface plasmon propagation in a pair of metal nanowires coupled to a nanosized optical emitter,” Opt. Lett. 33, 851 (2008), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-8-851. [CrossRef]   [PubMed]  

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2009 (1)

H. M. Gong, L. Zhou, X. R. Su, S. Xiao, S. D. Liu, and Q. Q. Wang, “Lighting up dark plasmons of Bi-crystal silver ring-nanoantenna to enhance exciton-plasmon interactions,” Adv. Funct. Mater. 19, 298( 2009).
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2008 (18)

S. Zou, “Light-driven circular plasmon current in a silver nanoring,” Opt. Lett. 33, 2113 (2008), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-18-2113.
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X. Peng and I. Kamiya, “Two methods to prepare nanorings/nanoholes for the fabrication of vertical nanotransistors,” Nanotechnology 19, 315303 (2008).
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H. G. Liu, C. W. Wang, J. P. Wu, Y. I. Lee, and J. Hao, “Gold and silver nanorings formed at the air/water interface,” Colloid Surf. A-Physicochem. Eng. Asp. 312, 203 (2008).
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Z. H. Yuan, W. Zhou, Y. Q. Duan, and L. J. Bie, “A simple approach for large-area fabrication of Ag nanorings,” Nanotechnology 19, 075608 (2008).
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A. Drezet, C. Genet, and T. W. Ebbesen, “Miniature plasmonic wave plates,” Phys. Rev. Lett. 101, 043902 (2008).
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A. W. Clark, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Nanophotonic split-ring resonators as dichroics for molecular spectroscopy,” Appl. Phys. Lett. 93, 023121 (2008).
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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, 494 (2008).
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Y. Gorodetski, A. Niv, V. Kleiner, and E. Hasman, “Observation of the spin-based plasmonic effect in nanoscale structures,” Phys. Rev. Lett. 101, 043903 (2008).
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A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171 (2008).
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N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nature Mater. 7, 31 (2008).
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N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351 (2008).
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K. Li, L. Clime, L. Tay, B. Cui, M. Geissler, and T. Veres, “Multiple surface plasmon resonances and near-infrared field enhancement of gold nanowells,” Anal. Chem. 80, 4945 (2008).
[Crossref] [PubMed]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, “Symmetry breaking in plasmonic nanocavities: Subradiant LSPR sensing and a tunable Fano resonance,” Nano Lett. 8, 3983 (2008).
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E. M. Larsson, F. Hao, L. Eurenius, E. Olsson, P. Nordlander, and D. S. Sutherland, “Plasmon hybridization in stacked double gold nanorings with reduced symmetry,” Small 4, 1630 (2008).
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F. Hao, E. M. Larsson, T. A. Ali, D. S. Sutherland, and P. Nordlander, “Shedding light on dark plasmons in gold nanorings,” Chem. Phys. Lett. 458, 262 (2008).
[Crossref]

A. Dmitriev, C. Hägglund, S. Chen, H. Fredriksson, T. Pakizeh, M. Käll, and D. S. Sutherland, “Enhanced nanoplasmonic optical sensors with reduced substrate effect,” Nano Lett. 8, 3893 (2008).
[Crossref] [PubMed]

C. M. Dutta, T. A. Ali, D. W. Brandl, T. H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129, 084706 (2008).
[Crossref] [PubMed]

S. D. Liu, M. T. Cheng, Z. J. Yang, and Q. Q. Wang, “Surface plasmon propagation in a pair of metal nanowires coupled to a nanosized optical emitter,” Opt. Lett. 33, 851 (2008), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-33-8-851.
[Crossref] [PubMed]

2007 (16)

A. Mary, D. M. Koller, A. Hohenau, J. R. Krenn, A. Bouhelier, and A. Dereux, “Optical absorption of torus-shaped metal nanoparticles in the visible range,” Phys. Rev. B 76, 245422 (2007).
[Crossref]

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
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V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
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A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Multiple plasmon resonances from gold nanostructures,” Appl. Phys. Lett. 90, 143105 (2007).
[Crossref]

A. W. Clark, A. K. Sheridan, A. Glidle, D. R. S. Cumming, and J. M. Cooper, “Tuneable visible resonances in crescent shaped nano-split-ring resonantors,” Appl. Phys. Lett. 91, 093109 (2007).
[Crossref]

A. K. Sheridan, A. W. Clark, A. Glidle, J. M. Cooper, and D. R. S. Cumming, “Fabrication and tuning of nanoscale metallic ring and split-ring arrays,” J. Vac. Sci. Technol. B 25, 2628 (2007).
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T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, “Annular nanoantenna on fibre micro-axicon,” J. Microsc. 229, 354 (2007).
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M. A. Suarez, T. Grosjean, D. Charraut, and D. Courjon, “Nanoring as a magnetic or electric field sensitive nano-antenna for near-field optics applications,” Opt. Commun. 270, 447 (2007).
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E. M. Larsson, J. Alegret, M. Käll, and D. S. Sutherland, “Sensing characteristics of NIR localized surface plasmon resonances in gold nanorings for application as ultrasensitive biosensors,” Nano Lett. 7, 1256 (2007).
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S. Wang, D. F. P. Pile, C. Sun, and X. Zhang, “Nanopin plasmonic resonator array and its optical properties,” Nano Lett. 7, 1076 (2007).
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F. Hao, P. Nordlander, M. T. Burnett, and S. A. Maier, “Enhanced tenability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities,” Phys. Rev. B 76, 245417 (2007).
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S. Seo, H. C. Kim, H. Ko, and M. Cheng, “Subwavelength proximity nanolithography using a plasmonic lens,” J. Vac. Sci. Technol. B 25, 2271 (2007).
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W. S. Liao, X. Chen, J. Chen, and P. S. Cremer, “Templating water stains for nanolithography,” Nano Lett. 7, 2452 (2007).
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H. Rochholz, N. Bocchio, and M. Kreiter, “Tuning resonances on crescent-shaped noble-metal nanoparticles,” New J. Phys. 9, 53 (2007).
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K. Y. Jung, F. L. Teixeira, and R. M. Reano, “Au/SiO2 nanoring plasmon waveguides at optical communication band,” J. Lightwave Technol. 25, 2757 (2007).
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Y. Lei, W. Cai, and G. Wilde, “Highly ordered nanostructures with tunable size shape and properties: A new way to surface nano-patterning using ultra-thin alumina masks,” Prog. Mater. Sci. 52, 465 (2007).
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2006 (16)

G. Shen and D. Chen, “Self-coiling of Ag2V4O11 nanobelts into perfect nanorings and microloops,” J. Am. Chem. Soc. 128, 11762 (2006).
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B. Wang and G. P. Wang, “Plasmonic waveguide ring resonator at terahertz frequencies,” Appl. Phys. Lett. 89, 133106 (2006).
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S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508 (2006).
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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, 243902 (2006).
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Y. B. Zheng, S. J. Wang, A. C. H. Huan, and Y. H. Wang, “Fabrication of large area ordered metal nanoring arrays for nanoscale optical sensors,” J. Non-Cryst. Solids 352, 2532 (2006).
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S. M. Yang, S. G. Jang, D. G. Choi, S. Kim, and H. K. Yu, “Nanomachining by colloidal lithography,” Small 2, 458 (2006).
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F. Sun, J. C. Yu, and X. Wang, “Construction of size-controllable hierarchical nanoporous TiO2 ring arrays and their modifications,” Chem. Mater. 18, 3774 (2006).
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S. Zhao, H. Roberge, A. Yelon, and T. Veres, “New application of AAO template: A mold for nanoring and nanocone arrays,” J. Am. Chem. Soc. 128, 12352 (2006).
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G. Duan, W. Cai, Y. Luo, Z. Li, and Y. Lei, “Hierarchical structured Ni nanorings and hollow sphere arrays by morphology inheritance based on ordered through-pore template and electrodeposition,” J. Phys. Chem. B 110, 15729 (2006).
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S. Wang, G. J. Yu, J. L. Gong, Q. T. Liu, H. J. Xu, D. Z. Zhu, and Z. Y. Zhu, “Large-area fabrication of periodic Fe nanorings with controllable aspect ratios in porous alumina templates,” Nanotechnology 17, 1594 (2006).
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G. Laurent, N. Félidj, J. Grand, J. Aubard, and G. Lévi, “Raman scattering images and spectra of gold ring arrays,” Phys. Rev. B 73, 245417 (2006).
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J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, “Resonant and non-resonant generation and focusing of surface plasmons with circular gratings,” Opt. Express 14, 5664 (2006), http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-14-12-5664.
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S. Kim, J. M. Jung, D. G. Choi, H. T. Jung, and S. M. Yang, “Patterned arrays of Au rings for localized surface plasmon resonance,” Langmuir 22, 7109 (2006).
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H. Wang, Y. Wu, B. Lassiter, C. L. Nehl, J. H. Hafner, P. Nordlander, and N. J. Halas, “Symmetry breaking in individual plasmonic nanoparticles,” Proc. Natl. Acad. Sci. 103, 10856 (2006).
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A. Mary, A. Dereux, and T. L. Ferrell, “Localized surface plasmons on a torus in the nonretarded approximation,” Phys. Rev. B 72, 155426 (2006).
[Crossref]

Z. Liu, J. M. Steele, H. Lee, and X. Zhang, “Tuning the focus of a plasmonic lens by the incident angle,” Appl. Phys. Lett. 88, 171108 (2006).
[Crossref]

2005 (6)

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Lett. 5, 1726 (2005).
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P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607 (2005).
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G. L. Liu, Y. Lu, J. Kim, J. C. Doll, and L. P. Lee, “Magnetic nanocrescents as controllable surface-enhanced Raman scattering nanoprobes for biomolecular imaging,” Adv. Mater. 17, 2683 (2005).
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Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5, 119 (2005).
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D. Marczewski and W. A. Goedel, “The preparation of submicrometer-sized rings by embedding and selective etching of spherical silica particles,” Nano Lett. 5, 295 (2005).
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X. W. Zhang, N. F. Chen, and F. Yan, “Heteroepitaxial gold (111) rings on mica substrates,” Appl. Phys. Lett. 86, 203102 (2005).
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2004 (7)

X. Y. Kong, Y. Ding, R. Yang, and Z. L. Wang, “Single-crystal nanorings formed by epitaxial self-coiling of polar nanobelts,” Science 303, 1348 (2004).
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C. R. L. P. N. Jeukens, M. C. Lensen, F. J. P. Wijnen, J. A. A. W. Elemans, P. C. M. Christianen, A. E. Rowan, J. W. Gerritsen, R. J. M. Nolte, and J. C. Maan, “Polarized absorption and emission of ordered self-assembled porphyrin rings,” Nano Lett. 4, 1401 (2004).
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S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 Terahertz,” Science 306, 1351 (2004).
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J. M. McLellan, M. Geissler, and Y. Xia, “Edge spreading lithography and its application to the fabrication of mesoscopic gold and silver rings,” J. Am. Chem. Soc. 126, 10830 (2004).
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K. L. Hobbs, P. R. Larson, G. D. Lian, J. C. Keay, and M. B. Johnson, “Fabrication of nanoring arrays by sputter redeposition using porous alumina templates,” Nano Lett. 4, 167 (2004).
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F. Yan and W. A. Goedel, “Preparation of mesoscopic gold rings using particle imprinted templates,” Nano Lett. 4, 1193 (2004).
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J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transf. 89, 11 (2004).
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2003 (6)

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
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S. O. Demokritov, A. A. Serga, V. E. Demidov, B. Hillebrands, M. P. Kostylev, and B. A. Kalinikos, “Experimental observation of symmetry-breaking nonlinear modes in an active ring,” Nature 426, 159 (2003).
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E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “Ahybridization model for the plasmon response of complex nanostructures,” Science 302, 419 (2003).
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N. Jiang, G. G. Hembree, J. C. H. Spence, and J. Qiu, “Nanoring formation by direct-write inorganic electron-beam lithography,” Appl. Phys. Lett. 83, 551 (2003).
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D. Granados and J. M. Garcia, “In(Ga)As self-assembled quantum ring formation by molecular beam epitaxy,” Appl. Phys. Lett. 82, 2401 (2003).
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T. Raz, D. Ritter, and G. Bahir, “Formation of InAs self-assembled quantum rings on InP,” Appl. Phys. Lett. 82, 1706 (2003).
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2002 (1)

K. A. Matveev, A. I. Larkin, and L. I. Glazman, “Persistent current in superconducting nanorings,” Phys. Rev. Lett. 89, 096802 (2002).
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2001 (3)

S. P. Li, D. Peyrade, M. Natali, A. Lebib, and Y. Chen, “Flux closure structures in cobalt rings,” Phys. Rev. Lett. 86, 1102 (2001).
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E. M. O. Jariwala, P. Mohanty, M. B. Ketchen, and R. A. Webb, “Diamagnetic persistent current in diffusive normal-metal rings,” Phys. Rev. Lett. 86, 1594 (2001).
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R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292, 77 (2001).
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2000 (1)

A. Lorke, R. J. Luyken, A. O. Govorov, and J. P. Kotthaus, “Spectroscopy of nanoscopic semiconductor rings,” Phys. Rev. Lett. 84, 2223 (2000).
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1997 (1)

J. M. Garcia, G. Medeiros-Ribeiro, K. Schmidt, T. Ngo, J. L. Feng, A. Lorke, J. Kottaus, and P. M. Petroff, “Intermixing and shape changes during the formation of InAs self-assembled quantum dots,” Appl. Phys. Lett. 71, 2014 (1997).
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1994 (1)

1972 (1)

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

Aizpurua, J.

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transf. 89, 11 (2004).
[Crossref]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[Crossref] [PubMed]

Alegret, J.

E. M. Larsson, J. Alegret, M. Käll, and D. S. Sutherland, “Sensing characteristics of NIR localized surface plasmon resonances in gold nanorings for application as ultrasensitive biosensors,” Nano Lett. 7, 1256 (2007).
[Crossref] [PubMed]

Ali, T. A.

F. Hao, E. M. Larsson, T. A. Ali, D. S. Sutherland, and P. Nordlander, “Shedding light on dark plasmons in gold nanorings,” Chem. Phys. Lett. 458, 262 (2008).
[Crossref]

C. M. Dutta, T. A. Ali, D. W. Brandl, T. H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129, 084706 (2008).
[Crossref] [PubMed]

Anderton, C. R.

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, 494 (2008).
[Crossref] [PubMed]

Aubard, J.

G. Laurent, N. Félidj, J. Grand, J. Aubard, and G. Lévi, “Raman scattering images and spectra of gold ring arrays,” Phys. Rev. B 73, 245417 (2006).
[Crossref]

Bahir, G.

T. Raz, D. Ritter, and G. Bahir, “Formation of InAs self-assembled quantum rings on InP,” Appl. Phys. Lett. 82, 1706 (2003).
[Crossref]

Bie, L. J.

Z. H. Yuan, W. Zhou, Y. Q. Duan, and L. J. Bie, “A simple approach for large-area fabrication of Ag nanorings,” Nanotechnology 19, 075608 (2008).
[Crossref] [PubMed]

Blanco, L.

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transf. 89, 11 (2004).
[Crossref]

Bocchio, N.

H. Rochholz, N. Bocchio, and M. Kreiter, “Tuning resonances on crescent-shaped noble-metal nanoparticles,” New J. Phys. 9, 53 (2007).
[Crossref]

Bouhelier, A.

A. Mary, D. M. Koller, A. Hohenau, J. R. Krenn, A. Bouhelier, and A. Dereux, “Optical absorption of torus-shaped metal nanoparticles in the visible range,” Phys. Rev. B 76, 245422 (2007).
[Crossref]

Bozhevolnyi, S. I.

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508 (2006).
[Crossref] [PubMed]

Brandl, D. W.

C. M. Dutta, T. A. Ali, D. W. Brandl, T. H. Park, and P. Nordlander, “Plasmonic properties of a metallic torus,” J. Chem. Phys. 129, 084706 (2008).
[Crossref] [PubMed]

Bryant, G. W.

J. Aizpurua, L. Blanco, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Light scattering in gold nanorings,” J. Quant. Spectrosc. Radiat. Transf. 89, 11 (2004).
[Crossref]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. G. de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90, 057401 (2003).
[Crossref] [PubMed]

Burnett, M. T.

F. Hao, P. Nordlander, M. T. Burnett, and S. A. Maier, “Enhanced tenability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities,” Phys. Rev. B 76, 245417 (2007).
[Crossref]

Cai, W.

Y. Lei, W. Cai, and G. Wilde, “Highly ordered nanostructures with tunable size shape and properties: A new way to surface nano-patterning using ultra-thin alumina masks,” Prog. Mater. Sci. 52, 465 (2007).
[Crossref]

G. Duan, W. Cai, Y. Luo, Z. Li, and Y. Lei, “Hierarchical structured Ni nanorings and hollow sphere arrays by morphology inheritance based on ordered through-pore template and electrodeposition,” J. Phys. Chem. B 110, 15729 (2006).
[Crossref] [PubMed]

Chang, D. E.

D. E. Chang, A. S. Sørensen, P. R. Hemmer, and M. D. Lukin, “Strong coupling of single emitters to surface plasmons,” Phys. Rev. B 76, 035420 (2007).
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Zhao, S.

S. Zhao, H. Roberge, A. Yelon, and T. Veres, “New application of AAO template: A mold for nanoring and nanocone arrays,” J. Am. Chem. Soc. 128, 12352 (2006).
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N. I. Zheludev, S. L. Prosvirnin, N. Papasimakis, and V. A. Fedotov, “Lasing spaser,” Nat. Photonics 2, 351 (2008).
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V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, “Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry,” Phys. Rev. Lett. 99, 147401 (2007).
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Zhou, J.

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Nanotechnology (3)

X. Peng and I. Kamiya, “Two methods to prepare nanorings/nanoholes for the fabrication of vertical nanotransistors,” Nanotechnology 19, 315303 (2008).
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Z. H. Yuan, W. Zhou, Y. Q. Duan, and L. J. Bie, “A simple approach for large-area fabrication of Ag nanorings,” Nanotechnology 19, 075608 (2008).
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Nat. Photonics (1)

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Nature (2)

S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J. Y. Laluet, and T. W. Ebbesen, “Channel plasmon subwavelength waveguide components including interferometers and ring resonators,” Nature 440, 508 (2006).
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Supplementary Material (1)

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Figures (9)

Fig. 1.
Fig. 1. (a). Cross section structures of perfect and split Au NRs of circular, where R is ring radius, r is the rod radius, d = 30 nm is the gap width, and the light polarization is fixed along y-axis. (b). Extinction spectra for perfect NRs with different R, where the incident angle φ = 90°. (c). Extinction spectra for split NRs with different R, where φ = 0. (d). Field intensity I distributions for perfect Au NRs obtained at the cross section with R = 200 nm, where the excitation wavelengths are 1555, (e). 897, and (f). 666 nm, respectively. (g). I distributions for split Au NRs with R = 100nm, where the excitation wavelengths are 1626, and (h). 659 nm, respectively. The attached multimedia shows the time evolution processes of perfect NRs that under oblique incident excitations (Media 1).
Fig. 2.
Fig. 2. (a). Extinction spectra for perfect Au NRs of circular with different environmental refractive index n, where R = 100 nm, φ = 90°, and the thin solid line is the spectra for φ = 0 with n = 1.33. (b). Extinction spectra for the same sized split Au NRs of circular with different environmental n, where φ = 0°.
Fig. 3.
Fig. 3. (a). λ RES shifts that related to the resonance position in n = 1.33 for different resonance modes. (b). λ SP versus excitation wavelength for a rod with r = 25 nm, and the average λ SP for different modes are labeled.
Fig. 4.
Fig. 4. (a). Cross section structures of perfect and split Au NRs of square, where R is ring radius, T is the thickness, H is the height, d and w are the widths of middle and side gaps, respectively, and θ is the angle between the two side gaps. (b). I distributions obtained at the cross section for perfect Au NRs of square with R = 92nm, (c). 170 nm, (d). 250 nm, (e). 330 nm, (f) 406 nm, and (g) 482 nm, where T = 45 nm, H = 30 nm, the excitation wavelength is 800 nm, φ = 85°, and the local field enhancement has reach the maximum for different modes.
Fig. 5.
Fig. 5. (a). I distributions for perfect NR with φ = 0. (b) 30° and (c) 90°, where the excitation wavelength is 800 nm, R = 250 nm, T = 45 nm, and H = 30 nm.
Fig. 6.
Fig. 6. (a). I distributions for perfect NR (type 1), (b) split NR with 2 gaps (type 2), (c) 1 gaps (type 3), and (d) 3 gaps (type 4). Where the excitation wavelength is 800 nm, φ = 85°, d = w = 30 nm, R = 250 nm for type 1 and 2, R = 275 nm for type 3 and 4, λ = 52° for type 2, and θ = 80° for type 4. (e) I distribution of dipole antennas, where the gap width is 30 nm, the length of a single rod is 142 nm, and the field enhancement has reached the maximum.
Fig. 7.
Fig. 7. Local field intensity enhancement versus φ for different structures.
Fig. 8.
Fig. 8. (a). I distributions for split NRs of type 2 with θ = 48°, (b) 52°, and (c) 60°, where w = 30 nm, φ = 85°, and R =250 nm. (d) I distributions with θ = 52° for w = 10 nm, (e) 26 nm, and (f) 44 nm. (g) The relationship between local field enhancement I Int and θ when w = 30 nm (circle point), as well as the relationship between I Int and w when θ = 52° (square point).
Fig. 9.
Fig. 9. (a). I distributions for split NRs of type 4 with θ = 70°, (b) 80°, and (c) 96°, where w = 30 nm, φ = 85°, and R =275 nm. (d) I distributions with θ = 80° for w = 0, (e) 26 nm, and (f) 44 nm. (g) The relationship between local field enhancement I Int and θ when w = 30 nm (circle points), as well as the relationship between I Int and w when θ = 80° (square points).

Tables (2)

Tables Icon

Table 1. The Resonance Wavelengths as Well as Their Corresponding λ SP that Shown in Fig. 1(b).

Tables Icon

Table 2. λ SP for Different Resonance Modes with Different Environmental Refractive Index n.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

k 2 2 k 2 J 0 ' ( k 2 R ) J 0 ( k 2 R ) k 1 2 k 1 H 0 ' ( k 1 R ) H 0 ( k 1 R ) = 0
C N × λ SP / 2 ( N = 2,4,6 …… )
C M × λ SP / 2 ( M = 1,3,5 …… )

Metrics