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Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 4 — Apr. 1, 2009
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High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation

S. D. Liu, Z. S. Zhang, and Q. Q. Wang  »View Author Affiliations


Optics Express, Vol. 17, Issue 4, pp. 2906-2917 (2009)
http://dx.doi.org/10.1364/OE.17.002906


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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

1. 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). [CrossRef] [PubMed]

], template method [8–17

8. 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). [CrossRef]

], molecular beam epitaxy [18–22

18. 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). [CrossRef]

], and polyol method [23

23. G. Shen and D. Chen, “Self-coiling of Ag2V4O11 nanobelts into perfect nanorings and microloops,” J. Am. Chem. Soc. 128, 11762 (2006). [CrossRef] [PubMed]

, 24

24. 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). [CrossRef]

]. The properties and possible applications for porphyrin NRs [25

25. 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). [CrossRef]

], semiconductor NRs [26

26. A. Lorke, R. J. Luyken, A. O. Govorov, and J. P. Kotthaus, “Spectroscopy of nanoscopic semiconductor rings,” Phys. Rev. Lett. 84, 2223 (2000). [CrossRef] [PubMed]

], magnetic NRs [27

27. S. P. Li, D. Peyrade, M. Natali, A. Lebib, and Y. Chen, “Flux closure structures in cobalt rings,” Phys. Rev. Lett. 86, 1102 (2001). [CrossRef] [PubMed]

, 28

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, 243902 (2006). [CrossRef]

], normal metal NRs [29–31

29. 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). [CrossRef] [PubMed]

], and noble metal NRs [32–54

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]

] have been well studied. Noble metal NRs or ring-like structures were proposed to be used for negative index of refraction [32

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

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]

], wave guiding [34–36

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

], miniature plasmonic wave plates [37

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

], focusing of surface plasmons [38

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

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]

], surface enhanced Raman scattering (SERS) [40–45

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]

], biosensors [46–50

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]

], and nanoantennas [51

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

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]

]. Noble metal NRs are particularly attractive for sensing applications due to their large cavity volumes and uniform electric fields inside the ring [48

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]

]. And the refractive index sensitivities of NRs are substantially larger than those of nanodisks with similar diameters [47

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]

].

Recently, symmetry broken systems have been drawn much attentions [55–60

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]

]. It is found that Cu split rings have sharp trapped-mode resonances [61

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]

], and Ag split NRs can be used to term a “lasing spaser” [62

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

]. Multipolar plasmons are excited in NRs with symmetry broken, and multipolar plasmon resonances (MPRs) have been found in the spectra [63–67

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]

]. Sheridan et al. argued that split NRs have MPRs [64–66

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]

]. While Hao et al. also found that under oblique incident excitations, MPRs appear in perfect NRs for retardation effects [67

67. 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]

]. 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

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]

]. 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

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]

], and Dmitriev et al. proved that a pillar can be used to reduce substrate effect [68

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]

]. By using the dyadic Green’s tensor approach and plasmon hybridization method, Mary et al. [69

69. 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]

, 70

70. 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]

] and Dutta et al. [71

71. 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]

] 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

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

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]

], but the local field enhancement is much weaker than that of dipole antennas [72

72. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607 (2005). [CrossRef] [PubMed]

].

In this paper, the spectra and near field distributions for NRs with symmetry broken have been calculated by discrete dipole approximation (DDA) [73

73. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491 (1994), http://www.opticsinfobase.org/abstract.cfm?URI=josaa-11-4-1491. [CrossRef]

] and finite difference time domain (FDTD) methods [74

74. A. Taflove and S. C. Hagness, Computational electrodynamics: The finite-difference time-domain method (Artech House, Boston, 2005).

], 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).

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

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

]. MPRs have been found in the spectra, as so called dark plasmons are excited [67

67. 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]

]. 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

76. 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). [CrossRef]

, 77

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]

],

k22k2J0'(k2R)J0(k2R)k12k1H0'(k1R)H0(k1R)=0
(1)

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……)
(2)

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.

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

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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

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]

], 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……)
(3)

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

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]

,69–71

69. 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]

]. 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

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°.

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

67. 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]

]. 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.

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

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4. Local field enhancements of Au ring-nanoantennas

NRs of square have the same property as NRs of circular [67

67. 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]

], 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.

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.

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

78. 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). [CrossRef] [PubMed]

, 79

79. 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]

]. 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

72. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607 (2005). [CrossRef] [PubMed]

]. 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.

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.

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).

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

72. P. Mühlschlegel, H. J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607 (2005). [CrossRef] [PubMed]

]. 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).

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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OCIS Codes
(130.6010) Integrated optics : Sensors
(240.6680) Optics at surfaces : Surface plasmons
(160.4236) Materials : Nanomaterials

ToC Category:
Optics at Surfaces

History
Original Manuscript: January 16, 2009
Revised Manuscript: February 10, 2009
Manuscript Accepted: February 10, 2009
Published: February 11, 2009

Virtual Issues
Vol. 4, Iss. 4 Virtual Journal for Biomedical Optics

Citation
S. D. Liu, Z. S. Zhang, and Q. Q. Wang, "High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation," Opt. Express 17, 2906-2917 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-4-2906


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References

  1. 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). [CrossRef] [PubMed]
  2. 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). [CrossRef] [PubMed]
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