Tunable Plasmon Resonances and Enhanced Local Fields of

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Tunable Plasmon Resonances and Enhanced Local Fields of Spherical Nanocrescents Tengfei Wu, Shaobo Yang, and Xingfei Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp3114122 • Publication Date (Web): 29 Mar 2013 Downloaded from http://pubs.acs.org on March 31, 2013

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The Journal of Physical Chemistry

Tunable Plasmon Resonances and Enhanced Local Fields of Spherical Nanocrescents Tengfei Wu, Shaobo Yang, and Xingfei Li*

*Corresponding Author: Address: 92 Weijin Road, Nankai District, Tianjin 300072, People’s Republic of China Tel.: 86-022-27403707 Fax: 86-022-27403707 Email: [email protected] Affiliation: State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, People’s Republic of China

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ABSTRACT: The tunable plasmon resonances of nanostructures with sharp features play an important role in the surface-enhanced spectroscopy. The maximum enhancement factor can be achieved by tuning the resonance wavelengths. In this study, the discrete-dipole approximation was used to investigate the resonance modes of the spherical nanocrescents which possess the hot spots located at the ring-tip. We applied the plasmon hybridization theory to interpret the excitation and shift of resonance modes of the nanostructure with reduced symmetry. The resonance wavelengths can be tuned from the visible to the near infrared regime by varying the geometrical parameters. The intra-particle coupling at the ring-tip explained the significant influence of the incident light polarization on the enhancement of local fields. The spherical nanocrescents can be developed as a powerful substrate in surface-enhanced spectroscopy for the tunable plasmon resonances and enhanced local fields. Keywords: tunable resonance modes, local field enhancement, plasmon hybridization, reduced symmetry, incident light polarization


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INTRODUCTION The extraordinary optical properties of metallic nanoparticles come from surface plasmons confined to nanoparticles known as the localized surface plasmon resonance (LSPR).1 The LSPR is responsible for the localized electromagnetic field enhancement that enables many molecular detection techniques such as LSPR wavelength-shift sensing,2 surface-enhanced infrared absorption spectroscopy (SEIRA),3 surface-enhanced Raman scattering (SERS),4, 5 surface-enhanced fluorescence (SEF),6 and plasmon resonance energy transfer (PRET).7 The locally enhanced electromagnetic fields, called “hot spots”, can be achieved through plasmonic coupling between adjacent nanoparticles which relies on crucial control of the nanogap between aggregated nanoparticles.8 However, the lack in stability and reproducibility of aggregated colloids of metallic nanoparticles limit the spatial resolution and specificity.9 Differing from the inter-particle coupling enhancement, the nanostructures with sharp features present hot spots located near individual nanoparticles. Various nanostructures are proposed as sensing substrates to enhance local fields and improve the spatial resolution, such as nanotips,10 nanoprisms,11 nanocubes,12 and nanorice.13 The spherical nanocrescent (SNC) is a unique structure that possesses not only sharp features but also plasmonic coupling at the single-particle level. The numerical studies explained the intra-particle plasmonic coupling phenomenon between the sharp tip and nanocavity resonance modes.14 Shumaker-Parry and co-workers presented the method for the fabrication of cylinderical nanocrescents (CNCs) that are supported on the substrate.15 Lee and co-workers has made both crescent-shaped holes16 and the 3D symmetric SNCs dispersed in solution.17 A novel dimmer nanostructure architecture featuring two symmetrically arranged CNCs with opposing, nanometer-sized tips in close proximity was fabricated by Vogel and co-workers to achieve a


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strong and highly localized electrical near-field in the gap region between the tips.18 All these structures are similar in some sense, but the optical response is different. According to the Lee’s method, a monolayer of randomly distributed polymer nanospheres is firstly formed on a substrate to fabricate the gold SNC nanostructure. Then, a gold layer is deposited on the surfaces of polymer nanospheres by electron beam evaporation. The substrate is kept rotating at a certain angle with respect to the gold target during deposition. Therefore, the SNC nanostructure has the geometrical features of both nanotip and nanoring on the sub-10nm sharp edge area, expanding the hot spots from a tip to a circular line.19 As such, the SNC nanostructure will not require multi-step lithographic processes to create hot-spots via inter-particle hybridization in contrast to the CNCs. Due to the rotational symmetry of the SNCs, the dependence of the structural orientation with respect to linear polarization of light will not be found, thus making their potential use easier. For the enhanced fields located at the ring-tip, the SNC nanostructure can be established as an effective substrate in biological and biochemical sensing, such as SERS.20 However, the distribution of the nanospheres has an obvious influence on the reproducibility of the SNC nanostructure which will be critical in practical applications. A recent review gives an overview over available techniques to prepare non-close packed colloidal monolayers.21 Another review shows applications in nanostructure generation of such monolayers.22 The non-close packed colloidal monolayers might allow an array of isolated SNCs without interconnections between adjacent nanoparticles. The technique will provide an easy and robust fabrication of the SNC nanostructure. In order to develop the nanostructure as an ultra-sensitive probe, it is desirable to tune the optical properties to match the specific spectrum regime of the application.23 The maximum enhancement of SERS occurs when the plasmon resonance wavelength is located near the


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midpoint between the incident wavelength and the wavelength of the Raman scattered photon.24 The SEIRA enhancement increases as the LSPR frequency overlaps more extensively with the frequency of the probed molecular vibration.3 In addition, the control of the magnitude and the extent of localization of field enhancement are critical for optimizing the signals and spatial resolution of the microscopy probes used in surface-enhanced spectroscopy.23 Recently, the optical properties and local field enhancement (LFE) of the CNCs were investigated experimentally and theoretically.25,26 The performance of CNCs for dielectric sensing was analyzed. 27, 28 The 2D approximation was also employed to analyze the plasmon tuning and LFE maximization of the SNCs;29 however, a rigorous study of 3D symmetric SNCs is desirable. In this paper, we present a numerical research on the plasmon resonance properties of 3D symmetric SNCs. We used the plasmon hybridization theory to interpret the resonance modes excited in the SNCs. Subsequently we investigated the influence of the geometrical parameters on the plasmon resonances of the SNCs. The resonance wavelengths can be tuned from the visible to the near infrared to match the specific spectrum regime for a certain application. The dependence of the plasmon resonances and LFE on the incident light polarization was also studied. The intra-particle coupling at the ring-tip is a significant factor which results in the enhancement of the local fields. METHODS The discrete-dipole approximation (DDA) is a flexible and powerful technique for computing scattering and absorption of electromagnetic waves by targets with arbitrary geometries.30, 31 The software package DDSCAT 7.2 was used to solve Maxwell’s equations to study extinction spectroscopy and local fields around the gold SNC nanostructure.32


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In this approximation, the extinction spectroscopy is characterized by extinction efficiency factor:33 2 Qext = Cext / π aeff

(1)

2 where Cext is the extinction cross section, aeff is the effective radius of the particle and π aeff is the

cross section of the particle. Typically the SNC is replaced by an array of point-dipoles (j = 1, ... , N) with the local field Ej, located at positions rj, which is the sum of the incident and retarded fields of the other N − 1 point-dipoles:33 E j = Einc , j − ∑ Ajk Pk

(2)

k≠ j

where Einc,j is the local field at position rj due to the incident plane wave, −AjkPk is the contribution to the local field at rj due to the point-dipole at location rk, including retardation effects. Pk is the point-dipole moment at rk, and Ajk is a 3×3 matrix. The gold SNCs can be fabricated by rotational deposition of a thin gold layer on polymer nanospheres at certain angles and subsequent dissolution of the sacrificial nanospheres.17 The SNC geometry can be controlled by modifying the deposited layer thickness, the deposition angle, and the size of the nanospheres. The SNC structure can be recognized as evolving from a concentric nanoshell by an offset of the core that induces an opening at the nanoparticle surface as shown in Figure 1a. The incidence angle is defined by θ. This structure is modeled as the overlapping between the nonconcentric sphere and cavity where r is the radius of cavity, R is the radius of sphere, and ∆ is the center - center distance as depicted in the Figure 1b. Clearly, the radius of the polymer nanosphere is r and the deposited layer thickness t = R + ∆ – r. The overlapping of two nanostructures results in some dispersive point-dipoles distributed near the


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ring-tip of the SNC structure. In the calculations, we removed these point-dipoles and kept the edge continuous. The parameter d is the diameter of the opening at the ring-tip and the deposition angle can be represented by the ratio δ = 2r / d. The inter-dipole separation was set at 1 nm for good calculation accuracy. The refractive index of surrounding medium was 1.333 for water and the wavelength-dependent refractive index of bulk gold was adopted in all calculations.34 RESULTS AND DISCUSSION We applied the plasmon hybridization to describe the optical properties of the SNCs as the interaction between plasmons supported by the nonconcentric sphere and cavity. For the concentric nanoshells, the plasmon hybridization only occurs between sphere and cavity plasmons of the same order.35 When the symmetry is broken, the sphere and cavity plasmons of all multipolar indices (l) mix and interact with each other at the inner/outer interfaces of the SNCs.36, 37 As depicted in Figure 2a, the dipolar mode of the sphere ωs not only the dipolar mode of the cavity ωc of the cavity ωc

(l )

(1)

(1)

can now interact with

but also the quadrupolar and higher order modes

(l = 2, 3, … , ∞). The incident light is transversely polarized with respect to

the symmetry axis. This interaction results in the splitting of the plasmon resonances and an admixture of all primitive cavity plasmons at different orders into the two new resonances of the SNCs: the lower energy dipolar bonding plasmon mode ω− antibonding plasmon mode ω+

(1)

( 2)

and the higher energy dipolar

. Similarly, the quadrupole of the sphere ωs

interact with all multipole of the cavity ωc bonding mode ω−

(1)

(l )

(2)

can now

(l = 1, 2, … , ∞), resulting in the quadrupolar

and antibonding mode ω+

( 2)

of the SNC nanostructure. The antibonding


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ω+

(1)

and ω+

( 2)

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modes are hardly excited because they are higher energy and interact weakly

with the incident light. Since the incident light is transversely polarized, the ω−

(1)

and ω−

( 2)

modes are referred to as transverse bonding modes in this paper. Higher order bonding modes may be excited which are not represented in Figure 2a. In Figure 2b, the spectrum of a concentric nanoshell (inner radius: 50 nm, outer radius: 65 nm) shows the dipolar and quadrupolar bonding modes at 710 and 580 nm, respectively. For the concentric nanoshells, the dipolar and quadrupolar bonding modes are resulted by the splitting of the plasmon resonances due to the dipole - dipole and quadrupole - quadrupole interaction between plasmons of sphere and cavity, respectively. The extinction spectrum of the SNCs with δ = 2.6, and t / r = 30 / 50 nm is also plotted. The resonance peaks observed at about 870 and 680

nm correspond to the transverse dipolar bonding ω−

(1)

and quadrupolar bonding ω−

( 2)

modes,

which is confirmed by the profiles of LFE shown in Figure 2c and d. The LFE is defined as the amplitude ratio between the incident field and the local field, 10log|E/Einc|. The noticeable LFE located at the ring-tip demonstrates the excitation of intra-particle coupling in the SNCs. For the SNC nanostructure, the symmetry breaking results in the interaction between plasmons of different multipolar orders of sphere and cavity. This interaction leads to a stronger splitting of the plasmon resonances. In Figure 2b, the red-shift of the dipolar and quadrupolar bonding modes can be observed because these modes of SNCs are located at lower energetic position in contrast with those of concentric nanoshells. The red-shifts can be controlled by the hybridization intensity which is influenced by the degree of symmetry breaking. When δ is large, the interaction of the multipoles results in an admixture of dipole components in the quadrupolar and higher order modes. These modes thus become dipole active and can be easily excited by light.


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The strong peak intensity of ω−

( 2)

is due to the plasmon hybridization which brings in

significant dipole components into the quadrupolar mode. The third resonance at ~590 nm corresponds to the octupolar mode according to the LFE profiles shown in Figure 2e. Since the plasmon resonances are highly dependent on the geometrical parameters, the resonance wavelengths of the SNCs can be tuned by varying the shape and size of the nanostructure. The geometry shape of the SNCs is determined by the parameter δ and the ratio t / r. First, we studied the influence of the ratio δ on the wavelength and strength of plasmon

resonances. Figure 3 shows the calculation results about the extinction spectra with different δ. Here, t and r are fixed at 30 and 50 nm, respectively. The incidence angle θ is 0° and the incident light is transversely polarized with respect to the symmetry axis. As the ratio δ decreases, the

ω−

(1)

and ω−

( 2)

are both blue-shifted because of the increase in the degree of symmetry

breaking. For the octupolar mode, the resonance strength is quite weak and no obvious resonance peak is observed. The enhanced symmetry breaking results in a decrease in the interactions between the plasmon modes of sphere ωs

(l )

and cavity ωc

(l )

. As presented in Figure 3, the

red-shifts can be tuned by the strength of interactions. The reduced strength of interactions results in the decrease in the red-shifts of ω−

(1)

and ω−

( 2)

as the ratio δ decreases. Thus, the blue-

shifts are observed in Figure 3. However, the shifts is caused not only by the change in interactions but also by a change in energetic position of the parental modes (sphere ωs cavity ωc

(l )

).

(l )

and

For the CNC nanostructure, such inhomogeneities were incorporated into the

coupling model to explain the shift of resonance modes.38, 39 Since the radius of cavity r is fixed at 50 nm, the plasmon mode of cavity ωc

(l )

is set at a fixed energetic position for SNCs with


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different δ. The energetic position of sphere mode ωs

(l )

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is slightly changed for the SNCs

because the sphere radius R changes from 64 nm to 57 nm with the decrease in δ. For the SNC nanostructure, the change in strength of interactions between parental plasmon modes is the main reason for the shifts of the ω−

(1)

and ω−

( 2)

as the increase in degree of symmetry breaking.

Besides, the change in energetic position of ωs

(l )

also contributes to the blue-shifts of the two

transverse bonding modes. The LFE profiles further support the interpretation (Figure S6). The reduced interactions also results in the decrease in dipole components which are mixed in the quadrupolar bonding mode ω−

( 2)

, leading to the decrease in the peak amplitude. In the SNC

nanostructure, where the number of oscillating electrons decreases with the decrease in δ, the convolution of the amplitudes of plasmon resonances is reduced. This does not, however, indicate the decrease in all resonance peaks. The peak amplitude at ω−

(1)

is nevertheless

enhanced as the ratio δ decreases. Actually, the interaction strength has little influence on the strength of ω−

(1)

mode when t and r are fixed. The extinction efficiency factor Qext is related to

2 the extincition cross section Cext and the cross section of nanoparticle π aeff . The values of the

extinction cross section Cext are very approximate at ω−

(1)

for SNCs with different δ shown in

Figure 3. It is clear that the effective radius aeff of SNCs will be reduced with the decrease in δ. The enhanced peak amplitude at ω−

(1)

shows a higher extinction efficiency for SNCs with small

cross section of nanoparticle. To study the effect of the deposition thickness t on the wavelength of plasmon resonances of SNCs, we consider varying the parameter t with the ratio δ fixed at 1.5. Other parameters are kept unchanged. The extinction spectra of SNCs as a function of thickness t are plotted in Figure


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4a. The two resonance peaks corresponding to ω−

(1)

and ω−

( 2)

are both red-shifted with the

decrease in thickness t, which is due to the enhanced strength of the interaction between the sphere and cavity plasmons at different orders. The ω−

(1)

mode is exponentially red-shifted with

the decrease in the thickness t as shown in Figure 4b. When the deposited gold layer becomes thinner, the plasmons of the sphere interact more strongly with the plasmons of the cavity. 40 This enhanced interactions lead to a stronger mixing between the modes at different orders, creating a greater shift of the resonances when the thickness t is reduced. Thus, the deposition thickness t shows a great tunability on the wavelength of the ω− deposited. For the ω−

( 2)

(1)

mode when a thin gold layer is

mode, the resonance wavelength is located at ~560 nm when the

thickness t is over 100 nm. Since the plasmon hybridization only introduces finite dipole components in the plasmon for the quadrupolar bonding mode, the ω−

( 2)

mode doesn’t show an

obvious exponential relationship between resonance wavelength and the thickness t. A strong dependence of the resonance wavelength on the SNCs size is shown by varying the radius r of the polymer nanosphere but keeping the ratio t / r = 0.6 and δ = 1.5. We studied the extinction spectra of the SNCs with r = 40, 50, 70 and 80 nm shown in Figure 5a. The transverse dipolar mode ω−

ω−

( 2)

(1)

is red-shifted from ~810 to ~1030 nm and the quadrupolar mode

is shifted from ~610 to ~660 nm with the increase in the radius r. A third resonance mode

appears as a shoulder (~600 nm) in the high energy mode for larger SNCs with r = 70 and 80 nm. The LFE profiles of the SNCs with r = 80 nm at wavelength of quadrupolar mode and ~600 nm were shown in Figure 5b and c. The LFE profiles show an octupolar pattern for the third


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resonance. The ω−

(1)

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mode will be greatly red-shifted in the near infrared regime when the

radius r is further increased. Figure 6 shows the hybridization diagram of SNCs when the incident light is axially polarized with respect to the symmetry axis. Similar to Figure 2a, this hybridization between plasmons of sphere and cavity results in the splitting of the plasmon resonances into new resonances: the axial bonding mode ω−

ω−

∗

(1)

and ω−

∗

( 2)

∗

(l )

and antibonding mode ω+

∗

(l )

(l = 1, 2, … , ∞). The

modes are easily excited by incident light because the bonding configurations

have in-phase oscillations. Since the ω−

∗

(1)

and ω−

∗

( 2)

modes have axial oscillations with

respect to the symmetry axis, the axial bonding modes are quite different from the transverse bonding modes which have transverse oscillations. Figure 7 shows the extinction spectra of the SNCs with the ratio δ = 1.5 and t / r = 30 / 50 nm, and the polarization varies with the change in the incidence angle θ. When incident light is axially polarized with respect to the symmetry axis (θ = 90°), the resonance peaks observed at about 720 and 590 nm correspond to the axial dipolar

ω−

∗

(1)

and quadrupolar ω−

∗

( 2)

modes, respectively. The axial dipolar mode ω−

∗

(1)

is located at

the wavelength of the valley in the extinction spectrum when incident light is transversely polarized (θ = 0°). As the incidence angle θ increases, the peak amplitude at ω− but the resonance peaks corresponding to ω−

(1)

and ω−

( 2)

∗

(1)

is enhanced,

peter out. The polarization results in

no shift of the resonance wavelengths, but has an influence on the intensity of each resonance mode.


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We summarized the LFE of the SNCs to further study the dependence of the plasmon resonances on the polarization. Figure 8a shows the LFE maximum of the SNCs (δ = 1.5, t / r = 30 / 50 nm) as a function of incidence angle θ and incident wavelength. The maximum value of the local fields occurs at the ring-tip for all cases in our study. The LFE is enhanced with the decrease in the incidence angle θ because of the gradually enhanced intra-particle coupling. Figure 8b and c show the profiles of LFE corresponding to ω−

∗

(1)

(θ = 90°). The intra-particle

coupling is hardly excited when the incident light is axially polarized. The profiles of LFE corresponding to ω−

(1)

(θ = 0°) are also plotted in Figure 8d and e. The strong intra-particle

coupling is excited by the ω−

ω−

∗

(1)

(1)

mode, resulting in the maximal LFE. The resonance mode

is greatly suppressed under the transverse polarization. The strength of the intra-particle

coupling is directly proportional to the intensity of the ω−

(1)

mode. The dependence of the LFE

on the incident light polarization can be explained by the intra-particle coupling which leads to a further enhancement of the local fields at the ring-tip of the SNC nanostructure. CONCLUSIONS In this study, the plasmon hybridization theory was applied to study the tunable plasmon resonances of the SNCs with reduced symmetry. The resonance wavelengths of the SNCs can be tuned from the visible to the near infrared regime by varying the shape and size parameters, including δ, t, and r. The resonance modes are red-shifted with the increase in the ratio δ. When the thickness t is reduced, the plasmon resonances are exponentially red-shifted. A strong redshift of resonance wavelengths is shown by increasing the radius r. The incident light polarization has no effect on the resonance wavelength, but leads to the change in the intra-


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Page 14 of 24

particle coupling at the ring-tip. The sharpness of the tip is a dominant factor determining the LFE of the SNCs, while the incident light polarization is another significant factor due to the intra-particle coupling. The geometrically tunable plasmon resonances and the significant LFE suggest that the SNCs can be developed as a powerful substrate in the surface-enhanced spectroscopy, such as SERS and SEIRA. The maximum enhancement factor (EF) can be achieved by tuning the position of the resonance wavelength relative to incident wavelength and the wavelength of the Raman scattered photon (or molecular vibration wavelength). ASSOCIATED CONTENT Supporting Information The influence of symmetry on the optical properties of NC structure, the comparison between calculated and experimental optical properties of CNCs and the LFE profiles of SNCs with different δ. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]. REFERENCES (1) Mayer, K. M.; Hafner, J. H. Localized Surface Plasmon Resonance Sensors. Chem. Rev. 2011, 111, 3828-3857. (2) Willets, K. A.; Van Duyne, R. P. Localized Surface Plasmon Resonance Spectroscopy and Sensing. Annu. Rev. Phys. Chem. 2007, 58, 267-297. (3) Bukasov, R.; Shumaker-Parry, J. S. Silver Nanocrescents with Infrared Plasmonic Properties as Tunable Substrates for Surface Enhanced Infrared Absorption Spectroscopy. Anal. Chem. 2009, 81, 4531-4535.


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(4) Stiles, P. L.; Dieringer, J. A.; Shah, N. C.; Van Duyne, R. P. Surface-Enhanced Raman spectroscopy. Annu. Rev. Anal. Chem. 2008, 1, 601-626. (5) Morton, S. M.; Silverstein, D. W.; Jensen, L. Theoretical Studies of Plasmonics Using Electronic Structure Methods. Chem. Rev. 2011, 111, 3962-3994. (6) Fort, E.; Grésillon, S. Surface Enhanced Fluorescence. J. Phys. D: Appl. Phys. 2008, 41, 013001. (7) Liu, G. L.; Long, Y. T.; Choi, Y.; Kang, T.; Lee, L. P. Quantized Plasmon Quenching Dips Nanospectroscopy via Plasmon Resonance Energy Transfer. Nat. Methods 2007, 4, 10151017. (8) Schatz, G. C.; Young, M. A.; Van Duyne, R. P. Electromagnetic Mechanism of SERS. Top. Appl. Phys. 2006, 103, 19-45. (9) Li, K.; Clime, L.; Cui, B.; Veres, T. Surface Enhanced Raman Scattering on Long-Range Ordered Noble-Metal Nanocrescent Arrays. Nanotechnology 2008, 19, 145305. (10) Ye, D.; Mutisya, S.; Bertino, M. Enhancement of Electric Field and Raman Scattering by Ag Coated Ni Nanotips. Appl. Phys. Lett. 2011, 99, 081909. (11) Cui, B.; Clime, L.; Li, K.; Veres, T. Fabrication of Large Area Nanoprism Arrays and Their Application for Surface Enhanced Raman Spectroscopy. Nanotechnology 2008, 19, 145302. (12) McLellan, J. M.; Li, Z. Y.; Siekkinen, A. R.; Xia, Y. The SERS Activity of A Supported Ag Nanocube Strongly Depends on Its Orientation Relative to Laser Polarization. Nano lett. 2007, 7, 1013-1017. (13) Benjamin, J.; Chen, Y.; McLellan, J. M.; Xiong, Y.; Li, Z. Y.; Ginger, D.; Xia, Y. Synthesis and Optical Properties of Silver Nanobars and Nanorice. Nano lett. 2007, 7, 10321036. (14) Kim, J.; Liu, G. L.; Lu, Y.; Lee, L. P. Intra-Particle Plasmonic Coupling of Tip and Cavity Resonance Modes in Metallic Apertured Nanocavities. Opt. Express 2005, 13, 83328338. (15) Shumaker-Parry, J. S.; Rochholz, H.; Kreiter, M. Fabrication of Crescent-Shaped Optical Antennas. Adv. Mater. 2005, 17, 2131-2134. (16) Wu, L. Y.; Ross, B. M.; Lee, L. P. Optical Properties of the Crescent-Shaped Nanohole Antenna. Nano lett. 2009, 9, 1956-1961.


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Figure 1. (a) Schematic and (b) geometrical parameters of the gold SNCs. Figure 2. (a) An energy-level diagram describing the plasmon hybridization in the SNCs resulting from the interaction between the plasmons of nonconcentric sphere and cavity. (b) The red-shift of the bonding modes due to the plasmon hybridization. The LFE profiles of the SNCs with δ = 2.6 at the wavelength of (c) dipolar, (d) quadrupolar and (e) octupolar modes, respectively. Figure 3. The extinction spectra of the SNCs with different δ: (a) δ = 1.8, (b) δ = 1.5, (c) δ = 1.3, (d) δ = 1.2, (e) δ = 1.1. Figure 4. (a) The extinction spectra of the SNCs with different t. (b) The shift of the resonance wavelength at the ω−

(1)

and ω−

( 2)

modes with different thickness t.

Figure 5. (a) The extinction spectra of the SNCs with different radius r. The LFE profiles of the SNC nanostructure with r = 80 nm at wavelength of (b) quadrupolar and (c) octupolar modes, respectively. Figure 6. The energy-level diagram describing the plasmon hybridization in the SNCs with the axially polarized incidence. Figure 7. The extinction spectra of the SNCs under different polarizations determined by the incidence angle θ: (a) θ = 0°, (b) θ = 30°, (c) θ = 45°, (d) θ = 60°, (e) θ = 90°.


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Figure 8. (a) LFE maximum as a function of the polarization and the incident wavelength. The LFE profiles of (b) the cross-section and (c) the ring-tip plane of the SNCs at the ω− The LFE profiles of (d) the cross-section and (e) the plane of ring-tip at the ω−

(1)

∗

(1)

mode.

mode.

Figure 1


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Figure 2


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Figure 3

Figure 4


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Figure 5

Figure 6


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Figure 7

Figure 8


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TOC


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Tunable Plasmon Resonances and Enhanced Local Fields of

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