Optical Properties of Gold Nanorings

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, Garnett W. Bryant, and F. J. Garcı́a de Abajo National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8423 Department of Applied Physics, Chalmers University of Technology, S-41296 Göteborg, Sweden Centro Mixto CSIC-UPV/EHU and Donostia International Physics Center (DIPC), Apartado 1072, 20080 San Sebastián, Spain (Received 13 August 2002; published 3 February 2003)

Metal nanoparticles exhibit a wide variety of optical phenomena [1] that have made them the center of considerable recent attention.Nanoparticles can be used to guide, enhance, emit, and modify optical fields, phenomena that can be used for novel technological applications such as photonic crystals [2], sensors based on surfaceenhanced Raman scattering (SERS) [3][4][5] and near-field microscopy [6].The optical response of a particular nanoparticle depends on its size and shape, which defines the intrinsic modes [7], as well as on the local dielectric environment [8].Interparticle coupling typically leads to energy shifts and splitting of degenerate modes, an effect that is prominent for regular arrays of nanoparticles [9] and can be utilized for the production of efficient SERS substrates [10], or as an electromagnetic probe for atomic scale objects in a scanning tunneling microscopy cavity [11].
In this Letter, we report on tunable optical modes and associated electromagnetic field confinement effects in Au nanorings with radii of the order 60 nm.We emphasize the intrinsic surface plasmon resonances (SPR) of the rings, which are experimentally observed by recording the extinction spectra of disordered layers of identical nanoparticles deposited on glass substrates.We demonstrate that the SPR wavelength can be tuned by varying the thickness of the ring walls, which determines the electromagnetic coupling between the inner and outer ring surfaces.It is argued that this phenomenon is analogous to electromagnetic coupling effects in thin metal films and nanoshells [12,13].As a support for this interpretation, we present detailed electrodynamic calculations that essentially reproduce the experimentally measured extinction spectra.The calculations also show that a sizable and remarkably uniform field enhancement effect occurs in the ring interior.
The Au rings are produced on soda-glass substrates using colloidal lithography according to the following procedure.
(i) Polystyrene (PS) colloidal particles (110 nm sulphate modified latex) are deposited by electrostatic selfassembly onto the glass substrates.(ii) A 15 to 40 nm thick gold film is evaporated onto the particle coated glass substrates.The thickness of this film controls the thickness d of the ring walls while the size of the PS particles determines the inner radius.(iii) Ar ion beam etching is then used to remove the Au film, during which secondary sputtering of material creates a gold shell around the sides of the PS particles.(iv) The remainder of the PS particles are removed by a UV-ozone treatment and subsequent water rinse, resulting in free standing Au nanorings.
For comparison, we also produced Au nanodisks by reversing the order of steps (i) and (ii), and by changing the shape of the PS particles by heat pretreatment to avoid the secondary buildup of material around the PS particle.The morphology of the samples were determined by scanning electron microscopy (SEM) and atomic force microscopy.All rings and disks had the same outer radius 60 nm while the heights were 40 and 20 nm, respectively.The thickness of the ring walls was determined independently through side-view SEM images [see Fig. 1(a)].Normalized optical extinction spectra were measured in a spectrophotometer using unpolarized light incident normal to the nanoparticle substrate.
The bulk nature of the disks is clearly seen in the SEM top view of Fig. 1(b), whereas the corresponding nanoring image in Fig. 1(c) shows an empty space surrounded by uniform walls.The close-up SEM image in Fig. 1(a) shows that the rings are slightly bulging outwards, a shape derived from the sphericity of the PS particles.Figures 1(b) and 1(c) also shows that the disk and ring samples exhibit approximately the same particle density, 1:4 and 1:7 10 9 particles=cm 2 , respectively.As the sampling area of the extinction measurement was approximately 0:7 cm 2 , the optical data are averaged over 10 9 particles.While the disks show an SPR peak well below 1000 nm (dashed curve), the nanorings exhibit near-infrared extinction peaks with a center wavelength extremely sensitive to the ratio between the ring thickness and radius d=a.For a constant external ring radius of a 60 nm, a redshift of almost 400 nm is observed by reducing the ratio d=a from 0.22 to 0.16 [i.e., from r 1 to r 3 in Fig. 2(a)].This shift is larger than the shifts induced by the interparticle interaction in close-packed nanoparticle arrays [9].
In order to elucidate the character of the SPR modes, numerical calculations of the extinction cross section for both types of particles (disks and rings) were performed for the geometrical parameters mentioned above.The dielectric functions for Au and substrate, i.e.SiO 2 , were taken from Ref. [14].Maxwell's equations were solved using the boundary element method [15], in which the electromagnetic field is expressed in terms of charges and currents distributed on the surfaces and interfaces of the structure under consideration.The customary boundary conditions for the electromagnetic field provide a set of linear integral equations, with charges and currents as unknowns, which are solved self-consistently in the presence of the external incident-light field by discretizing the integrals.In Fig. 2(b), the calculated extinction cross sections are plotted vs for disks (d) and for rings of different thickness as in the experiments (r 1 to r 3 ).The agreement between experiment and theory is excellent, both in terms of the peak positions and in the absolute and relative weights of the different surface plasmon resonances.The peak widths increase with decreasing wall thickness in both the experiments and in the theoretical model, although the calculated widths are clearly smaller than the measured ones in all cases.For the case of the rings, the calculations clearly indicate that even a small spread in d would give rise to a relatively large distribution of peak positions.It is thus likely that the large experimental peak widths are a result of inhomogeneous broadening, due to a finite distribution of wall thickness for the measured samples.
The large difference in the SPR position for disks and rings can be understood by analyzing the particular modes that are most efficiently excited for each type of particle.The extinction spectrum of disklike particles is dominated by a dipolar (l 1) mode, whose frequency depends on the particle size due to retardation effects in the intraparticle electromagnetic interaction [16].As the particle size increases, the different multipolar modes shift to the red according to a dispersion similar to the one shown in Fig. 3(a), where we have used a Drude-like dielectric function appropriate for Au (see caption).This particular calculation was performed for the lowest order modes of a spherical particle of radius a, for which analytical formulas are available through the simplified Mie theory [16].Although the exact mode positions differ between a disklike object and a sphere, the redshift with increasing size is maintained.However, for the small diameters under consideration here (a! p =c < 1), the redshift is not substantial.Turning to the nanorings, there is a strong electromagnetic coupling between the inner and outer ring walls when the thickness d is small compared to the ring radius a.This leads to a new scheme of polarization and results in mode splitting [see Fig. 3(b)] similar to the case of a thin metallic slab, which is characterized by symmetric and antisymmetric mode branches.In the longwavelength limit, appropriate to the particle sizes and wavelengths under discussion, the dispersion relation of the modes of a slab described by the Drude-like dielectric function given in the caption of Fig. 3 reduces to where !corresponds to the symmetric ÿ and antisymmetric mode frequencies, k is the wave vector, and d is the slab thickness.The effect of the SiO 2 substrate has been qualitatively incorporated by surrounding the slab with a medium of dielectric function " s 2:12.
In the present case, the wave vector k is related to the ring circumference 2a by k 2n 2a n=a, where n is the order of the mode.This relationship is illustrated in Fig. 3(b) for the first three (n 1 ÿ 3) symmetric (! ÿ ) and antisymmetric (! ) modes of a slablike ring.As the thickness of the walls increases, the modes converge to the surface plasmon mode of a planar surface !s !p = " o " s p .If the wall thickness is decreased instead, the symmetric modes redshift and eventually go to zero in the d a limit.This pattern of oscillation corresponds to a charge distribution with the same sign at the inner and outer surfaces of the wall, as shown in Fig. 3(b).It is the symmetric n 1 mode that is responsible for the near-infrared excitations observed in the nanorings, and accounts for the d=a dependence evident in the experimental and theoretical results shown in Fig. 2. The polarization pattern of this mode can be understood as a strong dipolar excitation that involves the entire ring perimeter, and where equal sign charges at opposite sides of the wall interact to a degree determined by the wall thickness.On the contrary, the antisymmetric branches correspond to patterns of oscillation of opposite sign along both walls.
An estimate of the peak position for the gold nanorings made from Eq. ( 1) by defining a 60 nm and d=a 0:1 results in a near-infrared wavelength 1110 nm.This is in general agreement with both the experiments and the more detailed calculations presented in Fig. 2. The simple analytical model [Eq.( 1)] thus qualitatively explains the observed extinction spectra.However, the effect of the vertical truncation of the ring, the fact that the wall surfaces are not parallel, and the actual configuration of the ring-substrate system lead to additional corrections that are correctly described by the numerical calculation presented in Fig. 2(b).In addition, the interaction between the upper and lower ring edges lowers the mode frequencies in comparison to an infinitely long ring.This effect has been confirmed by our calculations, although it is not included in the simple analytical model.The dependence on ring height is not as dramatic as the dependence on the d=a ratio.
Nanorings could serve as resonant nanocavities for holding and probing smaller nanostructures, such as biomolecules or quantum dots.We show in Fig. 4(a) the near-field vector distribution and field enhancement jEj=jE inc j in a horizontal plane through the middle of the r 1 nanoring modeled in Fig. 2. The incident wavelength is in resonance with the first symmetric mode ( 1000 nm).The electric field is substantially enhanced inside the ring cavity (green and yellow regions, corresponding to jEj=jE inc j 8-10), where it is rather homogeneous.The field distribution in a plane that contains the ring axis [Fig.4(b)] shows that the uniform enhancement is maintained through most of the cavity region even though the ring height is less than 1=2 the ring diameter.The enhancement factor reaches a maximum of jEj=jE inc j 50 at the upper and lower ends of the ring, indicating a buildup of charge at these ends which supports the field enhancement uniformly in the cavity.
Combined with the tunability of the peak position through the d=a ratio, the enhancement effects indicate potential applications in nonlinear optical phenomena (e.g., switching and all-optical transistors) as well as in improved near-infrared SERS sensitivity.In summary, it has been shown that ringlike nanoparticles exhibit tunable plasmon resonances in the near infrared that are not observed for solid particles of similar size.The volume confined by the nanoring is empty and therefore accessible to various sensing and spectroscopy applications at the nanometer scale.The experimentally observed optical response of these structures is well described by numerical simulations and the main features can be qualitatively understood from simple models of the charge oscillation patterns.The predictive character of these calculations allows one to tailor the shape of a particle in order to achieve excitation spectra on demand with controlled field enhancement.

Figure 2
Figure 2(a) shows experimental extinction spectra for disks and rings derived from the measured transmittance T I=I o , where I o is the intensity of the incident light and I is the intensity of the transmitted light.The experimental cross section ext is estimated from I ÿ I o ÿ ext NI o , where N is the 2-dimensional particle density.While the disks show an SPR peak well below 1000 nm (dashed curve), the nanorings exhibit near-infrared extinction peaks with a center wavelength extremely sensitive to the ratio between the ring thickness and radius d=a.For a constant external ring radius of a 60 nm, a redshift of almost 400 nm is observed by reducing the ratio d=a from 0.22 to 0.16 [i.e., from r 1 to r 3 in Fig.2(a)].This shift is larger than the shifts induced by the interparticle interaction in close-packed nanoparticle arrays[9].In order to elucidate the character of the SPR modes, numerical calculations of the extinction cross section for both types of particles (disks and rings) were performed for the geometrical parameters mentioned above.The dielectric functions for Au and substrate, i.e.SiO 2 , were taken from Ref.[14].Maxwell's equations were solved using the boundary element method[15], in which the electromagnetic field is expressed in terms of charges and currents distributed on the surfaces and interfaces of the structure under consideration.The customary boundary conditions for the electromagnetic field provide a set of FIG. 2. (a) Experimental extinction spectra of disks (d, dashed line) and rings (r, solid lines).The estimated wall thickness d of the rings is d 14 2 nm (r 1 ), d 10 2 nm (r 2 ), and d 9 2 nm (r 3 ), respectively.(b) Calculated extinction spectra for the same particles as in (a).The rings exhibit near-infrared features at larger wavelengths for thinner walls.The disks show a dipolar excitation at around 700 nm.

FIG. 3 .
FIG. 3. (a) Left: top view of dipolar and multipolar charge density patterns for disks.Right: dispersion of the lowest-order modes in a spherical particle of radius a characterized by a Drude-like dielectric function, " " o ÿ ! 2 p =! 2 .The values !p 8 eV and " o 9 5i were chosen to qualitatively represent gold in the spectral region under investigation.(b) Left: top view of the charge-density pattern in a nanoring for the antisymmetric (! ) and symmetric (! ÿ ) modes.Right: mode frequencies of nanorings as a function of d=a in the longwavelength limit.The rings are characterized by the same Drude-like dielectric function as in (a) and surrounded by a material with dielectric function " s 2:12.