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We use the finite difference time domain method to predict how optical plasmon properties are modified if the symmetrical geometry of gold shell nanostructures is broken. The simulations include three kinds of gold open shell nanostructures of nanobowls, open nanocages, and open eggshells. For all structures, the optical extinction spectra commonly display a distinct red shift when the full shell geometry is broken and a hyperbola-like dipolar plasmonic shift when the fractional height continuously decreases. The optical transitions of gold open shell nanostructures are explained by the plasmon hybridization theory combined with numerical calculations. Furthermore, the calculations exhibit that the local electric fields are strongly enhanced at the edges of the open nanoapertures on those symmetry-broken structures, which suggests a potential application in surface-enhanced Raman spectroscopy.
©2009 Optical Society of America
1. Introduction
Recently various gold (Au) shell nanostructures including Au nanoshells, Au nanocages, and Au nanorice have attracted considerable attention for scientists because of their highly favorable optical properties for drug delivery, hyperthermia, localized surface plasmon resonance (LSPR) sensing, and surface-enhanced Raman spectroscopy (SERS) [1–3]. More interestingly, it has been found that breaking the symmetry of the Au shell nanostructures results in a number of new optical phenomena. For example, nanoeggs composed of a nonconcentric core allow for an excitation mixing of dipolar components in all plasmon modes of the particles [4]. Nanocup and nanocap arrays show highly tunable optical properties, and they render their optical properties dependent on the angle and polarization of the incident light [5, 6]. Besides their unconventional optical properties arising from the broken symmetry of Au shell geometry, these asymmetrical nanostructures possess a common feature of an enhanced localized electric field (“hot spot”) with a suitable excitation light compared to the full Au shell nanostructures. Therefore, numerous research efforts have been performed to discover new optical properties of broken-symmetrical Au shell nanostructures.
Raman scattering from molecules adsorbed on metallic nanostructure’s surface is strongly enhanced due to the excitation of the local electric field. This gives rise to the well-known effect called SERS, one of the best possible label-free techniques for single molecular detection [7]. A single Au or Ag nanoparticle has been widely used as a SERS substrate to detect biomolecules due to the intrinsic plasmonic resonance. A further five to six orders of magnitude enhancement of SERS signals can be achieved from the interacting nanoparticles (dimers and multiparticle aggregates) [8]. However, the interparticle distance is difficult to control due to the random distribution of the nanoparticles on a substrate in conventional chemical preparation methods. Broken-symmetrical Au shell nanostructures, such as nanocrescents, have been proposed and demonstrated for the SERS application because of their independent enhancement of electric field instead of relying on interparticle coupling [9].
Very recently, Cho and Gracias have reported on the fabrication of metallic open nanocages by using a self-assembly process from well-established 2D nanoscale patterns but without an investigation on their optical properties yet [10]. We also have reported to fabricate asymmetrical Au nanobowls and Au semishells with highly tunable optical properties by using the ion milling technique [11,12]. The precise control of the broken-symmetrical geometry and the open nanoapertures from the top suggest Au nanobowls and semishells to be a potential SERS substrate for the biomolecular detection. Different ion milling time allows us to remove Au from the top of the shell and to convert a nanoshell to a nanocup, a half-shell, and a nanocap, solely as a function of the fractional height that plays an important role in tuning the optical properties of the Au semishells. In this paper, we aim to extend the theoretical investigation of these optical properties to the different Au open shell nanostructures including nanobowls, open nanocages, and open eggshells. Their extinction spectra with different fractional heights are calculated by using the three-dimensional finite difference time domain (FDTD) method. The numerical calculations indicate a common and interesting trend for all three kinds of Au open shell nanostructures, which displays a “hyperbola-like” shift of the plasmonic response with decreasing the fractional height. This optical transition can be explained by the plasmon hybridization model. Furthermore, the FDTD calculations show strongly enhanced local electric fields at the edges of the open nanoapertures, compared to those of the corresponding full Au shells. The latter aspect provides interesting prospects for the SERS-based biomolecular detection.
2. Simulation method
Figure 1 displays the schematical geometry of the Au open shell nanostructures used in the simulation, showing the outer radius (R) for nanobowls, the cage length (L) for open nanocages, the longitudinal radius (U) and the transversal radius (r) for open eggshells, and the thickness (T) and the cutoff height (H) for all. The fractional heights (h) are defined as H/2R (nanobowl), H/L (open nanocage), and H/2r (open nanoegg), respectively. The FDTD calculations are carried out using the FDTD Solutions program from Lumerical Solutions, Inc. (Vancouver, Canada). The structures are normally illuminated by a total-field scattered-field (TFSF) source with an electric field vector parallel to the X axis. The wavelength of the TFSF source is varied from 400 to 1700 nm, and the amplitude is set to 1. A perfectly matched layer (PML) is used as the radiation boundary condition. The simulation region is 800 × 800 × 800 nm3 with a non-uniform mesh adapted to the spatial structure including a mesh override region of 320 × 320 × 320 nm3 with a maximum mesh step of 3 nm. The whole simulation region is assumed in a background with a relative dielectric constant of 1. The total complex-valued permittivity of Au is modeled by the combination of a Drude and a Lorentz model fitted to experimental data from Johnson and Christy [12]. Once the resonance frequencies are determined, on-resonance excitation is used to excite the individual mode to examine the corresponding field and charge distribution by using a mesh override region with a grid size of 1 nm. For the sake of simplicity, in this work all Au open shell nanostructures are modeled with sharp corners or edges and with a truncation plane parallel to the XY plane, which may produce a non-homogeneous shell thickness for some structure (e.g., Au nanobowl). We have checked that the presence of the sharp features may result in slight shifts of the plasmon resonance bands and obviously more pronounced field enhancement compared to the structures with round corners or edges. Moreover, we also simulated nanobowl structures with a homogeneous shell thickness (which also have less pronounced sharp features) and we do not observe any noticeable difference with our other results.
Fig. 1 Geometry illustration of the Au open shell nanostructures used in FDTD calculations: (a) a Au nanobowl, (b) a Au open nanocage, and (c) a Au open eggshell.
3. Results and discussion
Figure 2 indicates the calculated h dependent optical properties of a Au nanobowl (R = 130 nm, T = 15 nm in Fig. 2a), a Au open nanocage (L = 260 nm, T = 15 nm in Fig. 2b), and a Au open eggshell (U = 130 nm, r = 50 nm, T = 15 nm in Fig. 2c). Our calculations show a number of interesting results when the symmetrical geometries of those full shell nanostructures are broken. First, removing the small top part of the full shell nanostructures (i.e., when h = 0.875) results in a pronounced red shift of the dipolar plasmon resonance. Secondly, a common trend of the hyperbola-like dipolar plasmonic shift is observed when h is continuously decreased (from top to bottom in Fig. 2a, b, and c). Especially, when h equals 0.875 or 0.75 for the Au nanobowl and open nanocage, the quadrupolar resonance band is split into two bands (see arrows in Fig. 2a and b). Finally, their quadrupolar plasmon bands disappear and they end up with only dipolar plasmon resonances (i.e., when h = 0.125). More in detail, for the Au nanobowl (Fig. 2a), the dipolar plasmon band (842 nm) of the full nanoshell shifts to a higher wavelength in an earlier stage for 1 > h > 0.625 and shifts back to a lower wavelength, afterwards, for 0.625 > h > 0. The maximum red shift from 842 to 987 nm occurs when h is 0.625. Furthermore, the quadrupolar plasmon band (626 nm) first displays a red shift (643 nm), then starts to continuously blue shift and gradually attenuates for 0.75 > h > 0.375, and completely disappears when h is less than 0.375. It is also noticed that the quadrupolar band is split into a low energy band (643 nm) and a high energy band (578 nm) for h = 0.875. Au open nanocages with different h values show a rather analogous transition of extinction spectra as Au nanobowls including a hyperbola-like shift of the dipolar bands and a shift, splitting, and attenuation of the quadrupolar bands (Fig. 2b). The only difference is that the dipolar bands remain at the same wavelength (1139 nm) for the Au open nanocages when 0.875 > h > 0.625 instead of keeping moving like the Au nanobowls in the same h range. In despite of less calculation spectra for the Au open eggshells with different h, they show a hyperbola-like spectra shift as well. Additionally, we also observe the incident angle dependent optical properties for all Au open shell nanostructures (data not shown), which is very similar to the previous results [5,6]. For instance, for a Au open nanocage (i.e., h = 0.5) under the incident light from the top and side, a long-axis dipolar mode at a higher wavelength and a short-axis dipolar mode at a lower wavelength are excited, respectively, with the same quadrupolar mode excitation. Any light with an incident angle in between will excite a mixture of above two modes.
Fig. 2 Calculated fractional height (h) dependent optical properties of (a) a Au nanobowl (R = 130 nm, T = 15 nm), (b) a Au open nanocage (L = 260 nm, T = 15 nm), and (c) a Au open eggshell (U = 130 nm, r = 50 nm, T = 15 nm). Arrows in (a) and (b) indicate the splitting of the quadrupolar band for the Au nanobowl and open nanocage.
FDTD calculations not only provide the optical spectra of various Au open shell nanostructures but also offer us their electric near-field distribution profiles. Figure 3 shows the electric field profiles of a Au nanobowl, a Au open nanocage, and a Au open eggshell with different h values. They are excited at the wavelengths of the corresponding dipolar plasmon bands and quadrupolar plasmon bands. Taking the Au nanobowls with different h values as an example, the nanoshell (h = 1) exhibits a dipolar resonance feature at 842 nm and a quadrupolar feature at 626 nm; after the symmetrical geometry is broken, the resonances at 968 (h = 0.75) and 626 nm (h = 0.25) still display a dipolar character and are dominated by the local charge buildup at the edges of the top nanoaperture (see insets in Fig. 3). This charge buildup is accompanied by a strong enhancement of the local electric field (see “hot spots” in Fig. 3). However, the resonance at 620 nm for h = 0.75 shows a much weaker electric field with a quadrupolar feature. The Au open nanocage and open eggshell show a similar local charge buildup and electric field enhancement at the edges of the top nanoapertures when h is decreased at their dipolar resonance modes (Fig. 3). In addition, Au open nanocages exhibit enhanced electric fields at the bottom corners due to the sharp geometry feature at their dipolar and quadrupolar resonances. Au open eggshells display additionally enhanced electric fields at the longitudinal corners due to the plasmonic hybridization of a solid spheroid and an ellipsoidal cavity. All these strong enhanced fields indicate those Au open shell nanostructures to be potential SERS substrates.
Fig. 3 Electric field profiles of a Au nanobowl, a Au open nanocage, and a Au open eggshell with different fractional height (h) values. Insets: surface charge distribution on the top surfaces of a Au nanobowl (left, h = 0.75) and a Au open nanocage (right, h = 0.5).
Plasmonic hybridization theory is an effective tool to understand, design, and predict optical properties of metallic nanostructures [13–15]. Plasmonic properties of Au nanoshells, nanocages, and eggshells have been explained by using the plasmon hybridization between the outer shell surface and the inner shell surface [1,3]. The symmetry breaking induced and fractional height dependent spectral changes of the Au open shell nanostructures can also be explained in the framework of the plasmon hybridization model. Figure 4 shows the plasmon hybridization diagrams for nanobowls and open nanocages. The broken-symmetrical geometry allows the dipolar plasmons of nanoholes interact with the dipolar and quadrupolar plasmons of nanoshells or nanocages, respectively. Each interaction leads to a splitting with a low-energy “bonding” mode and a high-energy “anti-bonding” mode. Due to the limit of broken geometry, the hybridization between two dipolar modes is stronger than that between the quadrupole mode and the dipole mode, resulting in a greater energy splitting. Our calculated surface charge distribution diagrams for the dipolar and quadrupolar resonance modes of nanoshells (Fig. 4a) and nanocages (Fig. 4b) before and after hybridization confirm that the plasmons on the outer and inner surfaces of the nanobowls or the open nanocages have been re-distributed by following the plasmon hybridization model. The red shift of the dipolar band (1 > h > 0.625) can be attributed to the hybridization of the dipole of the full Au shell (nanoshell, nanocage, or eggshell) with the dipole of the nanohole. For example, for a nanobowl of h = 0.875 (Fig. 4a), the plasmon bands at 917, 643, and 579 nm can be assigned to the hybridized dipolar “bonding”, quadrupolar “bonding”, and quadrupolar “anti-bonding” mode, respectively. However, the high-energy dipolar “anti-bonding” mode locates at a higher energy region, usually interacts weakly with the incident light and can be further damped by the interband transitions in the metal [4,16]. Consequently, we do not observe the dipolar “anti-bonding” modes in our spectra. When the hole becomes larger or h becomes smaller, the hybridization leads to a lower energy “bonding” mode, which explains the red shift of the dipolar band of nanobowls. Once the aperture of the shell closes, the red shift disappears because of the lack of the hybridization and the absence of the charge buildup in the aperture. The blue shift of the dipolar band (0.625 > h > 0) can be ascribed to a geometrical transition, leading to a higher concentration of electric field lines inside the metal [17]. The quadrupolar mode also couples to the dipolar mode of the nanoholes, resulting in a splitting with a red-shift “bonding” band and a blue-shift “anti-bonding” band for large h values (e.g., h = 0.875). As h decreases, the cavity length of the quadrupolar excitations shrinks, which leads to a blue shift and attenuation [18]. It is also easy to understand that the dipolar bands remaining at the same wavelength (1139 nm) for the Au open nanocages for 0.875 > h > 0.625 is because of no change of the dipole-dipole hybridization between the nanocages and the nanoholes. For the open eggshells, the electric field along the longitudinal diameter can only excite the dipole mode, thus we can only observe the dipole-dipole hybridization between the eggshells and the nanoholes. To obtain more understanding, we compare our simulation spectra with some experimental data published recently about the open shell structures with different fractional heights [12, 19]. The hyperbola-like shift of the dipolar “bonding” resonance bands and the attenuation of the quadrupolar “bonding” bands are experimentally observed but with the limit of the latter only on large Au nanobowls. However, no experimental observation of the quadrupolar “anti-bonding” modes have been reported probably due to the fact that they are merged into the quadrupolar “bonding” modes resulting in a single, wider peak.
Fig. 4 Plasmon hybridization schemes and calculated surface charge distribution for (a) a nanobowl (h = 0.875) resulting from interacting nanoshell and nanoholes plasmons and for (b) an open nanocage (h = 0.75) from nanocage and nanoholes plasmons. Dipole-dipole and quadrupole-dipole hybridizations lead to a splitting with a low-energy “bonding” mode and a high-energy “anti-bonding” mode.
Another rather important parameter to evaluate is the maximum electric field intensity (|E|2max) of Au open shell nanostructures and their corresponding fractional heights, which is of high interest for the application of SERS. We have calculated the |E|2max and maximum extinction cross section (Qmax) of Au open nanocages with different fractional heights (Fig. 5 ). |E|2max largely increases from 108 to more than 230 when the symmetry of the Au nanocage is broken (h < 1) and reaches the maximum value of 303 when h = 0.625. We believe that this information may allow for the design and fabrication of optimized Au open shell nanostructures for SERS application. Additionaly, the relationship between Qmax and fractional height shows a consistent trend as the one between |E|2max and fractional height: reaching the maximum value of 9.62 when h = 0.625. This probably can be explained by the fact that the dipole-dipole interacting mode between the nanocages and the nanoholes reach the maximum hybridization when h = 0.625. The multiple factors including the effect from the sharp geometry feature contribute to the electric field enhancement in Au nanobowls and Au open eggshells. Therefore, we do not simply observe the fractional height dependent |E|2max effect in Au nanobowls and Au open eggshells and more detailed investigations are underway.
Fig. 5 Maximum extinction cross section (Qmax) and maximum electric field (|E|2max) intensity of Au open nanocages with different fractional height (h) values.
4. Summary
In summary, we have investigated the symmetry breaking induced optical properties of Au open shell nanostructures including nanobowls, open nanocages, and open eggshells by using the three dimensional FDTD method. The fractional height dependent optical properties are mainly attributed to the symmetry-broken geometry and are explained well by the plasmon hybridization model. The interaction of the dipolar plasmon resonance of the nanoholes with the dipolar and quadrupolar plasmon resonances of full shell nanostructures lead to the presence or spectral shift of new bonding and anti-bonding band in asymmetrical structures. In addition, calculations show that the local electric fields are strongly enhanced at the edges of the open nanoapertures when the symmetry of these structures is broken. The maximum electric field is reached when the fractional height is 0.625 for the Au open nanocages. These Au open shell nanostructures show a promising application in the SERS-based biomolecular detection.
Acknowledgment
The authors would like to thank all current and former members of the FNS research group for their valuable scientific input. P.V.D. acknowledges financial support from the FWO of Flanders.
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