Symmetry breaking of metallic nanoparticles results in many unique optical properties. We use the discrete dipole approximation method to study the optical properties of overlapped nanoshells which further break the rotational symmetry compared with the semishells. The optical properties of the nanoparticles can be tuned from the visible to near infrared regime by varying the geometry parameters and the hybrid components of nanoparticles. The calculated extinction spectra show the two-dimensional anisotropy of the angular optical response of the nanoparticles. The plasmon hybridization model provides a way to interpret the resonance modes of the nanoparticles. The tunable plasmon resonances, the enhanced local fields and the anisotropic optical properties suggest that the overlapped nanoshells have potential applications in surface-enhanced spectroscopy and “smart” coating in windows or display devices.
© 2013 OSA
Metallic nanoparticles have extraordinary optical properties known as the localized surface plasmon resonances (LSPR) which come from the collective oscillation of the conduction electrons excited by incident radiation [1,2]. The plasmon resonances, strongly dependent on particle geometry, create spectral absorption and scattering peaks . Symmetric nanoparticles, such as nanoshells consisting of a dielectric core and a thin metallic shell, have attracted significant research attention due to their highly tunable optical properties . The optical properties of nanoshells can be explained by the plasmon hybridization model which describes the plasmon response as an interaction between nanocavity and nanosphere plasmons .
For symmetric nanoparticles, plasmon hybridization only occurs between elementary plasmons supported by different nanoparticles of the same angular momentum . Symmetry breaking results in the interaction between elementary plasmons of all multipolar indies . Many unique optical properties of metallic nanoparticles originate from their reduced symmetry, such as anisotropy of the angular optical response  and Fano resonances . Reduction in symmetry of nanoshells by partially covering the dielectric core with metal generates a series of geometries termed “semishells”. Numerous efforts have been performed to discover novel optical properties of the semishells. Au semishells exhibit two distinct dipole plasmon resonances as a result of reduced symmetry, one parallel to the axis of symmetry (axial mode) and the other perpendicular to the axis of symmetry (transverse mode) . Au semishells exhibit a larger tuning range of optical properties and an enhanced local electromagnetic field compared with full nanoshells [11, 12]. For the electromagnetic “hot spots” at the sharp edges of semishells, Au semishells have been developed as surface-enhanced Raman spectroscopy (SERS) substrates to achieve high enhancement factor [13, 14]. The spectral and angular dependence of light scattering from Au nanoshells has been investigated as a true three-dimensional nanoantenna, enabling the application in nanophotonics [15, 16]. Recently, some further reduced-symmetry nanoparticles, breaking rotational symmetry of semishells, have been designed to support a range of novel optical phenomena. Perforated semishells - plasmonic semishells with specifically shaped and oriented perforations introduced into the metallic shell layer - can be tailored to control the far-field scattering profile and magnetic resonances at optical frequencies . The “two-dimensional” symmetry breaking of Au nanoshells with holes can induce the two-dimensional spatial asymmetry of optical properties of these nanoparticles .
Recently, Yu have reported on the fabrication of overlapped microshells which have potential application in nanophotonic devices due to the breaking of rotational symmetry . The overlapped nanoshells (OLNSs) can be fabricated by using nanoscale spheres as template. The nanostructure of OLNSs offers a tool to study into the plasmonic optical properties of hybrid nanoparticle systems . The OLNSs can be developed as effective substrate in surface-enhanced spectroscopy for the local fields enhancement (LFE) at the sharp edges . In this paper, the optical properties of the OLNSs were numerically investigated. We studied the two-dimensional anisotropy of angular optical response of OLNSs by changing the incident polarization. The plasmon hybridization model was used to interpret the two-dimensional anisotropy. The influences of geometry parameters and the substrate on the plasmon resonances of Au OLNSs were presented. The hybrid metallic OLNSs can be fabricated to tune the optical properties without varying the geometry parameters.
2. Simulation method
According to the Yu method, the OLNSs can be fabricated through two-step angled vapor deposition on a nanosphere template as shown in Fig. 1(a). First, the semishell i (orange) will be formed by depositing one component at a certain angle. Then another vapor deposition at another angle will be followed to form the semishell ii (red). Subsequently the OLNSs will be obtained by simply removing the nanosphere template. The two-step deposition induces the unique ringent hollows of OLNSs. The ringent angle θ between the edges is decided by the deposition angle of the two steps.
Three-dimensional numerical simulations were carried out with an open-source software package DDSCAT 7.2 applying the “discrete dipole approximation” (DDA) method. The incident radiation propagates in the + X direction with the polarization vector parallel to the Y axis as shown in Fig. 1(b). The bodies of OLNSs are set semitransparent to exhibit the ringent hollow. The orientation angles (Θ, Φ) specify the orientation of OLNSs with respect to the incident light. The elevation angle Θ is the angle between + X direction and orientation vector of OLNSs. When azimuth angle Φ = 0°, the orientation vector of OLNSs will lie in the XOY plane. The mid-sectional views of the OLNSs are shown in Figs. 1(c) (side) and 1(d) (front). Clearly, the hollow is a spherical nanocavity and the inner contour of the OLNSs is part of a sphere with radius r. In the simulations, the outer contour of each section passing through the axis A1A2 is defined as semi-ellipse shown in Fig. 1(c). As shown in Fig. 1(d), the mid-section (front) can be characterized by two nonconcentric circles where r is the inner radius, R is the outer radius, and δ is the center-center distance. Here, the thickness of the OLNSs is defined as t = R + δ – r. Thus, the geometry of OLNSs can be characterized by the values of θ, r, and t. The dipole number was set between ~200000 and ~400000 for various nanoparticles. The refractive index of surrounding medium was 1.333 for water and the wavelength-dependent refractive indices of Au, Ag, Cu, Al and Pt were adopted in all simulations .
3. Results and discussion
The semishells support one-dimensional anisotropy of the angular optical response. To compare the extinction spectra of Au OLNSs with those from Au semishells, we first investigated the dependence of the optical properties of Au semishells on the incident polarization. The incident polarization can be controlled by the orientation angles (Θ, Φ). The rotational symmetry of the semishells is presented in Fig. 2(a). The shell thickness and inner radius are set at 30 nm and 50 nm, respectively. The outer radius of the semishells is identical to the radius R of OLNSs (θ = 90°, t = 30 nm and r = 50 nm). Figures 2(b) and 2(c) show the semishells orientations with respect to the incident light when the angles (Θ, Φ) are set at (0°, 0°-90°) and (90°, 0°), respectively.
The elevation angle Θ provides the control of the anisotropy of angular optical response as shown in Fig. 2(d). Two modes excited at ~870 nm and ~650 nm correspond to transverse dipole and quadrupole modes, respectively. When azimuth angle Φ is fixed at 0° and elevation angle Θ varies from 0° to 90°, the axial dipole (~730 nm) and quadrupole (~600 nm) modes are excited and gradually enhanced. The intensities of transverse dipole and quadrupole modes are reduced with the increase in Θ. However, the change in azimuth angle Φ has no influence on the optical properties of Au semishells as shown in Fig. 2(e). Because the geometry of OLNSs breaks the rotational symmetry, the nanoparticles can support two-dimensional anisotropy of the angular optical response relative to the semishells. Figures 3(a)-3(c) show the extinction spectra of Au OLNSs with different (Θ, Φ). Figures 3(d)-3(f) show the OLNSs orientations with respect to the incident light when the angles (Θ, Φ) are set at (0°, 0°), (90°, 0°), and (0°, 90°), respectively. The mid-sectional LFE profiles are also plotted for each orientation at resonance wavelengths. The thickness t and inner radius r are set at 30 nm and 50 nm, respectively. The ringent angle θ are fixed at 90°.
Compared with the semishells, the OLNSs support the similar anisotropy of the angular optical response. When the angles (Θ, Φ) = (0°, 0°), the transverse dipole (~1160 nm) and quadrupole (~670 nm) resonances can be clearly recognized from the extinction spectrum and profiles of LFE at resonance wavelengths. Additionally, the axial dipole (~800 nm) and quadrupole (~610 nm) modes are excited and gradually enhanced when azimuth angle Φ is fixed at 0° and elevation angle Θ varies from 0° to 90° as shown in Fig. 3(a). When the elevation angle Θ is fixed at 0°, the azimuth angle Φ provides another dimensional control of the anisotropy of the angular optical response relative to the semishells as shown in Fig. 3(b). Here, the incident light is referred to as longitudinal polarized for (Θ, Φ) = (0°, 90°). The enhancement of longitudinal dipole mode (~850 nm) and attenuation of transverse dipole mode (~1160 nm) are both observed. However, the plasmon resonance at low wavelength shows a blue-shift with the increase in Φ. The phenomena can be interpreted as the overlap of the transverse quadrupole mode (~670 nm) and longitudinal quadrupole mode (~630 nm). The resonance wavelengths of the two modes are very close and the intensity of the longitudinal quadrupole mode is quite strong relative to the axial quadrupole mode. The two modes are overlapped and no obvious splitting of peaks can be recognized. Thus, the phenomena of enhancement of one resonance mode and attenuation of another are not observed at low wavelength regime. Three plasmon resonances can be recognized from each extinction spectrum as shown in Fig. 3(c). The anisotropy of the angular optical response of Au OLNSs is more evident when both Θ and Φ vary between 0° and 90°. Both the intensities and the wavelengths of resonance modes can be tuned by varying the orientation angles (Θ, Φ). Any incident polarization excites a mixture of the transverse, longitudinal and axial resonance modes. The transverse dipole mode (~1160) shows the decrease in intensity but no shift of wavelength. The longitudinal and axial dipole modes overlap and exhibit one resonance peak varying between 810 and 850 nm. Besides, the resonance peak varies between 620 and 660 nm corresponding to the overlapped quadrupole modes. It is concluded that the optical properties of OLNSs are strongly dependent on the incident polarization. The acute sensitivity of OLNSs to the incident polarization might conceivably serve as the basis of a “smart” coating in windows or display devices .
To explain the two-dimensional anisotropy of the angular optical response, we extend the plasmon hybridization model for semishells (nanocups) / nanoeggs [6, 24] to OLNSs with rotational asymmetry. For OLNSs, the cavity-sphere hybridization model no longer applies. Instead, the cavity-ellipsoid model is used to approximately interpret the optical properties of OLNSs. As shown in Fig. 4(a), the core offset between the cavity and ellipsoid results in the model nanostructure which is similar to the geometry of OLNSs. The symmetry breaking results in the interaction between primitive plasmons of different multipolar orders of cavity ωc,l and ellipsoid ωeps,l. This interaction leads to a stronger splitting of the plasmon resonances into two new modes of the OLNSs: the lower energy bonding plasmon mode ω- and the higher energy antibonding plasmon mode ω+. The antibonding modes are hardly excited because they interact weakly with the incident light. For the geometry symmetry, the sphere supports one dipole mode. However, the ellipsoid supports two dipole modes: transverse (~610 nm) and axial (~560 nm) plasmons as shown in Fig. 4(b). When (Θ, Φ) = (0°, 0°), the interaction between cavity plasmon and transverse plasmon of ellipsoid results in transverse bonding dipole and quadrupole modes of OLNSs. The axial bonding modes of OLNSs are excited when the incident light is axially polarized (Θ = 90°, Φ = 0°). The interaction between cavity plasmon and axial plasmon of ellipsoid results in the longitudinal bonding modes for OLNSs when (Θ, Φ) = (0°, 90°). Figure 4(c) shows the extinction spectra of the model nanostructure under three polarizations. The two-dimensional anisotropy of the angular optical response is identical to the OLNSs. Thus, the optical properties of OLNSs can be properly interpreted by the cavity-ellipsoid hybridization model.
The influence of the ringent angle θ on the optical properties of Au OLNSs is summarized. Figure 5 shows the calculation results about extinction spectra and the front mid-sectional profiles of LFE of Au OLNSs with different θ. The inner radius r and thickness t are set at 50 and 30 nm, respectively. The orientation angles (Θ, Φ) which decide the orientation of OLNSs with respect to the incident light fixed at (0°, 0°). When ringent angle θ is 60°, the dipole, quadrupole, and octupole plasmon resonances can be clearly recognized from the extinction spectrum and profiles of LFE at resonance wavelengths as shown in Fig. 5(a). The plasmon resonances at about 1270, 710 and 600 nm correspond to transverse dipole, quadrupole and octupole modes, respectively. For the octupole mode, the electromagnetic enhancement region located at the tip is small. When the ringent angle θ is increased (θ = 90°, 120° and 150°), the transverse dipole and quadrupole resonance modes are recognized as shown in Figs. 5(b)-5(d). The dominant resonance at ~760 nm is transverse dipole mode and the small peak at ~570 nm corresponds to quadrupole mode for the single semishell (θ = 180°) as shown in Fig. 5(e) . However, a small peak at ~750 nm is observed in the spectrum of Au OLNSs with θ = 150°. For the case of θ = 150°, the geometry of OLNSs is similar to the single semishell. Besides, the optical properties of Au OLNSs approximate to that of single Au semishell when the ringent angle θ is close to 180°. Thus we interpret the peak at ~750 nm as resulting from transverse dipole mode of a single semishell. It is noticed that both the transverse dipole and quadrupole resonance wavelengths are blue-shift as the ringent angle θ increases. The blue-shift can be explained by the cavity-ellipsoid hybridization model. As θ increases, and the cavity moves further outside of the ellipsoid, the primitive plasmon modes hybridize more weakly, resulting in a subsequent blue-shift of the multipole modes. For θ = 60°, the hybridization is strong; thus, the octupole mode is excited. The reduced hybridization leads to the enhancement in intensity of transverse dipole mode but results in the decrease in intensity of transverse quadrupole mode. Because of the enhanced fields located at the sharp edge of ringent hollow, the OLNSs have potential application in biological and biochemical sensing, such as SERS and SEIRA. The geometry of nanoparticle provides a way to tune the optical properties of OLNSs to match the specific spectrum regime of the application by changing the ringent angle θ. The tunable optical properties are quite desirable to achieve the maximum enhancement factor of the applications in SERS  and SEIRA .
We also studied the influence of inner radius r on the optical properties of OLNSs. Here, the thickness t and ringent angle θ are fixed at 30 nm and 90°, respectively. The orientation angles of Au OLNSs with respect to the incident light are set as (Θ, Φ) = (0°, 0°). In Fig. 6(a), three plasmon resonances can be recognized in the extinction spectra of Au OLNSs with r = 100 and 150 nm. Figures 6(b)-6(d) show the front mid-sectional LFE profiles of Au OLNSs (r = 100 nm) at resonance wavelengths. The plasmon resonances at about 1670, 780, and 630 nm correspond to transverse dipole, quadrupole, and octupole modes, respectively. With the reduced symmetry of OLNSs, the multipole primitive ellipsoid plasmon modes can hybridize with all multipole cavity plasmon modes. The resulting higher order modes can contain dipole element; thus the multipole modes are easily excited by incident light. When the radius r is increased from 50 to 150 nm, the red shifts can be observed from the extinction spectra in the transverse modes, from ~1160 to ~2230 nm for transverse dipole mode, ~670 to ~900 nm for transverse quadrupole mode, and ~630 to ~710 nm for transverse octupole mode. The resonance modes of OLNSs will be greatly red-shifted in the near infrared regime when the radius r is further increased.
We investigated the influence of material on the extinction spectra of OLNSs for achieving highly tunable optical properties. According to the fabrication method, it is feasible to fabricate hybrid metallic OLNSs consisting of two components. The semishell i and ii will be composed of different components. Here, we studied the optical properties of hybrid metallic OLNSs which are composed of Au and another metal, including Ag, Cu, Al and Pt. The extinction spectra of OLNSs composed of only one metal are presented in Fig. 7(a) for comparison. The thickness t and inner radius r are set at 30 nm and 50 nm, respectively. The ringent angle θ are fixed at 90°. The incident light is transversely polarized with respect to the ringent hollow (Θ = 0°, Φ = 0°). The optical properties of Ag OLNSs and Cu OLNSs are similar to that of Au OLNSs. Two plasmon resonances can be observed from extinction spectra of hybrid metallic OLNSs as shown in Fig. 7(b). The resonance wavelengths of Au-Ag OLNSs (~1130 nm, ~640 nm) interpolates between that of Au OLNSs (~1160 nm, ~670 nm) and that of Ag OLNSs (~1090 nm, ~580 nm). The phenomenon is also observed for Au-Cu and Au-Al OLNSs. For multilayer nanoshells, deposition of a second metal overlayer can completely change the resonance wavelengths of the nanoparticles . Because the semishell i is partially covered by the semishell ii, both the two components contribute to the optical properties of the hybrid OLNSs. However, a linear dependence of the resonance wavelengths on the ratio of each metal is not justified when describing the optical properties of hybrid nanoparticles . The plasmon band of the hybrid material is quite different from a pure metal. Actually, the plasmon resonances of hybrid nanoparticles depend critically on the correct dielectric function of the alloy . Compared with the semishells, the hybrid construction of OLNSs provides an additional way to tune the optical properties without changing the shape of the nanoparticles.
According to Yu method, a metal film is produced on the substrate and a “shadow” area is created to the opposite side of the metal coating . Here, the substrate is modeled as a finite, flat, cylindrical slab with a “shadow” hole in the center. The slab radius is three times as large as the outer radius of OLNSs. The thickness t and inner radius r are set at 30 nm and 50 nm for OLNSs, respectively. The ringent angle θ are fixed at 90°. The modeled “shadow” hole is similar to that of the “shadow” area created during the practical deposition process. Figure 8(a) shows the extinction spectra of a circular slab, the modeled substrate and a single OLNS supported on the substrate. The nanosphere template is ignored in this calculation. The front mid-sectional views of the OLNS and substrate are shown in Fig. 8(b). The OLNS is set as isolated from the “shadow” hole without interconnections between the nanoparticle and substrate. The broad band of the dominant resonance (~1400 nm) is observed for the slab. For the modeled substrate, a peak at ~650 nm and a weak red-shift of dominant resonance is produced because of the “shadow” hole. The plasmon resonances of the “shadow” hole may be overlapped by the broad band of slab mode; thus, only one broad dominant peak is observed in the extinction spectrum of the modeled substrate. When the OLNS is supported on the modeled substrate, two dominant resonances (~1370 and ~1690 nm) are observed. In Fig. 8(c), the strength of local fields near the “shadow” area is close to that of single OLNS at wavelength of dipole mode (Fig. 5(b)). Figure 8(d) shows a much stronger local fields near the “shadow” compared with a single OLNS. We interpret the resonance at ~1690 nm as the hybridization between the plasmons of OLNS and the “shadow” hole. The hybridization results in the enhanced local fields which will be helpful to improve the enhancement factor (EF) for SERS. Because the enhancement of local fields is not found at ~1370 nm, the resonance might correspond to the slab resonance. Here, only one pair of OLNS and “shadow” hole is analyzed. In practice, many “shadow” holes are created and might overlap during the deposition process. The interconnections between the OLNSs and substrate might exist. The hybridization will be quite complex and might reduce the EF for SERS. To resolve the “shadow” influence issue, the method developed by Liu  can be used to immobilize the OLNSs on a second substrate with ringent hollow oriented upwards. The method might be helpful to potential application of OLNSs in SERS.
In conclusion, we have numerically investigated the optical properties of OLNSs which break the rotational symmetry by using the three dimensional DDA method. By analyzing the influence of incident polarization, the OLNSs exhibit the ability to support two-dimensional anisotropy of the angular optical response due to the rotational asymmetry relative to the semishell. The anisotropic optical properties of OLNSs show a promising application of OLNSs in “smart” coating in windows or display devices. Multipolar resonance modes are easy to be excited in OLNSs with small ringent angle θ or large inner radius r. The resonance wavelengths of OLNSs can be tuned from the visible to near infrared regime by varying the geometry, material and incident polarization. Thus, the OLNSs can be developed as a powerful substrate in SERS and SEIRA for the tunable plasmon resonances and enhanced local fields. The hybrid metallic OLNSs provide an additional factor to tune the resonance wavelengths and serves as a new nanostructure to study the plasmonic optical properties of hybrid nanoparticle systems. The influence of the substrate should be considered for the practical applications of the OLNSs. The plasmon hybridization model provides a reasonable way to interpret the tunable plasmon resonances and two-dimensional anisotropy of angular optical response.
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