1. Introduction

Gold (Au) nanoshells, consist of a dielectric core surrounded by an ultrathin Au shell, have attracted significant research attention at present due to their highly tunable optical properties and excellent biocompatibility. They have a broad range of spectroscopic and biomedical applications such as localized surface plasmon resonance (LSPR) sensing [1], drug delivery [2], biomedical imaging [3], and cancer therapeutics [4]. The optical properties of Au nanoshells are greatly dependent on geometry and local dielectric environment. For a given composition of core and surrounding medium, the plasmon resonances of the Au nanoshells can be tuned from the visible region to the near-infrared region by changing the ratio of the core size to shell thickness [5].

Reducing the symmetry of Au nanoshells by excising a part of the nanoshell generates a series of semishells which include ‘nanocaps’, ‘half-shells’ and ‘nano-cups’ [6]. The semishells offer a number of interesting optical properties. The plasmon resonances of these particles are influenced not only by geometric asymmetry, but also by the angle and the polarization of the incident light. As a result, arrays of these particles can serve as optically functional coatings that are simultaneous selective to wavelength and the angle of the incident light [7]. The nanocup also have a large field enhancement at the edge of the rim and have demonstrated as interesting substrates for surface-enhance Raman spectroscopy (SERS) based molecular detection [8, 9]. Moreover, The nanocup have the ability to redirect scattered light in a direction dependent on particle orientation and permittivity of substrate [10,11]. In the earlier study, the nanocup particles were often prepared by physical or chemical deposition onto a polymer particle template [12]. Recently, the method involving an anisotropic etching process [8,13–15] has been developed to fabricate reduced-symmetrical Au semishells. It is like a perforation on the Au shell. The size and the position of the hole on the Au shell can be well controlled by the etching processes. The Au nanoshell with multiple holes onto the shell can be fabricated by this method [15].

In this paper, a new geometry of the Au nanoshell with two holes is proposed. With an additional hole on the nanocup particle, the second ‘dimensional’ symmetry breaking is produced on the Au nanoshell, which results in the two-dimensional (along two symmetrical axes of the hole on nanoshell) angularly selective optical properties of the nanoshell. Compared with the nanocups, our design offers the additional dimensional angularly selectivity of the optical properties. It has great potential to develop new optical and biological applications. For example, coatings of these particles can function as angularly selective window glazing [16,17] that the extinction of the window can be very flexibly manipulated by the orientation of the window with respect to the incident light. In addition, making the second hole on the nanocup can red-shift the plasmon resonances of Au nanoparticles in the near-infrared region (700-1300 nm) that is suited to the biological detection [18].

2. Numerical method

In this work, we study the silica-gold nanoshell with one hole (nanocup) and with two holes on the gold shell as shown in Fig. 1 . In order to investigate the angle and polarization dependence of incident light, we study the spectral properties of nanoshell in the rectangular coordinate system as shown in Fig. 1(c), 1(d). The incident radiation propagates in the + x direction, and the target nanoshell can be adjusted to arbitrary orientation relative to the incident light in our simulations.

 

Fig. 1 (a) Mid-sectional view of a silica-gold nanoshell with a hole. (b) Mid-sectional view of a silica-gold nanoshell with two holes. (c) Schematic of the geometry of nanoshell with one hole. (d) Schematic of the geometry of nanoshell with two holes.

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We have simulated the optical properties of the proposed holes-on-nanoshell structures using DDSCAT 7.1 [19–21], the code of Draine and Flatau that exploits the discrete dipole approximation (DDA). In this scheme, the nanoparticle is approximated by a three-dimensional array of dipoles and the resulting optical behavior is obtained numerically. The nanoshell structures with holes we studied are in the size region (diameter about 100 nm) where successful particle fabrications have been reported [13, 14]. In the calculations, dipole numbers between 50000 and 65000 are set for various core-shell nanoparticles. The surrounding medium is water. The dielectric properties for gold are taken from ref [22]. The dielectric constant for silica is set to 2.04 and for water is 1.33.

3. Results and discussion

We first consider the Au nanoshell with the core radius R₁ = 38 nm and the shell radius R₂ = 50 nm which has a hole with radius r = 26 nm as shown in Fig. 1(a). In the system of the nanoshell with one hole as shown in Fig. 1(c), the polarization vector of incident light is along the z-axis. It is seen that the axis of the symmetry of the nanoshell with the hole is the x-axis. When we rotate the nanoshell along the y-axis, the angle between the E-field and symmetry axis of the particle is also changed, which influences the extinction spectrum of the particle as shown in Fig. 2 . Because the optical extinction spectrum of the Au semi-shells is mainly determined by the direction of the polarization vector and is almost independent of the direction of the k vector of the incident light [6], we only considered the acute angle α as shown in Fig. 1(c). In Fig. 2, we show the extinction spectrum of the nanoshell when the particle rotates along y-axis at α = 0°, 30°, 60°, and 90°. It is seen that the extinction peak at 764 nm weakens and disappears and the extinction peak at 642 nm emerges as the particle rotates from 0° to 90°. The resonance at 642 nm is usually called the axial (dipolar) mode parallel to the axis of symmetry and the resonance at 764 nm is the transverse (dipolar) mode perpendicular to the axis of rotational symmetry as described in ref [14]. If we rotate the particle along other coordinate axis (such as x-axis or z-axis), the extinction spectrum of the nanoshell does not change because the angle between the E-field and symmetry axis of the particle is unchanged. Thus the optical properties of Au nanoshell with one hole are one-dimensional (rotation along the y-axis) angularly and spectrally selective as Fig. 2 shows.

 

Fig. 2 Extinction efficiency of the nanoshell with a hole (r = 26 nm) at the rotational angle α = 0°, 30°, 60°, and 90° along y-axis.

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Inspired by the optical properties by Au nanoshell with one hole, we propose a two-hole (with the radius r₁ and r₂) structure of Au nanoshell with the core radius R₁ = 38 nm and the shell radius R₂ = 50 nm as shown in Fig. 1(b) (d). The E field of incident light is along the z-axis. The symmetrical axes of the two holes with different size on the Au shell are perpendicular to each other. In this case, two symmetrical axes in nanoshell each for one hole are fictitiously considered. The symmetrical axis for the up-side hole is y-axis and the symmetrical axis for the left-side hole is x-axis as shown in Fig. 1(d). When the Au nanoshell rotates along the y-axis, the angle between the E-field and the symmetrical axis of the left-side hole is changed but the angle between the E-field and the symmetrical axis of the up-side hole is fixed. However, when the Au nanoshell rotates along the x-axis, the angle between the E-field and the symmetrical axis of the up-side hole is changed but the angle between the E-field and the symmetrical axis of the left-side hole is fixed. Because the change of angle between the E-field and symmetry axis of the particle can induce the change of extinction spectrum of the particle, both of above cases can change the extinction spectrum of the particle. As a result, the Au nanoshell with two holes we suggested can perform two-dimensional (rotation along the y-axis and the x-axis) angular and spectral selectivity of optical properties. Note that, the purpose of the second hole is to provide the additional anisotropic optical properties relative to the nanocup. Actually we may place the second hole at else positions on the Au shell. However, we can obtain the largest anisotropic optical properties along the y-axis and the x-axis when the symmetrical axes of the two holes are set to be perpendicular to each other. Thus we can control the extinction of the nanoshell by manipulating the orientation of nanoparticle to the incident light easily along the two perpendicular dimensions, which have potential to develop the ‘smart’ coating in windows or display devices [17].

In Fig. 3(a) , we show the extinction efficiency of the nanoshell with two holes (r₁ = 16 nm and r₂ = 26 nm) when the particle rotates along y-axis at α = 0°, 30°, 60°, and 90° with fixed rotation angle β = 0°. It is seen that the changing of dipolar resonance modes in extinction spectrum at different angles are similar to the spectrum of the nanoshell with one hole. A physically intuitive understanding of this analogy is that the two adjacent holes on the shellcan be almost regarded as one big cleft which performs similar behaviors on the plasmon resonances like one large hole on the shell [6]. The extinction of the transverse (dipolar) mode resonance at 989 nm disappears and the extinction of the axial (dipolar) mode resonance at 707 nm appears as the particle rotates from α = 0° to 90°. In Fig. 3(b), we also show the extinction of the nanoshell when the particle rotates along x-axis at β = 0°, 30°, 60°, and 90° with fixed the rotation angle α = 0°. It is also seen that the extinction peaks at 989 nm (the transverse mode) and at 670 nm (the axial mode) are present when the rotation angle β of the particle is 0° and 90°, respectively. To clearly see the dependence of extinction on the wavelength and angle, the rough contour maps of extinction efficiency with the varying wavelength and rotational angle α (at intervals of 10°) with β = 0° and β (at intervals of 10°) with α = 0° are shown in Fig. 3(c) and 3(d). It is seen that the Au nanoshell with two holes has the two-dimensional (rotation along the y-axis and the x-axis) angular and spectral selectivity of optical properties.

 

Fig. 3 Extinction efficiency of the nanoshell with two holes (r₁ = 16 nm, r₂ = 26 nm) (a) at the rotational angle α = 0°, 30°, 60°, and 90° along y-axis (β = 0°), (b) at the rotational angle β = 0°, 30°, 60°, and 90° along x-axis (α = 0°), (c) with the varying wavelength and rotational angle α at β = 0°, (d) with the varying wavelength and rotational angle β at α = 0°,

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To investigate the influence of the size of the hole, we calculated the extinction of the particle with different sizes of the two holes (r₁ = 16 nm, r₂ = 10, 16, 22, 26 nm) at α = 0°, 90° (β = 0°) rotation angle of the particle and the two holes (r₁ = 10 nm, r₂ = 10, 16, 22, 26 nm) at β = 0°, 90° (α = 0°) rotation angle of the particle. As shown in Fig. 4 , the distinct red shifts can be seen at 0° rotation angle of the particle and the relative small blue shifts can be seen at 90° rotation angle of the particle when the size of upside hole increases in both cases. It is similar to the previous results of nanocup that the transverse modes red shifts whereas the axial modes blue shifts with the increase of hole size [13,15]. We also show the comparison of the shifts of extinction peaks of the nanoshell with one hole and with two holes in Fig. 5 . We can see that the extinction peaks of the nanoshell with two holes red-shift compared with the nanoshell with one hole (nanocup). The extinction peaks of the nanoshell with two holes at 0° rotation angle of the particle moves into the near-infrared region (700-1300 nm) where the biological tissues are transparent. This provides an alternative way that tunes the plasmon resonances of core-shell Au nanoparticles into the near-infrared “biological window” instead of increasing the ratio of the nanoparticle’s core size to its shell thickness [5].

 

Fig. 4 Extinction efficiency of the nanoshell (a) with two holes of different sizes (r₁ = 16 nm, r₂ = 10, 16, 22, 26 nm) at the rotational angle α = 0°, and 90° along y-axis (β = 0°) and (b) with two holes of different sizes (r₁ = 10 nm, r₂ = 10, 16, 22, 26 nm) at the rotational angle β = 0°, and 90° along x-axis (α = 0°).

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Fig. 5 The shifts of extinction peaks of the nanoshell with one hole (black) of different r (r = 10, 16, 22, 26 nm) at α = 0°, and 90°, the nanoshell with two holes (red) of different r₂ (r₂ = 10, 16, 22, 26 nm, r₁ = 16 nm) at α = 0°, and 90° (β = 0°), the nanoshell with two holes (blue) of different r₂ (r₂ = 10, 16, 22, 26 nm, r₁ = 10nm) at β = 0°, and 90° (α = 0°).

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4. Summary

In summary, we have numerically studied the optical properties of the Au nanoshell with two holes whose symmetrical axes are perpendicular to each other. We show that the extinction spectrum of the Au nanoshell with two holes can be two-dimensionally controlled by rotating the particle along the different symmetrical axis. In addition, the increasing of size of the hole can further red shift the extinction peaks in near-infrared region of “biological window”. The proposed Au nanoshell with two holes has the potential to develop the new optical applications for two-dimensional angular and spectral selectivity. Furthermore, we suggest the conception of the “two-dimensional” symmetry breaking in the nanoparticle, which can induce two-dimensional spatial asymmetry of optical properties of nanoparticles. The idea of two-dimensional symmetry breaking might provide new research interest on the associated effects of symmetry breaking on the nanoparticles [23,24].