Metallic nanoparticles possess a lot of intriguing optical properties due to the localized surface plasmon resonances (LSPR) they support.^[1] They show remarkable ability to confine light at nanoscale,^[2–4] leading to giant enhancement of electromagnetic field,^[5,6] which makes incredibly weak physics processes observable. This can be exemplified by the enhanced optical processes, including second harmonic generation (SHG),^[7–10] multiphoton luminescence,^[11] and surface-enhanced Raman scattering.^[12] When two or more nanoparticles are placed together, a new set of hybridized collective plasmonic modes^[13,14] can be observed due to their near field coupling. As a result, molding metallic nanoparticles to control their interactions can offer an effective approach to tailoring the field distribution in near field,^[15] and also the spectral lineshape^[16,17] and the scattering pattern in the far-field.^[18,19] Shaping the scattering pattern, especially to achieve the directional scattering, is of significance to many fields such as nanoantennas, sensors, and photovoltaic devices.^[18,20,21] As most materials have only dominant electric responses, conventional approaches to shape effectively the scattering patterns are mostly based on the engineering of the electric responses of various structures, such as optical Yagi–Uda antennas, V-shaped antennas, and bimetallic dimmers.^[18,22–27] Recently, sub-wavelength high-index all-dielectric particles have also been used to manipulate the scattering direction^[28,29] due to the resonance of their electric and magnetic modes and the low loss. Conventionally, the directional scattering is manipulated by carefully tuning the geometric parameters. However, this method is costly and, to certain extent, limited by the accuracy of fabrication process. Moreover, the dynamic control of the directional scattering is also highly desirable, which cannot be easily obtained in the geometry changing way.

Alternatively, the phase transition materials provide an effective way to control the far-field responses of nanostructures. Vanadium dioxide (VO₂), as a typical phase transition material, can be readily changed from semiconductor to metal state by controlling the ambient temperature.^[30–34] This intriguing characteristic has been widely used to actively tune the plasmon response of metallic structure.^[35,36] Dicken et al. reported a frequency-tunable metamaterial by deposing split-ring resonators on a VO₂ film in the mid-infrared region.^[37] Ye and Drope investigated the plasmonic behavior of gold dimers tuned by a VO₂ nanoparticle in the gap.^[38] Recently, thin VO₂ films have also been used to actively tune the beam steering angle of slot arrays^[39] and switch the propagation direction of surface plasmon polariton (SPP) on metallic slabs.^[40] Though a Yagi–Uda antenna for switchable radiation with VO₂ has been proposed,^[41] the structure needs a rather complicated fabrication process. To the best of our knowledge, a simpler and readily fabricated structure with VO₂ for switchable directional scattering has not been reported yet. In this paper, we design an asymmetric Au–VO₂ nanodisk dimer for realizing switchable directional scattering. The directional scattering of the asymmetric dimer can be turned on/off by changing the VO₂ nanodisk from metal to semiconductor state. We envision that our results may pave a way in potential applications of compact thermo-optical sensors, directional surface plasmon resonance bio-sensing, and integrated nanophotonic systems.

The structure of the asymmetric Au–VO₂ nanodisk dimer is schematically shown in Fig. 1. This asymmetric dimer consists of two nanodisks of Au and VO₂ characterized by the following geometry parameters: height T = 10 nm, and diameters D_Au = 100 nm, D_VO2 = 200 nm. These two nanodisks with a surface-to-surface separation of 140 nm are placed in a vacuum ambient. The structure is under the excitation of a plane-wave with the propagation direction along the positive z axis and the polarization direction along the y axis. To study the scattering properties of the asymmetric dimer, we perform a full-wave simulation by the finite-difference time-domain (FDTD) method using commercial Lumerical Numerical Solutions. The permittivity of Au is obtained from empirically fitting the data of Johnson and Christy with the multi-coefficient model built in the software,^[42] while the optical constants of VO₂ in metal and semiconductor states are taken from Ref. [43]. A perfectly matched layer (PML) boundary condition is used to mimic our structure in an infinitely large free space.

Fig. 1.

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Fig. 1. (color online) Schematic view of an asymmetric dimer consisted of Au and VO2 nanodisks. The incident plane-wave propagates in the positive z direction with the polarization along the y direction. The Au–VO2 nanodisks with a separation gap L = 140 nm are positioned along the x axis. The sizes of these two disks are: thickness T = 10 nm, diameter DAu = 100 nm for Au disk and DVO2 = 200 nm for VO2 disk.

The resonance wavelength of the dipole mode residing in the isolated Au (VO₂) nanodisk is determined from its scattering spectrum, as shown in Figs. 2(a) and 2(b). It can be seen that the peak around 700 nm (1500 nm) corresponds to the electric dipole mode of the Au nanodisk^[44] (metallic VO₂ nanodisk^[45]). This is further confirmed by the distributions of surface charge at the resonant wavelengths, as shown in Figs. 2(c) and 2(d). The scattering spectra of the VO₂ nanodisk indicate that LSPR exists in metallic VO₂ nanodisk at high temperature (355 K) but almost disappears in the semiconductor state at low temperature (300 K). It is attributed to the rise of intermediate states during the semiconductor-to-metal phase transition (SMT),^[46,47] where these intermediate states can enhance the carrier density by increasing temperature. We investigate the far field scattering of the Au–VO₂ nanodisk dimer at the wavelength of 1.064 μm and examine the electromagnetic mode of VO₂ nanodisk at the semiconductor state. It is shown in Fig. 2(e) that, the VO₂ nanodisk at the wavelength of 1.064 μm gives purely electric dipole mode with a weaker charge confinement than that in metallic state.

Fig. 2.

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Fig. 2. (color online) (a) Scattering spectrum of individual Au nanodisk. (b) Scattering spectra of individual VO2 nanodisk in the metallic (355 K) and semiconductor (300 K) states. (c) and (b) Calculated charge distributions at the resonant wavelength of Au (metallic VO2) nanodisk indicated in (a) and (b), respectively. (e) Charge distribution of semiconducting VO2 nanodisk excited at the wavelength of 1.064 μm.

We then employ a widely adopted two-dipole model^[26,27,48] to describe the far-field scattering properties of the asymmetric dimer composed of Au (VO₂) nanodisks. To achieve directional scattering from the asymmetric dimer when the VO₂ nanodisk is in metallic state, we pay attention to the light scattered in the opposite directions along the line connecting the two particles, i.e., the opposite directions along the x axis in Fig. 1. The scattering intensity along this line is determined by , where p_Au(VO2) is the amplitude of the Au (VO₂) dipole, k = λ/2π is the wave vector, l is the distance between the two dipoles, and Δφ represents the intrinsic phase difference between them. The last term, describing the interference of the two dipoles, plays a significant role in achieving the directional scattering. Directional scattering would be obtained if interference is constructive in the positive x direction and destructive in the opposite direction. In the ideal case, the cosine function reaches the maximum value of perfect constructive interference (kl – Δφ = 2πn, n is an integer) when light propagates in the positive x direction, whereas it has the minimum value of perfect destructive interference (– kl – Δφ = π +2πn) for light propagating in the negative x direction. This is equivalent to the condition of l = λ/4 and Δφ = π/2. The intrinsic phase difference Δφ is determined by the complex particle polarizability, which can be calculated analytically with an approximation model in Ref. [27]. Figure 3(a) shows the scattering spectra of the asymmetric dimer with the VO₂ nanodisk in metallic and semiconductor states. A spectral peak of the Au nanodisk is prominent around 700 nm. The VO₂ nanodisk is a much weaker scatterer, so its dipole mode resonance (∼1500 nm) is not easily discernible as a well-defined peak in the scattering spectra. The intrinsic phase differences between the two dipoles are shown in Fig. 3(b), where the red and blue curves correspond to VO₂ nanodisk in metallic and semiconductor states, respectively. It indicates that the intrinsic phase difference Δφ is close to π/2 between the two dipolar resonances of the asymmetric dimer when the VO₂ nanodisk is in metallic state, so the ideal case that interference of scattered light is perfect constructive in the positive x direction and perfect destructive in the opposite direction can be realized. Consequently, the directional scattering can be achieved in the wavelength range between dipolar resonances of the dimer with a precise tuning of the distance l, which corresponds to the dimer separation (center-to-center separation) of the two nanodisks. In order to achieve the directional scattering at a commercial laser wavelength of λ = 1.064 μm, the optimized l = 290 nm is adopted in our design. On the other hand, for the VO₂ nanodisk in semiconductor state, the ideal case of interference is no longer obtained and the directional scattering almost disappears. Thus, a switchable directional scattering can be achieved with the phase transition of the VO₂ nanodisk.

Fig. 3.

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Fig. 3. (color online) (a) Scattering spectra of the asymmetric Au–VO2 nanodisk dimer at 355 K (red curve) and 300 K (blue line). The inset is a magnified spectrum for the resonant peak corresponding to metallic VO2 nanodisk. (b) Comparison of the relative phase difference between the dipoles in the asymmetric Au–VO2 nanodisk dimer when VO2 nanodisk is in metallic state (red curve) and semiconductor state (blue curve).

Now we examine the electric field intensity distribution of the scattering light in the far-field at the excitation wavelength of 1.064 μm. Figures 4(a) and 4(b) display the normalized three-dimensional (3D) map of the far-field scattering intensity when the VO₂ nanodisk is in the metallic and semiconductor states, respectively. It shows a highly directional scattering in the positive x direction when the VO₂ nanodisk is in the metallic state at 355 K, and the directional scattering almost disappears when the VO₂ nanodisk changes to semiconductor state at 300 K. For a clear comparison, figures 4(c) and 4(d) show the normalized far-field scattering patterns of the asymmetric nanodisk dimer in polar coordinates of xy and xz planes when the VO₂ nanodisk is at different temperatures. To qualify the scattering directionality of the system, we introduce the directivity, i.e., a decibel comparison of scattering intensity in the opposite direction (10log₁₀(I_p/I_n)),^[49,50] where I_p(n) is the scattering intensity in the positive (negative) x direction. It is found that the directivity can reach ∼ 40 dB at 355 K, but it is only 2.3 dB at 300 K. This quantitative result indicates that a strongly directional scattering is achieved when the VO₂ nanodisk is in metallic state and it can be turned off with phase transition of the VO₂ nanodisk to the semiconductor state.

Fig. 4.

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	Fig. 4. (color online) (a), (b) Normalized 3D map of far-field scattering intensity for the asymmetric Au–VO2 nanodisk dimer with the optimized dimer separation l = 290 nm excited by a plane-wave at λ = 1.064 μm at 355 K and 300 K. (c), (d) The corresponding scattering patterns (|E|2) in xy (red curve) and xz (blue curve) planes at 355 K and 300 K.

To explain the difference of the far-field scattering patterns for the two cases, we introduce an interference model and analyze the amplitudes of the scattered light from individual Au (VO₂) nanodisk and far-field phase difference between them. Figures 5(a) and 5(b) show the far-field scattering amplitudes of individual Au (VO₂) nanodisk and the asymmetric Au–VO₂ nanodisk dimer, all of which are normalized by the maximum amplitude of the asymmetric dimer under the corresponding temperature. The phase differences |φ_Au – φ_VO2| between the two nanodisks under different temperatures are shown in Figs. 5(c) and 5(d). The amplitudes of individual Au (VO₂) nanodisks are the same in the xy plane (Fig. 5(a)), and the phase difference between them is close to zero at the scattering angle of 0°, whereas it changes to π at the angle of 180° for the VO₂ nanodisk in metal state (Fig. 5(c)), leading to a perfectly directional scattering in the positive x direction. However, for the VO₂ nanodisk in semiconductor state, besides an obvious difference in amplitudes of the Au and VO₂ nanodisks (Fig. 5(b)), the phase differences between them are close to π/2 at two horizontal scattering angles as above (Fig. 5(d)), so the directional scattering cannot be achieved.

Fig. 5.

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Fig. 5. (color online) (a), (b) Normalized far-field scattering amplitude patterns (|E|) of Au (blue dash curves), VO2 (green dash curves) nanodisks, and asymmetric Au–VO2 nanodisk dimer (red solid curves) in the xy plane under the excitation of 1.064 μm at 355 K and 300 K. (c), (d) Far-field phase difference |φAu – φVO2| between Au and metallic VO2, semiconductor state VO2 nanodisks, respectively.

In the following, we investigate the dependence of the directivity on the dimer separation. The results are displayed in Fig. 6. It is found that the directivity decreases when the dimer separation deviates away from the optimized separation of 290 nm as shown in Fig. 6(a). This can be further examined by three representative scattering patterns with dimer separations of 170 nm, 290 nm, and 410 nm, as shown in the upper panel of Figs. 6(b)–6(d). The corresponding directivities are 9.4 dB, 39.6 dB, and 8.0 dB for the dimer separations of 170 nm, 290 nm, and 410 nm, respectively. To unravel the directivity change in Figs. 6(b)–6(d), we depict the polar plot of their phase differences |φ_Au – φ_VO2| in the lower panel of Figs. 6(b)–6(d). It is found that the phase differences |φ_Au – φ_VO2| along the negative x direction are 0.78π, π, and 0.77π when the separation is increased from 170 nm to 290 nm and 410 nm. As a result, a nearly perfect destructive interference along the negative x direction (a high underlying directivity) is observed for the dimer separation of 290 nm. However, the partially destructive interference occurs as the dimer separation is deviated from 290 nm, resulting in a decreased directivity shown in Figs. 6(b) and 6(d). It is worth noting that the directivity change in Fig. 6(a) is as large as 32 dB, which achieves almost the same quantity to that mediated by the phase transition of VO₂ (37 dB). However, the phase transition controlled directivity can avoid the rather complex fabrication process of separation change, enjoying more flexibility.

Fig. 6.

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Fig. 6. (color online) (a) Dependence of directivity on dimer separation at ambient temperature of 355 K. (b)–(d) The normalized far-field scattering patterns (|E|2) of the asymmetric Au–VO2 nanodisk dimer (the upper panel) and corresponding phase differences |φAu –φVO2| between the two nanodisks (the lower panel) in xy planes with the dimer separations of l = 170 nm, l = 290 nm, and l = 410 nm, repsectively.

In summary, we have designed an asymmetric Au–VO₂ nanodisk dimer for switchable directional scattering. The two peaks, determined from the scattering spectrum, correspond to the electronic dipole modes of Au (metal VO₂) nanodisk, and the modes are confirmed by the distributions of surface charge. The phase difference between the two dipoles is large enough for satisfying the ideal case of interference for the scattered light propagating to the opposite directions along the line connecting these two nanodisks, which results in a strongly directional scattering with the directivity of ∼ 40 dB towards to the metallic VO₂ nanodisk. However, the directional scattering almost disappears (2.3 dB) when the VO₂ nanodisk changes to semiconductor state. We further propose an effective method to switch the directional scattering on/off based on the SMT of VO₂ nanodisk. This tunable directional scattering is well interpreted from far-field phase difference between the two nanodisks with an interference model. Our result may have potential applications in compact thermo-optical sensors, directional surface plasmon resonance bio-sensing, and integrated nanophotonic systems.