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We propose a novel approach to generate and tune a hot spot in a dipole nanostructure of vanadium dioxide (VO2) laid on a gold (Au) substrate. By inducing a phase transition of the VO2, the spatial and spectral distributions of the hot spot generated in the feed gap of the dipole can be tuned. Our numerical simulation based on a finite-element method shows a strong intensity enhancement difference and tunability near the wavelength of 678 nm, where the hot spot shows 172-fold intensity enhancement when VO2 is in the semiconductor phase. The physical mechanisms of forming the hot spots at the two-different phases are discussed. Based on our analysis, the effects of geometric parameters in our dipole structure are investigated with an aim of enhancing the intensity and the tunability. We hope that the proposed nanostructure opens up a practical approach for the tunable near-field nano-photonic devices.
©2013 Optical Society of America
1. Introduction
The interaction between a light and a metallic nanostructure is well known to provide an excitation of the electromagnetic surface mode, surface plasmon polaritons (SPPs), coupled with collective motion of conduction electrons [1]. If the geometry of a nanostructure is properly designed to support the plasmonic resonances, an enhanced field with several orders of magnitude to the incident field, a hot spot, can be locally formed at nanoscale [2]. The plasmonic hot spots provide novel means of overcoming the optical diffraction limit [3] and have triggered a considerable number of investigations in the field of biosensing [4], optical data storage [5], and active photonic devices [6–8]. For example, plasmonic nanoantennas, like dipole or bowtie nanoantennas, are the promising applications as compact solutions to the coupling between far-field radiations and nanoscale devices [9].
Analytical and experiment studies on the spectral and spatial characteristics of plasmonic hot spots have been extensively conducted and well established over the last decades. Interesting features of the hot spots have been reported by modifying the geometry of the nanostructures under plasmonic resonances [10, 11]. However, less interest has been devoted to the practical possibility of tuning a hot spot without changing their geometry. Such a possibility includes several applications such as a real-time control or a manipulation of the local intensity of light, which would promote the possibility of the gain control as an active optical nanoantenna. Moreover, an emission from a nanoscale emitter could be controlled using the modulation of the hot spot in the vicinity of the quantum dots or single molecules [12, 13]. Previously, several groups have reported the use of the metal-semiconductor transitions in some phase transition materials to tune the optical responses [14]. Especially, VO2 is one of the promising candidate material that exhibits a change in the complex permittivity arisen from the structural transition between the monoclinic to the tetragonal phases across the critical temperature in ultrafast timescales [15]. This change in optical responses makes VO2 a suitable active material for the integrated photonic components [16], memristive devices [17], thermal sensors [18], and electronic switches [19]. This transition can be introduced in any one of optical [20–24], thermal [18], or electrical [25] perturbations. Using VO2, there have been demonstrations on the frequency tunable metamaterials [26, 27] and the transmission modulations [28].
In this paper, we propose a novel approach to form and tune a hot spot in a dipole nanostructure of VO2 on an Au substrate. The tuning mechanism is based on the phase transition of the VO2. The proposed approach in this study is basically similar to the principles in the absorbing metamaterials integrated with periodic nanostructures based on VO2 phase transition [26, 27]. However, apart from the interests of the former studies on the far-field transmission (or reflection) in the specific wavelength, we study the dipole nanostructure with an emphasis on the manipulation of the near-field (the hot spot). First, we analyze the spatial and spectral characteristics of the hot spot at both phases (semiconductor and metallic) with fixed geometric configuration of the dipole nanostructure using a three-dimensional (3D) finite-element method (FEM). Based on these results, two mechanisms of tunability of the hot spot are investigated at both phases. After this, the dependencies on the geometrical parameters are also analyzed to provide a guide to the reliable design and use of the proposed device.
2. Proposed device and simulation model
Our proposed device consists of three layers as shown in Fig. 1. The top layer is the dipole nanostructure made of VO2 and placed on an Au substrate. Between the Au layer and the dipole nanostructure, a thin layer of silicon dioxide (SiO2) is placed as a separation. The thickness, length, and feed gap width of the dipole nanostructure are denoted by tVO2, lVO2, and gVO2, respectively. In our numerical calculations of 3D FEM method (COMSOL), we used the modified Debye dispersion model for the complex relative permittivity of the gold as
where ε∞ (11.575) is the infinite-frequency relative permittivity, εs (−15789) is zero-frequency relative permittivity, τ (8.71 × 10−15s) is the relaxation time, σ (1.6062 × 107S/m) is the conductivity, ε0 is the permittivity of the vacuum, and ω is the angular frequency [29]. We apply the SiO2 refractive index of 1.5 for all the considered wavelengths. For the precise simulation of the VO2 materials, we adopted the complex permittivity of VO2 in the wavelength of interest by fitting the experimental results to Tauc-Lorentz and Drude oscillator models as shown in Fig. 2(b) [30]. We also assume that the incident plane wave with a polarization along the x-axis is normally illuminated from the top-side of the nanostructure. In our simulation, the tunable intensity of the hot spot generated near the center of the dipole gap depending on the phase of the VO2 material is the main interest. Thus, we monitored electric field intensities from the calculated data along the cross-line of the center of the feed gap (red dotted line in Fig. 1(b)) considering practical situations. Then, the monitored data is normalized to the incident intensity (I0) for various incident wavelengths. Here, we define the maximum value in the normalized intensities as an intensity enhancement of a hot spot. And we will refer to the difference between the two cases for VO2 phases as the tunability of the hot spot.
Fig. 1 Schematic drawing of our proposed VO2 dipole nanostructure with a reflection configuration: (a) perspective, (b) cross-sectional, and (c) top view
Fig. 2 (a) VO2 phase-dependent spectral distributions of the intensity enhancement of the hot spots arisen inside of the dipole gap. Their enhancement differences between two phases are also shown as the tunability of the hot spots. The geometrical parameters are as follows: fixed tSiO2 (10 nm), gVO2 (30 nm), wVO2 (100 nm), lVO2 (400 nm), and tVO2 (100 nm). According to the phase of the VO2, two features of the near-fields responses are induced as depicts in the region A and B. (b) The real and imaginary parts of the dielectric functions of VO2.
3. Results and discussion
Figure 2(a) shows phase-dependent spectral distributions of the intensity enhancement of the hot spots arisen inside of the dipole gap and their differences between two phases as the tunability of the hot spots. In this calculation, the geometrical parameters are as follows: SiO2 thickness tSiO2 = 10 nm, dipole gap gVO2 = 30 nm, dipole width wVO2 = 100 nm, dipole length lVO2 = 400 nm, and dipole thickness tVO2 = 100 nm. There are two interesting regions (A, B) in this plot. The region A reveals a strong enhancement difference, meaning high tunability of the hot spot. This region is certainly attractive for the application of a tunable device, providing a 172-fold intensity enhancement at the semiconductor phase with an enhancement difference of 144 at the wavelength of 678 nm (the peak position of the region A). With an increment of the wavelength, the enhancement difference markedly reduces to the insignificant values around the region B. Although the tunability at the region B is negligible, it is worthwhile to analyze the response of the hot spot at the metallic phase in the region B. For instance, by introducing the red-shift of the intensity enhancement of the hot spot at the metallic phase, an increased enhancement difference can lead to the improved tunability. Moreover, by utilizing the response of the metallic phase, this device can be used as near-infrared tunable nanoantennas.
Before discussing the two different mechanisms at both phases, let us see the near-field intensity of the hot spot at both phases. The relative intensity distributions normalized by the incident intensity in the wavelength of 678 nm (peak position in the region A) on the x-z planes and y-z planes at the center of the gap are depicted in Fig. 3. The apparent difference in intensities between the two phases of VO2 can be observable. At the semiconductor phase, a strong hot spot is formed at the center of the feed gap. However, at the metallic phase, the intensity is less focused compared to that in the semiconductor phase. This contrast gives an efficient way of tunability of the hot spot. Considering the practical use of this device, the location of the hot spot can be an important factor. The peak intensity is located in the entire area of the feed gap and the edges of the dipole feed gap. This characteristic is advantageous in some applications such as nanoantennas to couple the hot spot field to a plasmonic waveguide or biosensors for more sensitive interaction between bio-materials and the hot spots at the feed gap.
Fig. 3 Spatial distribution of the normalized intensity in (a, c) semiconductor phase and (b, d) metallic phase at the labeled wavelength (region A). The color scale obtained from the semiconductor phase is equally applied to both phases. Thin white lines denote the geometrical boundaries of the structure.
The sign-inversion of the enhancement throughout the considered wavelength in Fig. 2(a) is arisen from two distinct resonances at both phases. To gain insights of these two resonances, we examine the near-field distributions at the labeled wavelength A and B. At first, we investigate the resonance occurring in the semiconductor phase (region A). Here, we note that in this region A, the complex permittivity of the VO2 at the semiconductor phase exhibits a high value in its real component (εvo2 = 7.8 + i2.3 at 678 nm) [30]. Thus, it is expected that the VO2 at this phase acts as a high refractive index dielectric material, which may collect the incident light inside of the VO2. This characteristics of VO2 is well understood and utilized for the modulation of near-infrared light through a periodic array of the subwavelength hole arrays in metal-VO2 films [28]. Consequently, the penetrated incident light forms the plasmonic mode on the Au substrate. The electromagnetic energy flowing into the VO2 dipole and SiO2 layer supports this phenomenon as shown by white arrows in Fig. 4(a). We also plot the plasmonic mode coupled to the VO2 dipole nanoantennas as depicted by the transverse (Ex), longitudinal electric field (Ez) and their vector plot in Figs. 4(a) and 4(b). One can see that the plasmonic mode forms the typical plasmonic standing wave pattern at the resonance wavelength in the semiconductor phase. This result implies a strong relation between the wavelength of the plasmonic mode and the dipole length to induce the enhanced hot spot at the dipole gap. On the other hand, at the metallic phase, the VO2 becomes a lossy metal (εvo2 = −5.7 + i10.3 at 900 nm) [30]. Thus, in the region B (metallic phase), the VO2 dipole nanostructure acts like a novel metal except the high intrinsic loss characteristic. In other words, the transverse (Ex) and the longitudinal electric fields (Ez) do not easily propagate along the direction of the VO2 dipole due to the high intrinsic loss of the VO2 at the metallic phase as shown in Figs. 4(c) and 4(d). Therefore, this characteristic only introduces a Fabry-Pérot-like resonance arisen along the longitudinal direction at the dipole feed gap.
Fig. 4 (a) The color map shows the Ex field distribution, and the arrows denote the power flow (time averaged) at the semiconductor phase of VO2 ((c) at the metallic phase). (b) The color map represents the Ez field distribution with vector plot of the electric field at the semiconductor phase ((d) at the metallic phase).
In order to characterize the dependence of the hot spots on the geometry, we have investigated the tunability of the hot spot according to the dipole length (lVO2), thickness (tVO2), and width (wVO2), as shown in Figs. 5(a)-5(c). The increment of the dipole length results in a red-shift of the peak wavelength at the semiconductor phase. And similar dependences on the dipole thickness and width appear as an increment of corresponding geometric parameters. It is noteworthy that in the viewpoint of the intensity enhancement at the semiconductor phase, we found that a local optimum in the maximum intensity enhancement can be obtained around the dipole thickness of 100 nm. As discussed in the earlier paragraph, the plasmonic mode propagating on the Au layer and its resonance in the dipole is the key factor to form the enhanced hot spot at the semiconductor phase. From the results of dipole length dependency in Fig. 5(a), we find that at the semiconductor phase, the dipole length at corresponding peak resonance conditions is related to the effective wavelength of the plasmonic mode propagating on the Au layer as follows: lVO2 1.25λspp, where λspp is effective wavelength of the plasmonic mode. This value can be extracted from the effective refractive index of a guided mode in the layered structure as shown in Fig. 5(d) by dotted lines. The inset of Fig. 5(d) shows the intensity distribution of the calculated plasmonic mode at the SiO2 layer. By modifying the aforementioned relation to provide analytical design parameters, the peak resonance wavelength at the semiconductor phase can be expressed as
where Re(neff) is the real part of the effective refractive index. Based on Eq. (2), and the calculated effective refractive index (Fig. 5(d), dotted lines) corresponding to the given geometry of the side section of the dipole, the peak resonance wavelengths are plotted according to the dipole length by the solid line in Fig. 5(d). The labeled small circles located on the solid lines in Fig. 5(d) are peak resonance wavelengths extracted from Figs. 5(a)-5(c). It is observed that these peak resonance wavelengths nearly correspond to the calculated peak wavelength and the dipole length. Hence, if the interested peak resonance wavelength and its geometry of the side section (width and thickness of the dipole) of the VO2 dipole are determined, an appropriate dipole length to generate a tunable hot spot can be designed from Fig. 5(d). In addition, required dipole lengths to get the peak resonance wavelength from 480 nm to 800 nm can be derived from the obtained effective refractive index. The thin and narrow dipole nanostructure as depicted by blue and red dotted lines in Fig. 5(d) shows lower value than the other cases. In these cases, it requires the considerable variation of the dipole length up to 900 nm to cover the entire interested wavelength. In contrast, if the dipole is thick and wide (over the 100 nm), the small fraction of the dipole length (below 600 nm) can cover the entire wavelength.Fig. 5 Spectral distribution of the intensity enhancement of the hot spot arisen inside of the dipole gap as a function of the (a) dipole length, (b) thickness, and (c) width at semiconductor phase (solid lines) and metallic phase (dotted lines) of the VO2. The other geometrical parameters except the varied one follow the configurations used in Fig. 2. Based on the underlying mechanism of the tunable hot spots, the peak wavelength positions (solid lines) of the intensity enhancement at the semiconductor phase are plotted after solving for the effective index (dotted lines) of the plasmonic mode propagating on the Au substrate at the given geometry (d). The labeled small circles in (d) correspond to the peak wavelength positions of the intensity enhancement obtained from (a)-(c).
In contrast to the responses of the hot spot in the semiconductor phase, spectral distributions at the metallic phase show broad and less enhanced characteristics as shown by dotted lines in Figs. 5(a)-5(c). Specifically, the spectral dependencies of the intensity enhancement have been observed only from the variations of the dipole thickness. It is noteworthy that these dramatic changes are attributed to the Fabry-Pérot-like resonance along the longitudinal direction at the feed gap as discussed before. High intrinsic loss characteristic of the VO2 at the metallic phase does not significantly affect this resonance in such a small feed gap thickness. However, along the direction of the dipole axis, the plasmonic mode suffers considerable high loss due to the relatively long dipole length compared to the feed gap thickness. This results in a slight shift of the peak wavelength as shown in Fig. 5(a).
The appropriate enhancement difference (tunability) of the hot spot can be obtained based on aforementioned analyses. By varying the dipole length and width, the peak resonance wavelength of the enhanced hot spot at the semiconductor phase can be tuned, while not affecting the peak resonance wavelength at the metallic phase. In addition, the increment of the dipole thickness which introduces a red-shift of the peak resonance wavelength at the metallic phase improves enhancement difference of the hot spot.
4. Conclusions
In conclusion, to make a tunable hot spot, we proposed a novel approach by which the hot spot could be generated and tuned in the dipole nanostructure by inducing the phase transition of the VO2. The proposed dipole nanostructure exhibits the strong enhancement difference near the wavelength of 678 nm with 172-fold intensity enhancement of the hot spot at the center of the feed gap. In detail, we investigated the physical mechanisms of the tunable hot spot at both metallic and semiconductor phases. Based on the underlying physics and numerical analysis, we found that the location of the peak resonance wavelength is related to the plasmonic mode propagating on the Au layer and the dipole length at the semiconductor phase. Finally, the geometry dependences of the dipole nanostructure are discussed to obtain the appropriate tunability of the hot spot. This gives us a useful guideline in designing the dipole nanostructure to make a high-intensity and tunable hot spot. We hope that our proposed method may allow the gain control of the emission and the coupling efficiency in real time, which are the important functions in the active integrated photonic devices, such as nanoantenna.
Acknowledgment
This work was supported by the National Research Foundation of Korea through the Creative Research Initiatives Program (Active Plasmonics Application Systems).
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