1. Introduction

The radiation emission pattern from a quantum system (such as a quantum dot or a fluorescent molecule) is similar to the emission pattern of an oscillating point dipole and is symmetrical to the axis of oscillation. There are several potential applications if the emission pattern from these quantum systems could be directed in desired directions. In past decade, researchers have employed photonic nanostructures such as photonic crystals [1], photonic cavities [2], metallic thin surfaces [3] and nanoantennas [4,5] to direct the radiation pattern from a quantum dot emission in certain directions.

Nanoantennas cannot only direct light from a florescent molecule in a desired direction with high efficiency, they can also the control polarization state of the radiation pattern [5]. It has been shown that the presence of nanoantennas can reduce the radiative decay time of fluorescent molecules [6]. It has been recently shown that the radiation pattern of nanoantennas can be tuned by changing the geometrical parameters of nanoantennas at the time of the nanoantenna fabrication [7]. However, changing the mechanical or structural parameters of a nanoantenna after the nanoantenna fabrication is almost impossible at nanoscale device level.

In order to obtain very a highly directive radiation pattern from nanoantennas, one methodology is to employ an array of directive nanoantennas such that radiation from the different nanoantennas could constructively interfere in only a particular direction. This highly directive radiation pattern can theoretically be steered if the phase at each nanoantenna source (or feed element), is varied. This concept being applied to optical nanoantennas is not entirely a new concept as in RF antennas it is common to use antenna arrays to steer the radiation pattern. The radiation pattern is steered in a desired direction by introducing a progressing phase shift between adjacent antenna array feed elements. As it is very difficult to controllably change the phase at each nanoantenna source (or feed element), one methodology of changing the phase difference between the different nanoantennas forming the array is to change the state of the material (from semiconductor state to the metallic state or vice versa) surrounding one or more of the nanoantennas. Researchers have previously reported switching in several properties of optical nanoantennas such as the resonance wavelength, the electric field enhancement, the absorption spectra, and the far-field spectra using asymmetrical nanostructures [8,9], phase change materials [10-12], liquid crystals [13], metamaterials [14], and variation of free-carrier densities of semiconductor disks [15]. However very few researchers have shown steering of the direction pattern of a nanoantenna at a given wavelength [12,13]. Haibo Li et al. have shown steering of the direction pattern using liquid crystal materials [13]. However, the response time of liquid crystal based devices is limited to milliseconds [16]. On the other hand, vanadium oxide (VO₂) based devices can switch at femtosecond timescales [17]. The state of VO₂ can be changed from the semiconductor state to the metallic state by changing its temperature or by applying electric fields or current [18]. There are two mechanisms which are thought to be responsible for this insulator to metal transition: Mott-Hubbard mechanism (based on the electron-electron interaction) [18] and the Peirels mechanism (based on the electron photon interaction) [19]. Since VO₂ displays both these mechanisms in different conditions, the underlying mechanism of the phase change is thought to be a combination of both these mechanisms depending on the condition of the V-V bonds. Plasmonic devices such as plasmonic waveguides or plasmonic sensors are very sensitive to wavelength change. Light can be coupled to these devices efficiently only at specific plasmon resonance wavelengths. Therefore, in order for the nanoantennas to couple light from quantum dots or florescent molecules to these devices, it is desirable to maintain operation of the nanoantennas in a very narrow wavelength range and to have switching in directivity at the same wavelength. P. Albella et al. [8] and T. Shegai et al. [9] have shown switching in directionality as a function of wavelength.

In this paper, we show that active steering of the radiation pattern of the nanoantennas is possible without changing the wavelength of operation. In order to realize this, we propose novel nanoantenna designs that use two or more Yagi-Uda nanoantennas placed near each other so that their radiations can interfere. By placing thin films of VO₂ over one or more of the Yagi-Uda nanoantennas forming an array, a phase difference can be introduced between the nanoantennas surrounded by a VO₂ film and those that are not surrounded by it. When the state of the VO₂ thin films surrrounding some of the nanoantennas is tunably changed, the phase difference between those nanoantennas and nanoantennas not surrounded by VO₂ thin films changes, thereby changing the overall radiation pattern of the nanoantenna array. The main objective of this paper is to achieve active steering of the nanoantenna radiation patterns (i.e. active change of the direction of the main lobe of the nanoantenna far-field direction pattern) upon tunably changing the state of the VO₂ thin films surrounding the nanoantenna structure.

We study several complex nanoantenna structures — being referred to as steerable nanoantennas (SNs) — formed by a combination of multiple Yagi-Uda nanoantennas and thin films of VO₂, so as to achieve the maximum possible steering of the radiation pattern upon changing the phase of the VO₂ thin films from the semiconductor phase to the metallic phase. We also demonstrate that the steerable nanoantennas being proposed can steer the radiation patterns ‘in the plane’ of the nanoantennas — this steering will be referred to as 'in-plane steering’. In-plane steering of the radiation pattern using plasmonic nanoantennas has not been shown previously. In previous work on steerable nanoantennas [12], the steeringmodeled was not 'in-plane' steering of the radiation pattern. Moreover, the maximum achievable steering of the radiation pattern was 45° when the phase of the VO₂ thin film was changed [12]. In this paper, we demonstrate that the maximum achievable steering of the radiation pattern is 90° for a two-element (i.e. containing 2 Yagi-Uda nanoantennas) steerable nanoantenna when the phase of the VO₂ thin film is changed from the semiconductor phase to the metallic phase. Moreover, it was observed that the radiation pattern of the steerable nanoantennas being proposed in our paper can be designed to be much more directed (i.e. with a lower half power beam width) as compared to previously reported steerable nanoantennas. By employing a four-element steerable nanoantenna, we also demonstrate a full 360° active steering of the radiation pattern, which has not been reported thus far by any research group. Moreover, we demonstrate that the radiation pattern can be actively steered in 12 different directions depending on the states of the four VO₂ thin films, which has also not been previously shown. The steerable nanoantennas can find applications in areas such as tunable on-chip plasmonic interconnects, networks on chip, or for selective excitation of fluorophores on a sensor chip. As an example, we can deposit different fluorophore-labeled biomolecules on different regions of a sensor chip using these steerable nanoantennas, and employ either a microscope objective (far-field collection) or an NSOM probe (near-field collection) to collect the fluorescence signals from these labeled molecules.

We propose several designs of steerable nanoantenna (SNs) structures and compare the steering behavior of these nanoantennas upon phase transition of the VO₂ films. The steerable nanoantenna (SNs) structures being proposed by us are: (a) a single Yagi-Uda nanoantenna 'SN0' surrounded by a VO₂ film, (b) a steerable nanoantenna 'SN1' consisting of two coplanar Yagi-Uda nanoantennas surrounded by a VO₂ film, see Fig. 1(i), (c) a steerable nanoantenna 'SN2' consisting of two coplanar Yagi-Uda nanoantennas, as shown in Fig. 1(a), with one of the Yagi-Uda nanoantennas being present inside a VO₂ film and the other being present in air, (d) a steerable nanoantenna 'SN3′ consisting of two coplanar Yagi-Uda nanoantennas, as shown in Fig. 1(e), with one of the Yagi-Uda nanoantennas being present inside a VO₂ film and the other being present in air and one of the nanoantennas being displaced in the x-direction by a certain distance ‘L’, (e) a steerable nanoantenna 'SN4' consisting of two coplanar Yagi-Uda nanoantennas, with each Yagi-Uda nanoantenna being present inside a VO₂ thin film but each VO₂ thin film being separated from the other by an air gap, and (f) a fully steerable nanoantenna 'SN5′ consisting of four coplanar Yagi-Uda nanoantennas, with each Yagi-Uda nanoantenna being present inside a VO₂ thin film but each VO₂ thin film being separated from the other VO₂ films by an airgap.

 

Fig. 1 Schematics showing different steerable nanoantennas (SNs): (a) SN2 consisting of two co-planar Yagi-Uda nanoantennas, with one of the Yagi-Uda nanoantennas being present inside a VO₂ film and the other being present in air, (e) SN3 consisting of two co-planar Yagi-Uda nanoantennas, with one of the Yagi-Uda nanoantennas being present inside a VO₂ film and the other being present in air and one of the nanoantennas being displaced in the x-direction by a certain distance ‘L’, and (i) SN1 consisting of two co-planar Yagi-Uda nanoantennas surrounded by a VO₂ film. Comparison of steering of the far-field radiation patterns for the different steerable nanoantennas: (b) SN2, (f) SN3, and (j) SN1. Note that the intensity values shown in the far-field radiation patterns are normalized through dividing by 1 × 10⁻¹². Far-field radiation patterns as a function of both θ and Φ: for (c) the semiconductor state and (d) the metallic state of the SN2 nanoantenna, for (g) the semiconductor state and (h) the metallic state of the SN3 nanoantenna, and for (k) the semiconductor state and (l) the metallic state of the SN1 nanoantenna.

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While designing the individual Yagi-Uda nanoantennas being employed in the steerable nanoantenna structures, it has to be noted that the optical radiation penetrates into the metal (of the plasmonic nanorod feed element) at optical frequencies which leads to oscillations of the free electron gas. Hence, at these frequencies the nanoantennas resonate at wavelengths that are shorter than the resonance wavelengths of nanoantennas having nanorod feed elements made from a perfect conductor [20,21]. Hence, the resonance wavelengths of actual Yagi-Uda nanoantennas are different from those of Yagi-Uda nanoantennas made from perfect conductors. In order to calculate the optimal dimensions for Yagi-Uda nanoantennas, several approaches can be followed. Taminiau et al. [4] had proposed to take standard parameters of a Yagi-Uda nanoantenna made up of perfect electrically conductive elements and compare its resonance length with that of an actual Yagi-Uda nanoantenna to calculate the scaling factor. It was then proposed to scale down all other nanoantenna elements with the same scaling factor [4]. Ivan S. Maksymov et al. have proposed anther approach using effective length theory [15,20]. They have calculated the optimal length of every element of the Yagi-Uda nanoantenna using the values of effective lengths for nanorod antennas. In this article, we are following this approach, with slight modifications, to determine the dimensions of the elements of a Yagi-Uda nanoantenna.

The proposed steerable nanoantenna (SN) structures can be fabricated by employing a combination of several processes such as electron beam lithography, reactive ion etching, etc. Details of the processes involved in the fabrication of the proposed steerable nanoantennas are provided in the Appendices A and B.

2. Methods

In order to design the individual Yagi-Uda nanoantennas, we first find the resonance wavelength for a single feed element on a substrate. Then we place only the reflector element near the feed element and calculate the forward ratio (FR), which can be defined as the ratio of the maximum value of the field in the forward direction to the maximum value of the field in the backward direction). We vary the spacing and the length of the reflector element to get the maximum FR. Once the parameters of the reflector are optimized, we place the director elements and follow the same procedure in order to obtain the optimal dimensions of directors.

For the calculation of the electromagnetic fields around the nanoantennas, we carried out Finite Difference Time Domain (FDTD) modeling using a commercial FDTD software (FDTD Solutions from Lumerical Inc.). In our FDTD simulations, a uniform grid size of 5 nm was employed for the entire simulation region. In these FDTD simulations, dipole sources having a wavelength of 1200 nm were placed inside the nanoantenna feed elements. The wavelength of 1200 nm was employed as it was calculated to be the resonance wavelength for the feed elements of Yagi-Uda nanoantennas. The axis of the dipole sources was taken to be parallel to the axis of feed elements. In the case of the two-element steerable nanoantennas, the center to center distance between the dipole sources of the two nanoantennas was taken to be 200 nm. In the case of the four-element steerable nanoantennas, the center to center distance between the dipole sources of the adjacent nanoantennas was taken to be 400 nm. In our simulations, while the length of the reflector 'R' was varied from 200 nm to 300 nm, the reflector spacing 'r' (i.e. spacing of the reflector from the feed element) was varied from 50 nm to 300 nm. Moreover, the director length 'D' was varied from 50 nm to 200 nm and the director spacing 'd' was varied from 50 nm to 200 nm. The total length of the feed element was taken to be 220 nm, which includes the gap between the two arms of the feed element of 20 nm. In our simulations, the thickness of the VO₂ layer was taken to be 50 nm. The height and the width of all the gold elements of the Yagi-Uda nanoantenna were taken to be 50 nm and 50 nm, respectively.

The calculated near-fields were transformed to the far-fields (determined at a distance of 1 meter from the nanoantenna) using this FDTD software. The calculated far-fields are maps of the electromagnetic fields on the surface of a half sphere having a radius of 1 meter, considering that the nanoantenna is placed at the center of the half sphere. These far-field maps are shown in Figs. 1(c), 1(d), 1(g), 1(h), 1(k) and 1(l). The variables θ and Ф shown in these maps are defined as shown in Fig. 1(a). Figure 1 shows a comparison of the far-field radiation patterns of three different steerable Yagi-Uda nanoantennas, for both the semiconducting and metallic states of the VO₂ thin films around the nanoantenna structures. Figures 1(b), 1(f), and 1(j) show the 2-D far-field radiation patterns of three different arrangements of steerable Yagi-Uda nanoantennas that were obtained by calculating the electric field intensity on the surface of the horizontal cross sections of the half spheres (having a radius of 1 meter) for θ = 89° and as a function of Ф. In the FDTD simulations, we employed the Lorentz-Drude dispersion relation model [10] for determining the dielectric constant of gold as well as for determining the dielectric constant of VO₂ in its metallic state. We employed the Lorentz dispersion relation model [10] for determining the dielectric constant of VO₂ in its semiconductor state. The variation of the real part (n) and the imaginary part (k) of the refractive indices of VO₂ with wavelength — for temperatures below 68 °C (i.e. for the semiconductor state of VO₂) and above 68 °C (i.e. for the metallic state of VO₂) — is shown in Figs. 2(a) and 2(b).

 

Fig. 2 (a) Variation of (a) the real part (n) and (c) the imaginary part (k) of the refractive indices of VO₂ with wavelength, for temperatures below 68 °C i.e. for the semiconductor state of VO₂ [10]. (b) Variation of (a) the real part (n) and (c) the imaginary part (k) of the refractive indices of VO₂ with wavelength, for temperatures above 68 °C i.e. for the metallic state of VO₂ [10].

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3. Results and discussion

Figures 1(c), 1(d), 1(g), 1(h), 1(k) and 1(l) show plots of the electric field intensity enhancement on the half spheres — for different values of θ — for the two states(semiconducting and metallic) of the VO₂ films around the nanoantennas. One can clearly observe from Fig. 1(j) that the main radiation lobe does not change its directions in the Ф direction (i.e. the lobe has same value of Ф = 90°) when the VO₂ thin film undergoes a phase transition from the semiconductor to the metallic states. This can be attributed to the symmetry of the steerable nanoantenna structure around the XY plane. Hence, this nanoantenna (SN0) is not truly a steerable nanoantenna as there is no steering of the main radiation lobe on changing the state of the VO₂ film. On the other hand, it can be observed from Fig. 1(f) that the radiation lobe can be steered from Ф = 120° (for the semiconductor state of the VO₂ thin film) to Ф = 90° (for the metallic state of the VO₂ thin film) upon phase transition of the VO₂ thin film in SN3 nanoantennas. Similarly, the radiation lobe can be steered from Ф = 110° (for the semiconductor state of the VO₂ thin film) to Ф = 75° (for the metallic state of the VO₂ thin film) upon phase transition of the VO₂ thin film in SN2 nanoantennas, as shown in Fig. 1(b). We can observe from Figs. 1(a) and 1(e) that we have broken the symmetry of structure around the XY plane by placing the VO₂ film only around one of the two Yagi-Uda Uda nanoantennas, thereby achieving the steering of the radiation lobes upon phase transition of the VO₂ thin film in the SN2 and SN3 nanoantennas.

Before studying complex steerable nanoantenna structures, we first studied the radiation pattern of a dipole source surrounded by a VO₂ film, which undergoes a phase transition from the semiconducting state to the metallic state. Subsequently, we studied the effect of nanoantennas, such as a nanorod antenna and a Yagi-Uda nanoantenna, as shown in Fig. 3(a), on the radiation pattern of a dipole source. While Fig. 3(b) shows the radiation pattern for a dipole source inside a VO₂ film, Fig. 3(c) shows the radiation pattern for a dipole source in the gap between the two nanorods forming the nanoantenna with the nanorods beingsurrounded by the VO₂ film. Figure 3(d) shows the radiation pattern for a dipole source inside the gap between the two nanorods forming the feed element of a Yagi-Uda nanoantenna, as shown in the inset in Fig. 3(d), the entire Yagi-Uda nanoantenna being embedded in a VO₂ thin film.

 

Fig. 3 (a) Schematic showing a Yagi-Uda nanoantenna embedded in a thin film of a phase change material (VO₂). Here 'D' is the length of director element, 'R' is the length of reflector element 'd' is distance of the director from the feed element, and 'r' is distance of the reflector from the feed element. Comparison of far-field radiation patterns (calculated in the plane of θ = 89°) for a quantum source placed inside: (b) a cavity of a VO₂ thin film, (c) a gap of gold nanorod antenna and (d) a gap of the feed element of a Yagi-Uda antenna for two states of the VO₂ thin film — i.e. the semiconductor state and the metallic state. Note that the intensity values shown in the far-field radiation patterns are normalized through dividing by 1 × 10⁻¹². The variation in the forward ratio (FR) of a Yagi-Uda nanoantenna surrounded by a VO₂ thin film, as a function of: (e) 'r' for different values of 'd' when the values of 'D' and 'R' were taken to be 60 nm and 200 nm, respectively, and (f) 'D' for different values of 'R' when the values of 'd' and 'r' were taken to be 60 nm and 150 nm, respectively. Here FR is defined as the ratio of the maximum value of the field in the forward direction to the maximum value of the field in the backward direction. (g)-(j) The effect of varying the length of the director element 'D' on the far-field radiation patterns of Yagi-Uda antennas embedded in a VO₂ thin film, for both the states of the VO₂ thin film.

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It can be seen from Figs. 3(b) and 3(c) that the presence of a nanorod dipole nanoantenna increases the radiation intensity of the dipole source, though the shape of radiation pattern remains the same in both the states of VO₂. This increased radiation intensity is due to reduction of radiative impedance as seen by the dipole in the presence of a dipole nanoantenna. However, the presence of a Yagi-Uda nanoantenna not only increases the radiation intensity but also directs the radiation in a particular direction, as shown in Fig. 3(d). The radiation pattern of a single Yagi- Uda nanoantenna is unidirectional. If a single Yagi-Uda nanoantenna is placed in a VO₂ thin film. one can expect two stable directions of the lobe corresponding to the two states of the VO₂ film (i.e. one corresponding to the semiconductor state and the other corresponding to the metallic state). However, due to the symmetry of the structure around the XY-plane, the lobe has a same angle 'Ф' for both the states, as shown in Fig. 3(d).

Further, we optimized the structural parameters of a Yagi-Uda nanoantenna to get maximum radiation intensity in one direction. In all the calculations, the height of the VO₂ thin film and of the gold nanorod elements of the Yagi-Uda nanoantenna were taken to be 50 nm. The VO₂ film and gold nanorods were placed on a SiO₂ substrate. The gap (G) between the feed elements was taken to be 20 nm, see Fig. 3(a). We studied the effect of varying the length of the director element 'D' and the distance of the reflector element 'r' from the feed element for the Yagi-Uda nanoantenna surrounded by a VO₂ thin film, see Figs. 3(e)–3(j). For a quantitative comparison of the directivity patterns of the nanoantennas, we have defined a term forward ratio (FR) as the ‘maximum value of the field in the forward direction’ divided by the ‘maximum value of the field in the backward direction’. For example, FR values were calculated to be 1, 1, and 1.866 respectively for the semiconductor state of the VO₂ film, as shown in Figs. 3(b)–3(d).

Higher values of FR for Yagi-Uda nanoantennas when compared with those for nanorod dipole nanoantennas or with only the dipole source imply that the Yagi-Uda nanoantenna radiates in one direction (forward direction) more than either the dipole nanoantenna or only the dipole source. Similar to RF Yagi-Uda antennas, the FR values for Yagi-Uda nanoantennas depends on various combinations of parameters ‘r’, ‘R’, ‘D’ and ‘d’ and the FR is maximum for certain combinations of these parameters. It can be observed from Figs. 3(e) and 3(f) that the FR is maximum (2.0940) for the semiconductor state of the VO₂ film for d = 60 nm, D = 60 nm, r = 150 nm and R = 200 nm. It can be observed from Fig. 3(e) that for a given value of ‘d’, FR attains a maximum value at a particular value of ‘r’. Similarly, for a given value of ‘R’, FR has a maximum value at a particular value of ‘D’, see Fig. 3(f). For the former case, the maximum value occurs because at that particular value of ‘r’, the phase difference between the light scattered from reflector and that emitted from the feed element is such that it constructively interferes in the forward direction and destructively interferes in the backward direction [15]. Similarly, for the case of the director, the path difference between the light scattered from the director and the light emitted from the feed element is such that it will interfere constructively in the forward direction. However, for the metallic state of the VO₂ film, the behavior is different. Light emitted from the feed element as well as the light scattered from the reflector and the director elements is heavily damped. For the metallic state of the VO₂ film, the dipole feed element of the Yagi-Uda nanoantenna is not resonant at the same wavelength as that for the Yagi-Uda nanoantenna with the VO₂ film in the semiconductor state. Therefore the Yagi-Uda nanoantenna loses its directivity properties for the metallic state of the VO₂ film. Researchers have shown that in the absence of any nanostructures, florescent molecules generate photons in random directions (i.e. there is an equal probability of photon propagation in all directions) and with random polarizations. However, if the same molecule is placed in a high enchantment spot of a nanoantenna, then the radiative impedance for the molecule changes and the decaying photon has a high probability to couple energy into localized surface plasmons of the nanostructure forming the nanoantenna [21]. These localized surface plasmons can out-couple into photons which are polarized along the nanoantenna axis and have a wavelength corresponding to the resonance wavelength of the nanoantenna.

After maximizing the directivity of a single Yagi-Uda nanoantenna inside a VO₂ film, we simulated a steerable nanoantenna (SN1) consisting of two coplanar Yagi-Uda nanoantennas near each other such that their far-field radiation patterns could interfere, with both the nanoantennas being surrounded by a VO₂ thin film. We first optimized the separation distance between the two Yagi-Uda nanoantennas for obtaining the maximum value of FR in the forward direction. When a phase difference was introduced between the dipole sources of the two Yagi-Uda nanoantennas, then the radiation pattern could be steered to some direction other than the normal direction (Ф = 90°). The effect of phase difference — between the sources of the two Yagi-Uda nanoantennas — on the radiation pattern of the steerable nanoantenna (SN1) is shown in Fig. 4. For these calculations, we used optimized parameters for both the Yagi-Uda nanoantennas forming the steerable nanoantenna SN1 — the results of the optimizations are shown in Fig. 3. We observe from Fig. 4 that there is a shift in the direction (Ф) of the main lobe for different phase differences between the sources of the two Yagi-Uda nanoantennas. We also observe that radiation pattern is symmetrical around the XY plane for 0° and 180° phase differences. For other phase differences, the radiation pattern is not symmetrical. Moreover, it can be observed from Figs. 4(c)–4(g) and Figs. 4(i)–4(m) that when the phase differences (between the dipole sources of the two Yagi-Uda nanoantennas) are 30° and 330°, the radiation patterns are mirror images of each other. Similarly, this can be observed when the phase differences are 90° and 270° or for other complementary pairs of phase differences. By introducing phase difference between the sources that are not 0° and 180°, we have broken the symmetry of the radiation pattern. We have to note here that by observing the radiation pattern, it is possible to estimate the phase difference between the sources of the two Yagi-Uda nanoantennas. So if one excites two quantum sources simultaneously using one excitation pulse and measures the emitted radiation pattern, then the phase difference between two quantum sources can be measured experimentally from the radiation pattern.

 

Fig. 4 (a) Schematic of a SN1 nanoantenna consisting of two co-planar Yagi-Uda nanoantennas surrounded by a VO₂ thin film. (b)-(m) Effect of phase difference between the dipole sources of the two Yagi-Uda nanoantennas on the far-field radiation pattern of the SN1 nanoantenna, the phase difference varying from 0° to 330°. Note that the intensity values shown in the far-field radiation patterns are normalized through dividing by 1 × 10⁻¹².

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It can also be noted from Fig. 4 that as the state of the VO₂ thin film layer is changed, there is almost no steering in the radiation pattern (for all values of phase differences between the sources of the two Yagi-Uda nanoantennas). This can be explained on the basis of the fact that as the SN1 nanoantenna has both the Yagi-Uda nanoantennas embedded in a VO₂ thin film layer, there is no phase difference introduced by either Yagi-Uda nanoantenna when there is a change in state of the VO₂ thin film. Hence in both the states of the VO₂ film, the shape of the radiation pattern is almost the same (i.e. the same value of Ф) with a reduced amplitude in the metallic state. This implies that SN1 is not an actively steerable nanoantenna as there is no steering of the main radiation lobe on changing the state of the VO₂ film.

In order to steer the radiation pattern by changing the state of the VO₂ thin film, we introduced an asymmetry in the VO₂ film. Such an arrangement, i.e. the steerable nanoantenna 2 (SN2), is shown in Fig. 5. In this nanoantenna structure, the VO₂ film is around one of the Yagi-Uda nanoantennas and the other Yagi-Uda nanoantenna is surrounded by air. The dimensions of the Yagi-Uda nanoantenna placed in air were selected such that it would provide maximum FR in air and those for the Yagi-Uda nanoantenna placed in the VO₂ film were such that it would provide maximum FR in the semiconductor state of the VO₂ thin film. Consider the first case corresponding to 0° phase difference between the dipole sources.

 

Fig. 5 (a) Schematic of a steerable nanoantenna 'SN2' consisting of two co-planar Yagi-Uda nanoantennas, with one of the Yagi-Uda nanoantennas being present inside a VO₂ film and the other being present in air. (b)-(m) Effect of phase difference between the dipole sources of the two Yagi-Uda nanoantennas on the far-field radiation pattern of the SN2 nanoantenna, the phase difference varying from 0° to 330°. Note that the intensity values shown in the far-field radiation patterns are normalized through dividing by 1 × 10⁻¹².

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Since one Yagi-Uda nanoantenna is surrounded by air, the change of state of the VO₂ film has no effect on the emitted radiation pattern from this nanoantenna. However, the Yagi-Udananoantenna placed in the VO₂ film will show a change in the amplitude of the radiation pattern as well as in the optical path difference of the radiated wave with a change in state of the VO₂ film. It has to be noted that the refractive index of the environment surrounding the Yagi-Uda nanoantenna is substantially different in the semiconductor state and in the metallic state. Since the radiation patterns of both the Yagi-Uda nanoantennas interfere, the overall radiation pattern changes when the state of the VO₂ thin film changes. Hence, the phase difference between light radiated from the air-Yagi-Uda nanoantenna and from the VO₂ film-Yagi-Uda nanoantenna will depend on state of VO₂. Different values of phase differences between the sources of the two Yagi-Uda nanoantennas also lead to different radiation patterns after interference. Theoretically, by introducing phase differences between the twosources, different radiation patterns can be generated. The phase difference between the two sources produce phase differences between the waves emitted from the two Yagi-Uda nanoantennas. We would like to mention here that experimentally controlling the phase of the individual dipole sources (such as quantum dots) is very difficult, and therefore it is very difficult to controllably obtain a phase difference between the emissions from the quantum dots. But, theoretically in the case of SN2 nanoantennas, one can engineer the required radiation patterns by changing the state of the VO₂ thin film as well as by controlling both the phase difference between the sources. We observe steering of the radiation pattern with a change in the state of the VO₂ film, for different phase differences between the sources of the two Yagi-Uda nanoantennas, see Fig. 5. It can be seen from Figs. 5(b)-5(m) that the direction of the radiation pattern, for SN2 nanoantennas with the VO₂ film in the semiconducting state, can be varied from 45° (for a phase difference between the sources of 300°) to 135° (for a phase difference between the sources of 0°). It can also be observed from Fig. 5 that the steering of each of these radiation patterns by — 30 ° to 60 ° — can be carried out by changing the phase of the VO₂ film from semiconducting state to the metallic state. It has to be noted that the steering of the direction pattern between the two states of the steerable nanoantenna SN2 is due to the phase change of the state of the VO₂ thin film and not due to a change in the resonance wavelength. Plasmonic waveguides and sensors are highly sensitive to resonance wavelength changes, therefore a device (such as a SN2 nanoantenna) which can switch or steer radiation at a constant wavelength is essential.

Figures 6(c) and 6(d) show steering of the near-field radiation pattern (i.e. the near-field distribution of the electric field intensity enhancement around the nanoantenna) of the steerable nanoantenna 'SN1', when the state of the VO₂ thin film surrounding one of the two Yagi-Uda nanoantennas changes from semiconducting state to metallic state (which can be achieved by either applying heat or electric field to the VO₂ thin film). It can be seen from Fig. 6(c) that the near-field radiation is primarily directed by SN1 in the direction which is ~20° to the left of the x-axis when the VO₂ thin film is in the semiconducting state. When thestate of the VO₂ thin film is changed to the metallic state, the near-field radiation is primarily directed by SN1 in the direction which is ~10° to the right of the x-axis, see Fig. 6(d). Hence, the near-field radiation pattern is steered by ~30° on changing the state of the VO₂ thin film surrounding one of the two Yagi-Uda nanoantennas from the semiconducting state to the metallic state. It can be observed that the maximum steering in the near-field radiation pattern of this steerable nanoantenna (SN1) is similar to the maximum steering of the far-field radiation pattern by the same nanoantenna, see Fig. 5(b). Steering of the near-field radiation pattern can be useful for selective excitation of fluorophores, quantum dots, or Raman active molecules present at different spatial positions on a sensor chip. The phase difference between light emitted from two Yagi-Uda nanoantennas can also be produced by shifting position (by an offset length 'L' as shown in Figs. 7(a) and 7(b)) of one of the Yagi-Uda nanoantennas with respect to the other nanoantenna. Moreover, it can be observed from Figs. 7(c)–7(h) that the radiation patterns are similar for the two cases — the first case when there is a phase difference between the sources of the two Yagi-Uda nanoantennas and the second case when the phase difference is produced from spatial shifting of the nanoantenna — for small spatial shifts (i.e. for small values of offset length 'L'). For small spatial shifts, a correlation was found to relate the phase difference between the sources of the two Yagi-Uda nanoantennas and the corresponding spatial shift of a nanoantenna in order to produce a similar radiation pattern, as shown in Fig. 7(b). It can be observed from Fig. 7(c) that the correlation is almost linear for small values of offset length (L). Hence, the offset length 'L' between the two Yagi-Uda nanoantennas forming the SN2 structure can be employed for obtaining different radiation patterns (for small values of 'L') instead of changing the phase difference between the emissions from the dipole emitters. It was also observed that for larger values of the spatial shift, the similarity between the two cases disappears as the radiated far-field amplitude decreases as inverse of the distance (from the nanoantenna).

 

Fig. 6 (a) Schematic of a steerable nanoantenna 'SN2' consisting of two co-planar Yagi-Uda nanoantennas, with one of the Yagi-Uda nanoantennas being present inside a VO₂ film and the other being present in air. (b) Far-field radiation patterns of the SN2 nanoantenna for both the states of the VO₂ thin film. Near-field radiation patterns of the SN2 nanoantenna for (c) the semiconductor state and (d) the metallic state of the SN2 nanoantenna. The phase difference between the dipole sources of the two Yagi-Uda nanoantennas was taken to be 30°. Note that the intensity values shown in the far-field radiation patterns are normalized through dividing by 1 × 10⁻¹².

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Fig. 7 A steerable nanoantenna (SN3) consisting of two Yagi-Uda nanoantennas, with one of the nanoantennas being present inside a VO₂ film and the other being present in air: (a) with a phase difference between the sources of the two nanoantennas and (b) with one of the nanoantennas being offset in the x-direction by a certain distance ‘L’. (c) Correlation to relate the phase difference between the sources of the two Yagi-Uda nanoantennas and the corresponding spatial shift of a nanoantenna. Similarity in the radiation pattern of SN3 having no spatial shift but having a phase difference between the sources of the two Yagi-Uda nanoantennas and the pattern of two Yagi-Uda nanoantennas having a spatial offset and not having a phase difference between their sources, for offset lengths (L) of: (d) 0 nm, (e) −90 nm, (f) 90 nm, (g) −150 nm, (h) 190 nm, and (i) 300 nm. Note that the intensity values shown in the far-field radiation patterns are normalized through dividing by 1 × 10⁻¹².

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We also designed another steerable nanoantenna 'SN4' consisting of two coplanar Yagi-Uda nanoantennas, with each Yagi-Uda nanoantenna being present inside a VO₂ thin film and each VO₂ thin film being separated from the other VO₂ thin film by an air-gap, see Fig. 8. In the design of this nanoantenna, one has to ensure that each VO₂ thin film section is individually addressable nano-heater lying underneath each VO₂ thin film such that the state of each VO₂ thin film section could be independently controlled. It can be observed from Fig. 8 that when the VO₂ thin film on the left (Film 1) is present in the metallic state and the VO₂ thin film on the right (Film 2) is present in the semiconducting state, the main lobe of the far-field radiation pattern has a value of Ф = 45°. On the other hand, when the VO₂ thin film on the left (Film 1) is present in the semiconducting state and the VO₂ thin film on the right (Film 2) is present in the metallic state, the main lobe of the far-field radiation pattern has a value of Ф = 135°. Hence, there is an active steering of 90° between these two cases. It has to be noted that this value of steering of the radiation pattern by 90° (by employing steerable nanoantennas) is the highest value of active steering reported thus far by any research group — with the highest previously reported value of the radiation pattern steering being 45°. It can also be observed from Fig. 8 that the half power beam width of this steerable nanoantenna (SN4) is larger than that for the steerable nanoantenna shown in Fig. 5 (SN2). In order to achieve a full 360 degree active steering of the radiation pattern by controlling the state of the VO₂ thin films, a fully steerable nanoantenna 'SN5′ was designed such that it consisted of four coplanar Yagi-Uda nanoantennas, with each Yagi-Uda nanoantenna being present inside a VO₂ thin film and each VO₂ thin film being separated from the other VO₂ thin films by an air gap, see Fig. 8(a). By employing four Yagi-Uda nanoantennas surrounded by individually addressable VO₂ thin films, one can have 16 possible states of SN5 as 16 different combinations of the states of the four VO₂ thin films — Film 1 to Film 4 in Fig. 9(a) — are possible depending on the states (metallic or semiconducting) of the VO2 thin films. We canobserve from Fig. 9(b) that the main lobe of the radiation pattern has a value of Ф = 90° when the states of four VO₂ thin films are semiconducting (S), semiconducting (S), metallic (M), and metallic (M), respectively, and that different values of Ф are possible for different combinations of the states of the four films — see Figs. 9(c)–9(j). The radiation patterns fornine of the 16 possible states are shown in Figs. 9(b)–9(j). We observed that the radiation patterns for 4 states (MMMM, SSSS, MSMS, SMSM) out of the 16 states are not directional. Hence, we can tunably steer the radiation pattern in 12 different directions covering almost 360°. It has to be mentioned that a full 360° active steering of the radiation pattern (which is demonstrated by the SN5 nanoantennas) has not been reported thus far by any research group. Moreover, we can tunably steer the radiation pattern in 12 different directions depending on the states of the four VO₂ thin films (which can be changed thermally [22] or electrically [18]), which has also not been previously shown. In the design of this nanoantenna, one has to ensure that all four VO₂ thin film sections have an individually addressable nano-heater (when heat is employed to achieve the phase transition of the VO₂ thin films) lying underneath each VO₂ thin film such that the state of each VO₂ thin film section could be independently controlled. In order to ensure better thermal isolation between the two Yagi- Uda nanoantennas, the air gaps can be filled by a material which is optically transparent but having low thermal conductivity [23,24]. The design of the SN5 nanoantennas can be simplified if the phase transition of the VO₂ thin films is achieved electrically (as this would alleviate the need for nanoheaters). In that case, four individually addressable nanoscale electrodes could be developed underneath and above the four VO₂ thin film sections to achieve the semiconductor to metal phase transition in the VO₂ thin films. By employing asteerable nanoantenna having the same architecture as SN5 but having N = 8 Yagi-Uda nanoantennas surrounded by individually addressable VO₂ thin films, one can have 2N = 28 possible states of the nanoantenna as 28 (256) different combinations of the states of the eight VO₂ thin films are possible depending on the states (metallic or semiconducting) of the VO₂ thin films. This can enable 360° active steering of the radiation pattern in possibly 256 different directions.

 

Fig. 8 Schematic of a steerable nanoantenna 'SN4' consisting of two co-planar Yagi-Uda nanoantennas, with each Yagi-Uda nanoantenna being present inside a VO₂ thin film and each VO₂ thin film being separated from the other VO₂ thin film by an air-gap and (Top) Far-field radiation patterns of the SN4 nanoantenna when film 1 and film 2 are in the metallic and the semiconductor states, respectively (in blue color) and when film 1 and film 2 are in the semiconductor and the metallic states, respectively (in red color). Note that the intensity values shown in the far-field radiation patterns are normalized through dividing by 1 × 10⁻¹².

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Fig. 9 (a) Schematic of a steerable nanoantenna 'SN5′ consisting of four co-planar Yagi-Uda nanoantennas, with each Yagi-Uda nanoantenna being present inside a VO₂ thin film and each VO₂ thin film being separated from the other VO₂ thin films by an air-gap. (b)-(j) Far-field radiation patterns of the SN5 nanoantenna for different combinations of the states of the four films, each film being in either the metallic (M) state or the semiconducting (S) state. Note that the intensity values shown in the far-field radiation patterns are normalized through dividing by 1 × 10⁻¹².

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4. Conclusions

We have described the active steering of the radiation pattern by complex nanoantenna structures (steerable nanoantennas) formed by a combination of two or more Yagi-Uda nanoantennas and thin films of a phase change material (VO₂). By employing FDTD simulations, we show that there is a steering of the radiation patterns of the nanoantennas on changing the phase of the VO₂ thin films. We have demonstrated 'in-plane' steering, i.e. steering of the radiation pattern in the plane of the nanoantennas, by employing the steerable nanoantennas being proposed. By employing a four-element steerable nanoantenna, we have demonstrated a full 360° active steering of the radiation pattern, which has not been reported thus far by any research group. This steerable nanoantenna consists of four co-planar Yagi-Uda nanoantennas, with each Yagi-Uda nanoantenna being present inside a VO₂ thin film but each individually addressable VO₂ thin film being separated from other VO₂ thin films by an air-gap. We have demonstrated that the radiation pattern can be tunably steered in 12 different directions using this four-element steerable nanoantenna depending on the states of the four VO₂ thin films, which has also not been previously shown. Moreover, we have demonstrated that the maximum achievable steering of the radiation pattern is 90° for a two element (i.e. containing 2 Yagi-Uda nanoantennas) steerable nanoantenna when the phase of the VO₂ thin films is changed. It was observed that the radiation pattern of the steerable nanoantennas being proposed in our paper can be designed to be much more directed as compared to previously reported steerable nanoantennas.

Appendix A Fabrication of SN2 steerable nanoantennas (SNs)

The proposed SNs can be fabricated by first growing crystalline VO₂ thin films on sapphire substrates and then employing a first electron-beam lithography step — consisting of an electron-beam exposure step using a positive E-beam resist (such as ZEP520A) and resist development, followed by reactive ion etching (RIE) to remove half the VO₂ thin film — see Fig. 10(d). This will be followed by another electron-beam lithography step, as shown in Fig. 10(e), resist development, and RIE into the VO₂ thin film to only remove VO₂ from regions where the gold Yagi-Uda nanoantenna would be present inside the VO₂ thin film — see Fig 10(f). This will be followed by another electron-beam lithography step on the non-VO₂ side to expose regions where gold would be deposited, as shown in Fig. 10(g), followed by resist development and gold electron-beam evaporation. This would be followed by a lift-off process to obtain the two-element Yagi-Uda nanoantenna structure. We will then again spin-coat the E-beam resist on both the VO₂ and the non-VO₂ regions. We will employ another electron-beam lithography step followed by development process to create a hole in the E-beam resist in the VO₂ region (just above the gap of the feed element), which will be followed by RIE to make a hole (having a diameter of ~ 10 nm) in the gap region between the two arms of the feed element of the Yagi-Uda nanoantenna. We will employ another electron-beam lithography step followed by the resist development process to create a hole in the E-beam resist in the non-VO₂ region (just above the gap of the feed element). We will then immerse the sample into a diluted solution of functionalized QDs. This will be followed by removal of the the resist which will also remove the QDs that do not go inside the nanoantenna gap regions. QDs will go into the two gap regions in the feed elements of the two Yagi-Uda nanoantennas, thereby completing the fabrication of an SN2 nanoantenna.

 

Fig. 10 Schematic showing the different processing steps involved in the fabrication of the SN2 steerable nanoantennas.

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Appendix B Fabrication of SN5 steerable nanoantennas (SNs)

The proposed SNs can be fabricated by first growing crystalline VO₂ thin films on sapphire substrates and then employing a first electron-beam lithography step — consisting of an electron-beam exposure step using a positive E-beam resist (such as ZEP520A) and resist development, followed by reactive ion etching (RIE) to remove the VO₂ thin film from a cross-shaped region — see Fig 11(b). This will be followed by another electron-beam lithography step, as shown in Fig 11(e), resist development, and RIE to remove VO₂ from regions where the gold Yagi-Uda nanoantennas would be present inside the VO₂ thin film — see Fig 10(f). This will be followed by gold electron-beam evaporation and lift-off process to obtain the four-element Yagi-Uda nanoantenna structure. We will then again spin-coat the E-beam resist and employ another electron-beam lithography followed by development process to create four holes in the E-beam resist (just above the gap of the feed element) which will be followed by RIE to make four holes (~ 10 nm diameter) in the gap regions between the feed elements of the Yagi-Uda nanoantenna. We will then immerse the sample into a diluted solution of functionalized QDs. This will be followed by the removal of the resist which will also remove the QDs that do not go inside the nanoantenna gap region. QDs will go into the four gap regions in the feed elements of the four Yagi-Uda nanoantennas, therebycompleting the fabrication of an SN5 nanoantenna. A similar procedure can also be employed for the fabrication of SN4 steerable nanoantennas.

 

Fig. 11 Schematic showing the different processing steps involved in the fabrication of the SN5 steerable nanoantennas.

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Funding

Ministry of Human Resource Development (MHRD) (RP03246G: UAY program, RP03417G: IMPRINT program), the Science and Engineering Research Board (SERB) (RP03055G), the Department of Biotechnology, the Ministry of Science and Technology (DBT) (RPO3150G, RPO2829G), and the Defense Research and Development Organization (DRDO) (RPO3356G).

Acknowledgments

We would also like to thank the Digital India Corporation. This publication is an outcome of the R&D work undertaken in the project under the Visvesvaraya PhD Scheme of Ministry of Electronics & Information Technology, Government of India, being implemented by Digital India Corporation (formerly Media Lab Asia).

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