1. Introduction

Plasmonic nanoantennas have attracted enormous interest in the last decade due to the promising applications based on these nanoantennas such as photodetection, solar cells, sensing, and integrated optical devices [1]. Several plasmonic nanoantennas such as nanorod [2], bowtie [3,4], log-periodic [5], and Yagi-Uda [6] nanoantennas have been extensively studied. Plasmonic nanoantennas can function both in excitation mode (receiving mode) as well as in emission mode (transmitting mode) [7]. In the excitation mode, when nanoantennas are excited by a beam of light, the incident field induces the collective oscillations of electrons in the nanoantennas known as localized surface plasmons (LSPs). This leads to the localization and enhancement of the electromagnetic fields around the nanoantennas in certain regions called hotspots. In the emission mode, plasmonic nanoantennas are excited by point sources, such as quantum emitters, by placing them in the vicinity of the plasmonic nanoantennas. Then, nanoantennas help the point source to radiate into the far-field. In the emission mode (i.e. the transmitting mode), the radiation pattern of the point source can be significantly altered through the nanoantenna modes [8]. Though nanoantennas can be used in excitation mode as well as emission mode, majority of them function well in excitation mode. However, the Yagi-Uda nanoantenna has extensively been studied in emission mode as it exhibits excellent directive properties in emission mode [6].

A typical Yagi-Uda nanoantenna comprises a feed element, a reflector, and three directors. Feed element is actively excited by the point source, whereas the reflector and directors are passively excited by the feed element. The constructive interference in one direction and destructive interference in the other directions between the radiation from all elements results in directional emission of the radiation [9]. Therefore, the main focus of the research community has been to study the directive properties of the Yagi-Uda nanoantennas [6,10–13]. Various configurations of Yagi-Uda nanoantennas have been explored to analyze and improve the directive properties of the Yagi-Uda nanoantennas [13–16]. In addition to the directive properties of the Yagi-Uda nanoantennas, the excitation rate and the emission rate of a quantum emitter, which is coupled to the near-field of resonant feed element of the Yagi-Uda antenna, is also enhanced [17].

One of the challenges while dealing with Yagi-Uda nanoantennas is to excite the feed element locally without illuminating the other elements of the Yagi–Uda nanoantenna. Local excitation of feed element can be achieved by placing a point source such as quantum dot in the vicinity of the resonant feed element of the Yagi-Uda nanoantenna [10]. The quantum dots in the vicinity of the feed element can be excited by focusing a laser beam through an objective lens or by employing a tapered waveguide such as a tapered optical fiber. Other methods such as titled feed element [12], plasmon-enhanced photoluminescence from feed element itself [18], and electrical driven feed element [19] have been explored successfully to excite the feed element locally. Moreover, there are other methods to locally generate light, such as using carbon nanotubes [20,21], using scanning tunneling microscopes [22,23], and employing inelastic electron tunnelling in optical nanoantennas [24,25]. With significant scientific advancements in areas such as local generation of light, nanoscale fabrication, and precise positioning control, the need for advanced on-chip applications based on Yagi-Uda nanoantennas is highly anticipated. One such application has been theoretically proposed in Ref. [26]. Moreover, the Yagi-Uda nanoantennas were directly employed in photodetection, resulting in fourfold improvement in the efficiency of a photodetector [27].

In this paper, we propose a device that can enable on-chip implementation of plasmon-enhanced light-matter interaction processes such as surface-enhanced Raman scattering (SERS) [28], plasmon-enhanced fluorescence [29], surface-enhanced infrared absorption spectroscopy [30]. The different plasmonic nanostructures employed for plasmon-enhanced light-matter interaction processes require an external source to excite the plasmonic nanostructures. In order to develop on-chip SERS sensing platforms, plasmonic nanoantennas have also been excited through evanescent fields of dielectric waveguides by fabricating them on top of the dielectric waveguides. We demonstrate for the first time that a Yagi-Uda nanoantenna can be employed to excite a plasmonic bowtie nanoantenna. The proposed device consists of a Yagi-Uda nanoantenna lying on the top of the substrate and a bowtie nanoantenna lying in a trench formed in the substrate (see Fig. 1(a)). We have chosen a standard five-element Yagi-Uda nanoantenna that could be easily fabricated on a substrate. Such nanoantennas have been fabricated in the past [10,12]. In future work, highly directive nanoantennas such as those described by Elsaid et al. [7] and Mahmoud et al. [13] could also be employed for on-chip implementation of SERS instead of a standard directive nanoantenna such as the five element nanoantenna on a substrate which has been employed in our work.

 

Fig. 1. (a) Schematic of a device consisting of a bowtie nanoantenna driven by a Yagi-Uda nanoantenna. (b) The 3D radiation pattern of the Yagi-Uda nanoantenna as a function of the polar angle θ and the azimuthal angle Φ. The radiation pattern of the Yagi-Uda nanoantenna: (c) as a function of Φ at θ = 48 °, in X-Y plane and (d) as a function of θ at Φ = 0°, in X-Z plane. The depth ‘D_T’ of the trench was taken to be 400 nm. The dimensions of the Yagi-Uda nanoantenna, for which the radiation pattern is shown, are as follow: L_F = 120 nm, G₁ =λ/4.4, G₂ = λ/4. The length of the reflector and the directors were taken to be 1.25 and 0.9 times of the length of the feed, respectively. The height and the width of the feed, reflector, and directors are taken to be 40 nm. The length ‘L_BNA’ of the bowtie nanoantenna and gap ‘g’ is taken to be 180 nm and 10 nm, respectively. (e) Spatial electric field distribution of a bowtie nanoantenna driven by a Yagi-Uda nanoantenna.

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When the Yagi-Uda nanoantenna is excited by a source, it radiates into the substrate towards the directors and derives the bowtie nanoantenna. The proposed device offers flexibility in the mode of excitation as the feed element of the Yagi-Uda nanoantenna can be excited electrically [19] as well as optically [10,12,18]. We show that at a wavelength of 785 nm, the electromagnetic field between the arms of the bowtie nanoantenna can be enhanced by a factor as high as ∼ 196 — even when the minimum gap between nanostructures is as large as 10 nm — which is useful for various applications. It is also found that this electric field enhancement is significantly large when compared with the maximum electric field enhancement (∼ 11) obtained for direct excitation of the bowtie nanoantenna by a point source or with the maximum electric field enhancement (∼ 34) obtained for plane wave excitation of the bowtie nanoantenna.

The electric field enhancements are also calculated at near-infrared wavelengths. For the Yagi-Uda nanoantenna driving a bowtie nanoantenna, an extremely large electric field enhancement of ∼ 945 is obtained at a wavelength of 1500 nm, even when the minimum gap between nanostructures is as large as 10 nm. The proposed device can be fabricated by employing methods such as electron beam lithography, metallization, and lift off as discussed in detail in Supplement 1, Section 2.

2. Results and Discussions

Figure 1(a) shows the schematic of the device consisting of a gold Yagi-Uda nanoantenna lying on a silica substrate and a gold bowtie nanoantenna lying in a trench in the silica substrate. The Yagi-Uda nanoantenna consists of five elements: one feed element, one reflector, and three directors. Finite-difference time-domain (FDTD) simulations, using a commercial software called Lumerical FDTD solution, were employed to calculate the various parameters such as resonance of different components, radiation pattern, and electric field enhancements at 785 nm wavelength. The design optimization of the Yagi-Uda nanoantenna is carried out by calculating the forward to backward (F/B) ratio which is the ratio of maximum electric field intensity in the forward direction to the maximum electric field intensity in backward direction, and is discussed in detail in Supplement 1 (Section 1, Fig. S2). The results of the optimized Yagi-Uda nanoantennas are presented in this paper. In order to design the device, the radiation pattern of the Yagi-Uda nanoantenna lying on a silica substrate is firstly calculated, and is shown in Fig. 1(b). From Fig. 1(b), it can be seen that the Yagi-Uda nanoantenna radiates along its axis towards the directors in the X-Y plane (i.e., Φ=0). A planer 2-D polar plot depicts this in a clear manner in Fig. 1(c). This ascertains the proper functioning of Yagi-Uda nanoantenna. In addition, it is also observed from Fig. 1(b) that the Yagi-Uda nanoantenna radiates at an angle (θ=48 °) from the –ve z-axis i.e., towards the substrate side. The radiation pattern of the Yagi-Uda nanoantenna in the X-Z plane towards the substrate side is separately shown in Fig. 1(d) using a semi-polar plot. A Yagi-Uda nanoantenna ― completely embedded in a dielectric medium ― tends to radiate in its plane. However, due to the asymmetric refractive index profile below and above the Yagi-Uda nanoantenna, the radiation pattern tilts towards the –ve z-axis in the X-Z plane [17,19]. Therefore, to excite the bowtie nanoantenna, a trench is created in the substrate, at a distance of 50 nm from the last director, such that the radiation from the Yagi-Uda nanoantenna can excite the bowtie nanoantenna placed in the trench. For a fixed angle θ, the depth of the trench (and therefore, the position of bowtie nanoantenna) depends on the horizontal distance between the bowtie nanoantenna and the Yagi-Uda nanoantenna. To keep the footprint compact, it is desirable to place the bowtie nanoantenna close to the Yagi-Uda nanoantenna.

Therefore, first, we fix the position of the bowtie nanoantenna at a distance of 250 nm from the last director (as this is experimentally realizable). Then, the depth of the trench is optimized by calculating the electric field enhancements between the arms of the bowtie nanoantenna by varying the depth of trench (see Supplement 1, Section 1, Fig. S3(a)). The spatial electric field profile of the bowtie nanoantenna (driven by the Yagi-Uda nanoantenna) for an optimal D_T is shown in Fig. 1(e). It is observed that an electric field enhancement of ∼196 is obtained at 785 nm wavelength. The large electric field enhancement is beneficial for many applications. For example, the SERS electromagnetic enhancement factor (EMEF) is equal to the fourth power of the electric field enhancement [28,31]; therefore, a SERS EMEF of ∼ 10⁹ can be obtained at 785 nm wavelength using the proposed device.

To demonstrate the advantage of employing a Yagi-Uda nanoantenna to excite the bowtie nanoantenna, we calculate the electric field enhancement between the arms of the bowtie nanoantenna for different excitation configurations. The spatial electric field distribution at 785 nm wavelength for the bowtie nanoantenna is shown in Fig. 2 for the following configurations: (a) a bowtie nanoantenna excited by a point source in the absence of a Yagi-Uda nanoantenna, (b) a bowtie nanoantenna excited by a plane wave source, and (c) a bowtie nanoantenna excited by a Yagi-Uda nanoantenna, which is excited by a point source. When the bowtie nanoantenna is excited by a stand-alone point source, i.e., in the absence of a Yagi-Uda nanoantenna, the electric field enhancement obtained is ∼ 11. In the case where the bowtie nanoantenna is excited by a plane wave source, the maximum electric field enhancement obtained is ∼ 36. Interestingly, when the Yagi-Uda nanoantenna — whose feed element is excited by the point source — is employed to excite the bowtie nanoantenna, the electric field can be enhanced by a factor of ∼ 196. This substantial increase in the electrical field enhancement, between the arms of the bowtie nanoantenna driven by a Yagi-Uda nanoantenna, can be attributed to the directive properties of the Yagi-Uda nanoantenna. A stand-alone point source radiates in all directions. Therefore, a small fraction of radiation emitted by the point source interacts with the bowtie nanoantenna. However, when the point source is coupled to the feed element of a Yagi-Uda nanoantenna, it radiates through the modes of the nanoantenna. Because of the directive properties of the Yagi-Uda nanoantenna, most of the radiation is transmitted in one direction. Consequently, such a substantial electric field enhancement is obtained.

 

Fig. 2. Schematic (top) and the spatial electric field distribution (bottom) of a bowtie nanoantenna for three configurations: (a) Bowtie nanoantenna excited by a point source in the absence of a Yagi-Uda nanoantenna, (b) Bowtie nanoantenna excited by a plane-wave source and (c) Bowtie nanoantenna driven by a Yagi-Uda nanoantenna, which is excited by a point source. The spatial electric field distributions were calculated at 785 nm wavelength of the incident light. The dimensions of the Yagi-Uda nanoantenna and of the bowtie nanoantenna are: L_F = 120 nm, G₁ = λ/4.4, G₂ = λ/4, L_R= 1.25 x L_F, L_D = 0.9 x L_F, L_BNA = 180 nm, g = 10 nm, D_T = 400 nm.

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To understand the role of resonances of different components of the device proposed by us, we calculate the electric field enhancement factor as a function of wavelength for various sizes of the bowtie nanoantenna. The Yagi-Uda nanoantenna, which is in resonance at 785 nm wavelength, is excited by a point source, and the electric field enhancement factor is calculated for various sizes of a bowtie nanoantenna, as shown in Fig. 3(a). It is observed that the maximum electric field enhancement occurs at 785 nm wavelength. This is expected because the Yagi-Uda nanoantenna used is in resonance at 785 nm wavelength. It can also be observed that, at 785 nm wavelength, the maximum electric field enhancement occurs for 180 nm length of the bowtie nanoantenna, as separately shown in Fig. 3(b). This is attributed to the fact that both ― the Yagi-Uda nanoantenna, which directs the power from the point source to the bowtie nanoantenna, as well as the bowtie nanoantenna having 180 nm length ― resonate at 785 nm wavelength (see Supplement 1, Section 1, Fig. S2).

 

Fig. 3. (a) Electric field enhancement in the gap present between the arms of a bowtie nanoantenna driven by a Yagi-Uda nanoantenna as a function of the wavelength, for different length of the bowtie nanoantenna. Electric field enhancement in the gap present between the arms of a bowtie nanoantenna driven by a Yagi-Uda nanoantenna as a function of: (b) the length of the bowtie nanoantenna at 785 nm wavelength and (c) the length of the feed element of the Yagi-Uda nanoantenna at 785 nm. The power radiated at 785 nm wavelength (normalized to the maximum power radiated) at angle θ = 48° as a function of the length of the feed element of the Yagi-Uda nanoantenna. The dimensions of the Yagi-Uda nanoantenna and bowtie nanoantenna (unless varied) are: L_F = 120 nm, G₁ = λ/4.4, G₂ = λ/4, L_R= 1.25 x L_F, L_D = 0.9 x L_F, L_BNA = 180 nm, g = 10 nm, D_T = 400 nm.

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To strengthen this fact, we calculate the electric field enhancement for various lengths of the feed element while keeping the bowtie nanoantenna length fixed at 180 nm (which is the resonance length of the bowtie nanoantenna for 785 nm wavelength). The results are shown in Fig. 3(c). The maximum electric field enhancement occurs at 120 nm length of the feed element, which is the resonance length of the feed element at 785 nm wavelength on the silica substrate. To clarify this more, we have plotted the power (normalized to maximum power) as a function of feed length transmitted at angle θ = 48°, as shown in Fig. 3(d) for 785 nm wavelength. It can be observed that maximum power transmitted by the Yagi-Uda nanoantenna occurs for a feed length of 120 nm. This indicates that maximum power from the source couples to the plasmonic mode of feed element having a length of 120 nm, as this is the resonance feed length of the gold feed element present on silica substrate at 785 nm wavelength. It can be concluded that the maximum electric field enhancement is obtained only when both, the bowtie nanoantenna as well as the Yagi-Uda nanoantenna, are in resonance with the wavelength emitted by the point source.

In addition to calculating the electric field enhancement at 785 nm wavelength, we also calculate the maximum electric field enhancements at various near-infrared wavelengths. The length of the feed element of the Yagi-Uda nanoantenna, the length of the bowtie nanoantenna, and the depth of the trench are optimized at various wavelengths in the near-infrared region to determine the highest possible electric field enhancement (see Supplement 1, Section 1, Fig. S5). The resonance length of the feed element ‘L_F’, the resonance length of the bowtie nanoantenna ‘L_BNA’ and the optmimum depth (D_T) of the trench obtained at different wavelengths are given in Table 1.

Table 1. Resonance length of the feed element of the Yagi-Uda nanoantenna (L_F) and of the bowtie nanoantenna (L_BNA) as well as the optimum depth (D_T) of the trench calculated at different wavelengths of the incident light

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The maximum electric field enhancement between the arms of the bowtie nanoantenna and SERS EMEF is shown in Fig. 4(a) and Fig. 4(b), respectively, with a Yagi-Uda nanoantenna driving the bowtie nanoantenna and without the Yagi-Uda nanoantenna. The position of the dipole source for the Yagi-Uda nanoantenna driving the bowtie nanoantenna and without the Yagi-Uda nanoantenna was kept the same, i.e. at a distance of 5 nm from one end of the feed element and at the same height as the Yagi-Uda nanoantenna. It is evident from Fig. 4 that the electric field enhancement with the Yagi-Uda nanoantenna is substantially large compared to the electric field enhancement without the Yagi-Uda nanoantenna. Moreover, the electric field enhancement increases at longer wavelengths and reaches up to ∼ 945 at 1500 nm wavelength. Higher electric field enhancements at longer wavelengths can firstly be attributed to the fact that the bowtie nanoantennas that are resonant at longer wavelengths, have larger lengths. These bowtie nanoantennas having larger lengths produce higher electric field enhancements compared to those of short bowtie nanoantennas (see Supplement 1, Section 1, Fig. S5(b)). Secondly, more power is radiated by the Yagi-Uda nanoantennas in the forward direction at longer wavelengths as compared to that at a shorter wavelengths (see Supplement 1, Section 1, Fig. S6). This can be attributed to the fact that the Yagi-Uda nanoantennas that are resonant at larger wavelengths have larger feed lengths, and that the nanoantennas with larger feed lengths will have better coupling with the nanoemitters. Hence, these nanoantennas with larger feed lengths will radiate more power in the forward direction. Therefore, more power is directed by the Yagi-Uda nanoantennas in the forward direction for longer wavelengths. From Fig. 4(b), it can be seen that a SERS EMEF of ∼ 8 × 10¹¹ can be obtained (between the arms of the bowtie nanoantenna) at a wavelength of 1500 nm in the presence of a Yagi-Uda nanoantenna. The spatial electric field distribution of a bowtie nanoantenna driven by a Yagi-Uda nanoantenna at different wavelengths is presented in Fig. 5. It is evident from Fig. 5 that, at the resonant wavlength (∼ 1500 nm), a maximum electric field enhancement occurs at the hotspot generated between the arms of the bowtie nanoantenna.

 

Fig. 4. (a) Maximum electric field enhancement between the arms of the bowtie nanoantenna, without the bowtie nanoantenna being driven by the Yagi-Uda nanoantenna (blue) and with the bowtie nanoantenna being driven by the Yagi-Uda nanoantenna (red), for different wavelengths of the incident light. (b) SERS EMEF calculated between the arms of the bowtie nanoantenna, without the bowtie nanoantenna being driven by the Yagi-Uda nanoantenna (blue) and with the bowtie nanoantenna being driven by the Yagi-Uda nanoantenna (red). The optimized lengths of the feed elements of the Yagi-Uda nanoantennas, the optimized lengths of the bowtie nanoantennas, as well as the depths of the trench are given in Table 1. Other important dimensions of the device are: G₁ = λ/4.4, G₂ = λ/4, L_R= 1.25 x L_F, L_D = 0.9 x L_F, g = 10 nm.

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Fig. 5. Spatial electric field distribution of a bowtie nanoantenna driven by a Yagi-Uda nanoantenna when the wavelengths of the incident light are: (a) 800 nm, (b) 900 nm, (c) 1000 nm, (d) 1100 nm, (e) 1200 nm (f) 1300 nm, (g) 1400 nm, and (h) 1500 nm wavelength. The optimized lengths of the feed elements of the Yagi-Uda nanoantennas, the optimized lengths of the bowtie nanoantennas, as well as the depths of the trench are given in Table 1. Other important dimensions of the device are: G₁ = λ/4.4, G₂ = λ/4, L_R= 1.25 x L_F, L_D = 0.9 x L_F, g = 10 nm.

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3. Conclusions

In conclusion, we have proposed a device in which a plasmonic bowtie nanoantenna is driven by a Yagi-Uda nanoantenna. The propsed device can enable on-chip implementation of plasmon-enhanced light-matter interaction processes. The FDTD method was employed to calculate the radiation pattern of the Yagi-Uda nanoantenna and the electric field enhancements between the arms of the bowtie nanoantenna, which is driven by the Yagi-Uda nanoantenna. We found that the electric field, between the arms of the bowtie nanoantenna with a gap as large as 10 nm, can be enhanced by a factor of ∼ 196 at 785 nm wavelength, leading to a SERS electromagnetic enhancement of ∼ 1.5 × 10⁹. The electric field enhancement obtained using proposed device is significantly higher compared to electric field enhancement obtained in case of direct excitation of the bowtie nanoantenna by a point source in the absence of the Yagi-Uda nanoantenna or in the case of direct excitation of a bowtie nanoantenna by a plane wave source. The calculation of the electric field enhancement at 785 nm wavelength ― for different lengths of a bowtie nanoantenna and the feed element of the Yagi-Uda nanoantenna ― reveals that the maximum enhancement is obtained only when both the Yagi-Uda nanoantenna and the bowtie nanoantenna are chosen to resonate at 785 nm wavelength. By optimizing the Yagi-Uda nanoantenna as well as the bowtie nanoantenna at different near-infrared wavelengths, a maximum electromagnetic field enhancement of ∼ 945 is obtained at a wavelength of 1500 nm, resulting in a SERS electromagnetic enhancement factor of ∼ 10¹¹.