Abstract
Nanoantennas play an important role as mediators to efficiently convert free-space light into localized optical energy and vice versa. However, effective control of the beam direction of a single nanoantenna remains a great challenge. In this paper, we propose an approach to steer the beam direction of a single nanoantenna by adjusting two antenna modes with opposite phase symmetry. Our theoretical study confirmed that the combination of even- and odd-symmetric modes with a phase difference of π/2 enables effective beam steering of a single nanoantenna whose steering angle is controlled by adjusting the amplitude ratio of the two antenna modes. To implement our theory in real devices, we introduced asymmetric trapezoidal nano-slot antennas with different side air-gaps of 10 and 50 nm. The trapezoidal nanoantennas can simultaneously excite the dipole and quadrupole modes in a single nanoantenna and enables effective beam steering with an angle of greater than 35° near the resonance of the quadrupole mode. In addition, the steering angle can also be controlled by adjusting the degree of asymmetry of the trapezoidal slot structure. We believe that our beam steering method for a single nanoantenna will find many potential applications in fields such as imaging, sensing, optical communication, and quantum optics.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nanoantennas that excel in confining optical energy in deep-subwavelength space have attracted significant research attention owing to their potential applications such as high-speed optical communication [1–6], quantum computing with single phonon sources [7–9] and detectors [10–12], nonlinear plasmonics [13–15], and single-molecule spectroscopy [16–18]. Recent advances in nanoantenna technology offer tremendous opportunities to control their functionality while maintaining extremely confined optical energy [19–21]. In particular, various nanoantenna configurations have been proposed to enable the control of the far-field radiation characteristics. For example, the Yagi–Uda [22–27], bull’s eye [28,29], and bimetallic nanoantennas [30] have demonstrated the ability to control the beam direction of the antenna from highly localized optical energy to the free space or vice versa. Here, the electromagnetic waves generated from a single feed nanoantenna are interfered by the electromagnetic waves from the surrounding antenna elements. These systems inevitably require the use of multiple antenna elements in an array form to adjust the phase interference and steer the beam direction. However, the method using multiple antenna elements not only consumes considerable space but also lowers the high-density optical energy by distributing energy to the surrounding antenna array. It is also challenging to ensure that all the array elements are precisely sized and positioned for accurate phase interference. The ability to steer the beam direction of a single nanoantenna would be a major breakthrough in the development of the next-generation nanoantenna-based photonic devices. For example, integrating a single quantum emitter into the engineered nanoantenna will enable a fast, bright and even directional quantum source in future quantum integrated circuits. It can also be applied not only to detect or focus light incident in a specific direction on nanometer space, but also to increase the efficiency of a single-molecule spectroscopy. One possible approach to steer the beam direction of a single nanoantenna is to utilize the higher order eigenmodes. This is because nanoantennas have several bright (even) and dark (odd) modes with relatively wide spectral bandwidths sufficient to overlap multiple eigenmodes [31,32].
In this paper, we propose an approach to steer the beam direction of a single nanoantenna by adjusting two antenna modes with opposite phase symmetry. Using a simple dipole antenna approximation, we theoretically verified that the beam of a single nanoantenna can be steered by exciting a mixture of even- and odd-symmetric modes. In particular, by setting the phase difference between the even- and odd-symmetric modes at π/2, the beam steering conditions are satisfied, and the steering angle is controlled by adjusting the amplitude ratio between the two modes. To implement our theory in a practical device, we introduced the asymmetric trapezoidal nano-slot antenna, with different side air-gaps of 10 and 50 nm. This structure simultaneously excites the dipole and quadrupole modes under planewave pumping conditions and has a beam steering angle of 35° or more, in proximity to the resonance of the quadrupole mode. In this case, the steering angle is adjusted according to the degree of asymmetry of the trapezoidal slot structure.
2. Theorical background
First, we investigated the theoretical possibility that the beam direction of a single nanoantenna could be steered by a combination of different eigenmodes of the antenna. To simplify the development of the theory, we approximated the antenna modes with dipole oscillations and calculated the far-field radiation patterns based on this model.
As shown in Fig. 1(a), we modeled the even-symmetric 1st mode of the nanoantenna with a single dipole oscillation. Here, the dipole moment is expressed by ${{\textbf d}_{\textbf e}} = \alpha {E_e}\hat{{\textbf z}}$, where Ee is the amplitude of the near electric field of the antenna mode and $\alpha $ is the coefficient of polarizability. So, the electric field in the far-field regime (${\textrm{E}_\textrm{e}}^\textrm{f}$) is calculated by ${\textrm{E}_\textrm{e}}^\textrm{f} = C{E_e}sin \theta ({1/r} )exp({ikr} )\; \hat{{\textbf x}}$ (see Appendix A), where $\theta $ is the polar angle, r is the distance between the dipole and the measuring point, and C is the constant coefficient. Accordingly, the time-averaged radiation power per unit solid angle ($\Gamma = dP/d\Omega \propto {|{{{\textbf E}_{\textbf e}}^{\textbf f}} |^2}$) is proportional to ${|{\textrm{sin} \theta } |^2}$, as shown in Fig. 1(a).
In a similar way, we approximated the odd-symmetric 2nd mode of the nanoantenna as two dipole oscillations a distance L apart and with a phase difference of $\pi $. In this case, the electric field in the far-field regime (${{\textbf E}_{\textbf o}}^{\textbf f}$) is calculated by ${{\textbf E}_{\textbf o}}^{\textbf f} ={-} iC({kL/2} ){E_o}sin\theta cos\theta ({1/r} )\textrm{exp}({ikr} )\; \hat{{\textbf x}}$ (see Appendix B), where Eo is the amplitude of the near electric field of the odd-symmetric antenna mode and k is the wavenumber. It follows that the time-averaged radiation power per unit solid angle of the 2nd mode is proportional to $\textrm{|}sin\theta cos\theta {\textrm{|}^\textrm{2}}$, as shown in Fig. 1(b).
When these two antenna modes are mixed together in a single nanoantenna, the radiation power per unit solid angle follows the relation $\Gamma \propto {|{{a_e}sin\theta - i{a_o}sin\theta cos\theta } |^2}$ (see Appendix C), where ae and ao are the complex coefficients that represent how much the even- and odd-symmetric modes are mixed in a single antenna. Thus, one can change the far-field radiation patterns by adjusting ae and ao, and under certain conditions, the radiation beam of the antenna will be steered.
We calculated the far-field radiation patterns based on Fig. 1(c), as a function of the mixture of ae and ao in polar coordinates, as shown in Figs. 2(a) and 2(b). When a single dipole oscillation (ae : iao = 1 : 0) or a double-dipole oscillation (ae : iao = 0 : 1) is present in the antenna, the far-field radiation exhibits a dipole or quadrupole radiation pattern, respectively. However, when the odd-symmetric quadrupole mode is added to the even-symmetric dipole mode (ae = 1, iao ≠ 0) or vice versa (ae ≠ 0, iao = 1), the antenna beam begins to be steered in a specific direction. As shown in Figs. 2(a) and 2(c), as iao is varied from 0 to ±1 at ae = 1, the far-field radiation of the dipole mode is steered with an angle $\delta\left(=\pi / 2-\theta_{\max }\right)$ from 0° to ∓30°, where ${\theta _{max}}$ is the polar angle at the maximum radiation power. In this condition, the far-field radiation shows the unidirectional beam with a single value of $\delta $ in the range of −30° ∼ 30°.
On the other hand, when the dipole mode is added to the quadrupole mode (or ae is varied from 0 to ±1 at iao = 1), the bidirectional far-field pattern of the original quadrupole mode is transformed into the unidirectional pattern in a specific range of ae, as shown in Figs. 2(d) and 2(e). For example, when ae approaches from 0 to 1 at iao = 1, one of the two directional beams is shifted from -45° to -30°, while the other beam moves from 45° to 90°. Here, the energy of the former beam occupies a high proportion of the total energy during ae approaches 1, while the energy of the latter beam weakens and eventually disappears, as shown in Fig. 2(e). For the condition of ae : iao = 0.5 : 1, one beam is directed to −36°, and the other to 57°. Here, the radiation power of the beam at −36° accounts for 96% of the total radiation power. If this condition (ae : iao = 0.5 : 1) is set as the boundary of the unidirectional beam, the maximum steerable angle of a unidirectional beam by the mixture of two eigenmodes of a single nanoantenna is ±36 °, as shown in Fig. 2(d).
3. Device design
To implement our theory in a practical device, we studied beam steering based on the air-slot nanoantennas. The air-slot nanoantennas, like other types of nanoantennas, have multiple resonant eigenmodes over a broad spectral range. The nanoantenna with a rectangular air-slot on a 100 nm thick gold film, shown in Fig. 3(a), has three x-polarized resonance modes in the wavelength range of 400–2000nm. Here, the slot length (L) and gap size (g) are 400 nm and 50 nm, respectively. The 1st and 3rd modes have electric fields with even symmetry with respect to the xy-plane; the 2nd mode has an electric field with odd symmetry. In the 1st mode (even mode), the electric field has a half wavelength sinusoidal distribution along the longitudinal z-direction of the air-slot, described by $\mathbf{E}(z)= \; E_{e} \sin (\pi z / L) \hat{\mathbf{x}}$, as shown in Fig. 3(b). In the 2nd mode (odd mode), the electric field has a full wavelength sinusoidal distribution along the z-direction, described by $\mathbf{E}(z)=E_{o} \sin (2 \pi z / L) \hat{\mathbf{x}}$. From the surface equivalence principle, the even-symmetric 1st mode and the odd-symmetric 2nd mode are approximated as a single magnetic dipole oscillation ($\mathbf{m}_{\mathrm{e}}=\alpha E_{e} \hat{\mathbf{z}}$) and two magnetic dipole oscillations ($\mathbf{m}_{\mathrm{o}}=\pm\left(\alpha E_{o} / 2\right) \hat{\mathbf{z}}$) with a phase difference of π, respectively [33–36] (see Appendix D). Thus, the 1st and 2nd modes show the dipole and quadrupole far-field radiation patterns, respectively, as shown in Figs. 3(c) and 3(d). Here, the simulations were conducted numerically by using a commercially available finite-difference time-domain (FDTD) software package (Lumerical Solutions, Inc.). The complex permittivity of gold was taken from Johnson and Christy’s experimental study [37] and fitted with the Drude model to conduct the simulation. The far-field patterns were calculated through the post processing of near-to-far field transformations using the near-field data obtained from the FDTD simulation [38].
When a x-polarized planewave is incident to the rectangular-slot nanoantenna, the 2nd mode with odd phase symmetry is not excited because of zero coupling with the normal-incident planewave ${\textbf k} = {k_y}\hat{{\textbf y}}$. Figure 3(e) shows the energy spectrum stored inside the nanoantenna under normal planewave pumping conditions, where all the energy values are normalized by the maximum energy value of the 1st mode. As shown in this figure, the 2nd mode is not excited. In order to steer the beam direction of a single nanoantenna, we must excite the odd-symmetric 2nd mode under these pumping conditions.
One way to excite the odd-symmetric 2nd mode is to break the symmetry of the slot geometry. As shown in Fig. 4(a), we reformed the symmetric rectangular slot with the asymmetric trapezoidal slot. Here, some amount of coupling of the 2nd mode is expected due to the distorted near-and far-field profiles by the asymmetric slot shape. We fixed the gap size (g2) on one side of the trapezoid at 50 nm and deformed the gap size (g1) on the other side from 40 to 5 nm. We can see in Fig. 4(b) that as g1 decreases, the symmetry of the near-field profiles of both 1st and 2nd modes is broken, and when g1 < 10 nm, the near electric-field is severely biased into the smallest gap in both 1st and 2nd modes. The radiation patterns of the 1st and 2nd modes are also slightly distorted, as shown in Fig. 4(c).
Figure 4(d) shows the energy spectrum stored inside the antenna as g1 decreases from 50 to 5 nm, under normal planewave pumping conditions. All the energy values are normalized by the maximum energy of the 1st mode for the antenna with g1 = 50 nm. We can clearly see that as g1 decreases (or as the degree of slot asymmetry increases), the odd-symmetric 2nd mode is highly excited. For the antenna with g1 = 40 nm, the normalized maximum energies for the 1st and 2nd mode increase to 1.08 and 0.03, respectively. When g1 decreases to 10 nm, the normalized maximum energies for 1st and 2nd modes further increase to 1.28 and 0.24, respectively. The quality factor of the 1st mode is calculated to be 5 for the antenna with g1 = 10 nm. This means that about 4.3% of the maximum energy of the 1st mode (λ1st = 1439 nm) exists near the resonance of the 2nd mode (λ2nd = 766 nm) in the spectrum, as shown in Fig. 5(b). This fact opens the possibility that the trapezoidal nano-slot antenna will have conditions (ae ≠ 0, ao ≠ 0) to steer the beam direction.
4. Beam steering of trapezoidal-slot nanoantenna
Through computational simulations, we confirmed that the trapezoidal-slot nanoantenna can steer the normal-incident planewave beam. To display the far-field patterns, we projected the angle of the far-field radiation from spherical coordinates onto the xz-plane, as shown in Fig. 5(a). To see the spectral responses at first, we fixed g1 and g2 at 10 nm and 50 nm, respectively. As estimated in Fig. 4(d), the 2nd mode is excited under normal planewave pumping, and the energy tail of the 1st mode extends near the resonance of the 2nd mode with a low quality-factor, as shown in Fig. 5(b). So, it is expected that the beam can be steered near the 2nd resonance mode (ao ≠ 0) because the energy of the 1st mode remains (ae ≠ 0) near the 2nd mode and the phase difference of π/2 (iao = real) can be found near the resonance of the 2nd mode [39]. As shown in Fig. 5(c), we examined the radiation patterns of the nanoantenna for wavelengths near the 2nd mode from 700 to 780 nm. At λ = 760 nm, the radiation beam of the nanoantenna shows the maximum steering of the planewave beam with an angle (δ) of −35.5°, which is almost identical to the theoretical maximum steering angle of 36.0° discussed in Fig. 2. Here, a very weak second radiation beam is observed at δ = 44.5°. At λ = 725 and 700 nm, δ are calculated to be −22.7° and −8.2°, respectively, and at λ = 780 nm, the beam shows the bidirectional radiation pattern.
Finally, we studied the effect of the degree of slot asymmetry on the beam steering. Figure 6 shows the far-field radiation patterns at wavelengths with the maximum steering angle, when g1 decreases from 40 to 10 nm and g2 is fixed at 50 nm. It is clear that the stronger the degree of asymmetry of the trapezoidal shape, the greater the beam steering angle. For g1 = 40, 30, and 20 nm, the maximum δ are calculated to be −0.9°, −13.6°, and −30.0°, respectively. At g1 = 10 nm, the radiation beam shows the steering angle of −35.5° close to the theoretically predicted maximum steering angle of 36°. The beam divergences, defined as the full-widths at half-maximum (FWHM) of the beam angle, are calculated to be 46°, 69°, 56° and 39° for the antennas with g1 = 40, 30, 20, and 10 nm, respectively. Here, the wide beam divergences are due to the small modal sizes of the 1st (even) and 2nd (odd) modes of the nanoantenna. Through the studies using the higher-order eigenmodes of the nanoantenna, we can reduce the width of the beam divergence. For example, the beam divergences of the 3rd and 5th modes show 27° and 20°, respectively.
5. Conclusion
We have proposed a novel method for beam steering of a single nanoantenna by exciting multiple antenna modes with opposite phase symmetries. Our theoretical and numerical studies confirmed that the combination of even- and odd-symmetric modes, with π/2 phase difference, allows for effective beam steering of a single nanoantenna. Here, the steering angle is controlled by adjusting the degree of mixing of the even- and odd-symmetric modes. We believe that our beam steering approach will pave the way for beam engineering of a single nanoantenna.
Appendix A: Radiation pattern of a single dipole oscillation
In the radiation zone ($kr \gg 1$), the electric-field (${{\textbf E}_{\textbf e}}^{\textbf f}$) of a single dipole, located at the origin, is given by,
Appendix B: Radiation pattern of two dipole oscillations
Suppose there are two oscillating dipoles, one of which is located at $({L/2} )\; \hat{{\textbf z}}$ with the dipole moment ${{\textbf d}_1} = ({\alpha {E_o}/2} )\hat{{\textbf z}}$, and the other is at ${\; } - ({L/2} )\; \hat{{\textbf z}}$ with the dipole moment ${{\textbf d}_2} ={-} ({\alpha {E_o}/2} )\hat{{\textbf z}}$. Then, the radiated electric field (${{\textbf E}_{\textbf o}}^{\textbf f}$) is given by
Appendix C: Beam steering by mixing two resonant modes
In this method, we determined the radiation pattern of the even and odd modes as follows:
Appendix D: Dipole oscillation modeling of slot-antenna modes
According to the surface equivalence principle, the fields outside an imaginary infinite 2D-plane are obtained by placing electric- and magnetic-current densities over the surface. For a small aperture in an infinitely extended perfect electric conductor, the aperture can be replaced solely by the magnetic surface current density (${{\textbf M}_{\textbf s}}$). Here, the magnetic surface current density can be determined with the knowledge of the tangential electric field (${{\textbf E}_{\textbf t}}$) on the surface of the aperture, ${{\textbf M}_{\textbf s}} ={-} 2\hat{{\textbf n}} \times {{\textbf E}_{\textbf t}}$, where $\hat{{\textbf n}}$ is the normal vector directed into the region of interest. Then, in the presence of the surface magnetic-current source, the electric field is given by
For the narrow-gap metal-insulator metal (MIM) trench, the electric field distribution follows the electric field polarized in the x-direction, due to the strongly enhanced field in that direction. The electric fields, polarized in the x-direction, of the even and odd modes are shown in Fig. 7. For the MIM rectangular trench, we approximated the electric field distribution (${{\textbf E}_{{\textbf even}}}$ and ${{\textbf E}_{{\textbf odd}}}$) of the resonant modes with sinusoidal functions, as follows:
where Eo and Ee represent the electric field amplitude at the antinode positions.As explained in the above section, the effective dipole moment can be obtained by integrating the tangential field in the rectangular aperture. Thus, the even mode can be modeled by a single dipole oscillation, and the corresponding dipole moment (${{\textbf m}_{\textbf e}}$) is given by
Funding
National Research Foundation of Korea (2017R1D1A1B03036010, 2019M3E4A1078663, 2020R1A2C2010967); KU-KIST School (2E30620-20-051); Korea University (Korea University Grant); Korea Institute of Science and Technology (KU-KIST School Project).
Disclosures
The authors declare no conflicts of interest.
References
1. M. S. Eggleston and M. C. Wu, “Efficient Coupling of an Antenna-Enhanced nanoLED into an Integrated InP Waveguide,” Nano Lett. 15(5), 3329–3333 (2015). [CrossRef]
2. M. Ayata, Y. Fedoryshyn, W. Heni, B. Baeuerle, A. Josten, M. Zahner, U. Koch, Y. Salamin, C. Hoessbacher, C. Haffner, D. L. Elder, L. R. Dalton, and J. Leuthold, “High-speed plasmonic modulator in a single metal layer,” Science 358(6363), 630–632 (2017). [CrossRef]
3. M. T. Hill, Y.-S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S.-H. Kwon, Y.-H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007). [CrossRef]
4. M. S. Eggleston, K. Messer, L. Zhang, E. Yablonovitch, and M. C. Wu, “Optical antenna enhanced spontaneous emission,” Proc. Natl. Acad. Sci. U. S. A. 112(6), 1704–1709 (2015). [CrossRef]
5. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460(7259), 1110–1112 (2009). [CrossRef]
6. M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482(7384), 204–207 (2012). [CrossRef]
7. T. B. Hoang, G. M. Akselrod, and M. H. Mikkelsen, “Ultrafast Room-Temperature Single Photon Emission from Quantum Dots Coupled to Plasmonic Nanocavities,” Nano Lett. 16(1), 270–275 (2016). [CrossRef]
8. B. Demory, T. A. Hill, C.-H. Teng, L. Zhang, H. Deng, and P.-C. Ku, “Plasmonic Enhancement of Single Photon Emission from a Site-Controlled Quantum Dot,” ACS Photonics 2(8), 1065–1070 (2015). [CrossRef]
9. A. F. Koenderink, “Single-Photon Nanoantennas,” ACS Photonics 4(4), 710–722 (2017). [CrossRef]
10. L. Tang, S. E. Kocabas, S. Latif, A. K. Okyay, D.-S. Ly-Gagnon, K. C. Saraswat, and D. A. B. Miller, “Nanometre-scale germanium photodetector enhanced by a near-infrared dipole antenna,” Nat. Photonics 2(4), 226–229 (2008). [CrossRef]
11. Y. Salamin, P. Ma, B. Baeuerle, A. Emboras, Y. Fedoryshyn, W. Heni, B. Cheng, A. Josten, and J. Leuthold, “100 GHz Plasmonic Photodetector,” ACS Photonics 5(8), 3291–3297 (2018). [CrossRef]
12. Y. Zhan, X. Li, D. Y. Lei, S. Wu, C. Wang, and Y. Li, “Enhanced Photoresponsivity of a Germanium Single-Nanowire Photodetector Confined within a Superwavelength Metallic Slit,” ACS Photonics 1(6), 483–488 (2014). [CrossRef]
13. M.-K. Kim, H. Sim, S. J. Yoon, S.-H. Gong, C. W. Ahn, Y.-H. Cho, and Y.-H. Lee, “Squeezing Photons into a Point-Like Space,” Nano Lett. 15(6), 4102–4107 (2015). [CrossRef]
14. M. Kauranen and A. V. Zayats, “Nonlinear plasmonics,” Nat. Photonics 6(11), 737–748 (2012). [CrossRef]
15. J. B. Lassiter, X. Chen, X. Liu, C. Ciracì, T. B. Hoang, S. Larouche, S.-H. Oh, M. H. Mikkelsen, and D. R. Smith, “Third-Harmonic Generation Enhancement by Film-Coupled Plasmonic Stripe Resonators,” ACS Photonics 1(11), 1212–1217 (2014). [CrossRef]
16. D. Punj, M. Mivelle, S. B. Moparthi, T. S. van Zanten, H. Rigneault, N. F. van Hulst, M. F. García-Parajó, and J. Wenger, “A plasmonic ‘antenna-in-box’ platform for enhanced single-molecule analysis at micromolar concentrations,” Nat. Nanotechnol. 8(7), 512–516 (2013). [CrossRef]
17. C. Zhan, X.-J. Chen, J. Yi, J.-F. Li, D.-Y. Wu, and Z.-Q. Tian, “From plasmon-enhanced molecular spectroscopy to plasmon-mediated chemical reactions,” Nat. Rev. Chem. 2(9), 216–230 (2018). [CrossRef]
18. S. Nie and S. R. Emory, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced Raman Scattering,” Science 275(5303), 1102–1106 (1997). [CrossRef]
19. J.-H. Kang, K. Kim, H.-S. Ee, Y.-H. Lee, T.-Y. Yoon, M.-K. Seo, and H.-G. Park, “Low-power nano-optical vortex trapping via plasmonic diabolo nanoantennas,” Nat. Commun. 2(1), 582 (2011). [CrossRef]
20. S. J. Yoon, J. Lee, S. Han, C.-K. Kim, C. W. Ahn, M.-K. Kim, and Y.-H. Lee, “Non-fluorescent nanoscopic monitoring of a single trapped nanoparticle via nonlinear point sources,” Nat. Commun. 9(1), 2218 (2018). [CrossRef]
21. J.-H. Song, J. Kim, H. Jang, I. Yong Kim, I. Karnadi, J. Shin, J. H. Shin, and Y.-H. Lee, “Fast and bright spontaneous emission of Er3+ ions in metallic nanocavity,” Nat. Commun. 6(1), 7080 (2015). [CrossRef]
22. T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi–Uda antenna,” Nat. Photonics 4(5), 312–315 (2010). [CrossRef]
23. K.-M. See, F.-C. Lin, T.-Y. Chen, Y.-X. Huang, C.-H. Huang, A. T. M. Yeşilyurt, and J.-S. Huang, “Photoluminescence-Driven Broadband Transmitting Directional Optical Nanoantennas,” Nano Lett. 18(9), 6002–6008 (2018). [CrossRef]
24. A. G. Curto, G. Volpe, T. H. Taminiau, M. P. Kreuzer, R. Quidant, and N. F. van Hulst, “Unidirectional Emission of a Quantum Dot Coupled to a Nanoantenna,” Science 329(5994), 930–933 (2010). [CrossRef]
25. T. Coenen, E. J. R. Vesseur, A. Polman, and A. F. Koenderink, “Directional Emission from Plasmonic Yagi–Uda Antennas Probed by Angle-Resolved Cathodoluminescence Spectroscopy,” Nano Lett. 11(9), 3779–3784 (2011). [CrossRef]
26. D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3D optical Yagi–Uda nanoantenna array,” Nat. Commun. 2(1), 267 (2011). [CrossRef]
27. F. Bernal Arango, A. Kwadrin, and A. F. Koenderink, “Plasmonic Antennas Hybridized with Dielectric Waveguides,” ACS Nano 6(11), 10156–10167 (2012). [CrossRef]
28. S. K. H. Andersen, S. Bogdanov, O. Makarova, Y. Xuan, M. Y. Shalaginov, A. Boltasseva, S. I. Bozhevolnyi, and V. M. Shalaev, “Hybrid Plasmonic Bullseye Antennas for Efficient Photon Collection,” ACS Photonics 5(3), 692–698 (2018). [CrossRef]
29. H. Aouani, O. Mahboub, N. Bonod, E. Devaux, E. Popov, H. Rigneault, T. W. Ebbesen, and J. Wenger, “Bright Unidirectional Fluorescence Emission of Molecules in a Nanoaperture with Plasmonic Corrugations,” Nano Lett. 11(2), 637–644 (2011). [CrossRef]
30. T. Shegai, S. Chen, V. D. Miljković, G. Zengin, P. Johansson, and M. Käll, “A bimetallic nanoantenna for directional colour routing,” Nat. Commun. 2(1), 481 (2011). [CrossRef]
31. N. Verellen, F. López-Tejeira, R. Paniagua-Domínguez, D. Vercruysse, D. Denkova, L. Lagae, P. Van Dorpe, V. V. Moshchalkov, and J. A. Sánchez-Gil, “Mode Parity-Controlled Fano- and Lorentz-like Line Shapes Arising in Plasmonic Nanorods,” Nano Lett. 14(5), 2322–2329 (2014). [CrossRef]
32. N. Verellen, P. Van Dorpe, D. Vercruysse, G. A. E. Vandenbosch, and V. V. Moshchalkov, “Dark and bright localized surface plasmons in nanocrosses,” Opt. Express 19(12), 11034–11051 (2011). [CrossRef]
33. J. D. Jackson, Classical Electrodynamics, 3 ed. (Wiley, 1999).
34. C. A. Balanis, Antenna theory: analysis and design, 3 ed. (Wiley-Interscience, 2005).
35. J. Kim, Y.-G. Roh, S. Cheon, J.-H. Choe, J. Lee, J. Lee, H. Jeong, U. J. Kim, Y. Park, I. Y. Song, Q. H. Park, S. W. Hwang, K. Kim, and C.-W. Lee, “Babinet-Inverted Optical Yagi–Uda Antenna for Unidirectional Radiation to Free Space,” Nano Lett. 14(6), 3072–3078 (2014). [CrossRef]
36. Y. Park, J. Kim, Y.-G. Roh, and Q. H. Park, “Optical slot antennas and their applications to photonic devices,” Nanophotonics 7(10), 1617–1636 (2018). [CrossRef]
37. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]
38. J. Yang, J.-P. Hugonin, and P. Lalanne, “Near-to-Far Field Transformations for Radiative and Guided Waves,” ACS Photonics 3(3), 395–402 (2016). [CrossRef]
39. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, and Z. Gaburro, “Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction,” Science 334(6054), 333–337 (2011). [CrossRef]