Open Access
Add to BibSonomy
Abstract
By using transmission-mode, scattering-type scanning near-field optical microscopy, we characterize the mid-infrared near-field properties of a Yagi-Uda antenna in the emission mode. The underlying near-field properties, including the near-field dipole-dipole coupling between antenna elements, are clearly observed. Moreover, even though most of the radiation energy is emitted into the substrate, by adopting two detector antennas, we managed to verify the unidirectionality and frequency-selectivity of the Yagi-Uda antenna in the air side. All the experimental results presented in this work are in good qualitative agreement with our numerical simulations. Our work on the Yagi-Uda antenna could help lead to novel methods for mid-infrared material analysis and bio-sensing. It should also be applicable in all-optical processing like radiation routers or a chromatic discriminator.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Antennas are essential components of all radio equipment and are widely used in communication devices. Recently, optical antennas have become reality through the development of sub-micrometer fabrication techniques, which are capable to convert propagating light into strongly enhanced optical near field in the nanoscale, and vice versa [1, 2]. Applications of optical antennas range in various topics, including beam forming [3], control of hot carriers [4,5], Raman spectroscopy [6], spontaneous emission enhancement and single molecule detection [1,7].
Mid-infrared radiation has a variety applications in material analysis [8,9] and nondestructive bio-sensing [10]. As to bio-sensing, mid-infrared radiation (2.5 to 50 μm) interacts poorly with molecules (< 10 nm) because of the large size mismatch. It is impossible to focus mid-infrared radiation into 10 nm scale by traditional methods due to the diffraction limit. Surface waves in the mid-infrared regime like surface phonon polaritions (SPhPs) [11] or graphene plasmons (GPs) [12–16] offer nanometer-scale confinement and strong field enhancement, which can overcome this obstacle and increase sensitivity of detection for both bio-sensing as well as material analysis. SPhPs [17,18] and GPs [19] have already been successfully excited via optical antennas in the mid-infrared regime, which can further be employed for both bio-sensing and material analysis.
In addition to the field enhancement, optical antenna is appealing for its ability to control the radiation direction. For instance, if all the signals propagate directly to the detector instead of dispersing in all directions, the sensitivity of detection would be increased. Optical Yagi-Uda antenna, inspired by the well-established designs for radio-frequencies, has received increasing attention in recent years [20–27]. Optical Yagi-Uda antenna can achieve a high directivity through placing several parasitic elements around a resonant feed element. Because of the differences in antenna lengths, the director (the shorter elements) couples capacitively to the feed element and the reflector (the longer elements) couples inductively to the feed element. The consequent strong near-field interaction of all elements leads to a high directivity in emission. Miscuglio et al. proposed that Yagi-Uda antenna could lead to a strong coupling and allow for directional propagation for GPs from numerical simulations [28].
Previous studies on Yagi-Uda antenna are mostly limited to the far-field properties in the visible or near-infrared range. To the best of our knowledge, Yagi-Uda antenna has never been experimentally studied about the near-field properties in the mid-infrared regime. Hence, little is yet known as to the nature of the underlying near-field properties, especially in the mid-infrared range. Dorfmüllerthe et al. measured the near-field properties of optical Yagi-Uda antenna in the receiving mode [24]. The directivity of antennas is manifested indirectly by local field enhancement at the feed element, which is dependent on the illumination direction. However, due to the limitation of their setup, only the near field of a fixed incident angle was measured. Besides, according to the Stokes relations [29], the receiving mode is not the reversal of the emission mode, which cannot reveal the near-field feature of Yagi-Uda antenna in the emission mode. Therefore, it is very necessary to study Yagi-Uda antenna in the emission mode. In this work, we aim to fill the gap of direct characterizing the near-field properties of the Yagi-Uda antenna in the emission mode at the mid-infrared regime.
2. Measurement principle and experimental setup
Using a transmission-mode scattering-type scanning near-field optical microscopy (s-SNOM, neaSNOM from neaspec GmbH), amplitude and phase images of the near field of the antenna were recorded as illustrated in Fig. 1. We used a metal-covered silicon tip to obtain a high signal-to-noise ratio [30,31]. All the parasitic elements were aligned along the y-direction, and the feed element was tilted by 45° with respect to the parasitic elements. A laser beam with a polarization along the x-direction was illuminated from below the substrate, thus allowing for exciting the dipole mode of the feed antenna while avoiding the excitation of the tip. During the scanning, the near-field of the antenna was scattered by the tip. A parabolic mirror on top of the substrate collected the scattered field and directed it toward a detector. An interfering reference beam spatially overlapped with this scattering field at the detector, yielding both the amplitude and phase via pseudoheterodyne detection. The polarization of the reference beam was parallel to the tip axis to probe the z-component of the near fields. In our experiment, the AFM tip vertically vibrated at a frequency Ω=69 kHz and with an amplitude of 60 nm. The oscillating mirror vibrated at a frequency M=298 Hz.
Fig. 1 Schematic setup of a transmission-mode scattering-type near-field optical microscopy. An x-polarized laser beam illuminates the antennas from the bottom of the CaF2 substrate. The near fields of the antennas excited by the incident laser are scattered by an AFM tip and then detected interferometrically with a reference beam, yielding amplitude and phase images of the near-fields.
3. Directivity
The angular dependence of the emission is quantified by the expression of directivity
where P(θ, ϕ) is the angular radiated power and the integral is over all solid angle. It is obvious that an isotropic radiator has a directivity of 1. In this work, the directivity and the calculated near-field maps were simulated using the finite element methods (FEM) in the commercially available software package COMSOL MULTIPHYSICS. All the dielectric values were interpolated from the well-known optical handbook by Palik [32]. Considering the total radiated power as well as the directivity, parameters are carefully chosen for the three-element Yagi-Uda antenna as: All the antenna have a thickness of 50 nm. The feed element with a width of 600 nm and a length of 3.10 μm is tilted 45° with respect to the x-axis. A director element with a width of 600 nm and a length of 2.43 μm is aligned 2.33 μm away from the feed element on the left side and a reflector element with a width of 600 nm and a length of 3.37 μm is aligned 2.11 μm away on the right side. The total far-field radiation power spectra of three-element Yagi-Uda antenna (director-feed-reflector, dfr, blue solid line) and five-element Yagi-Uda antenna (dddfr, red dashed line) are shown in Fig. 2(a), in which dddfr has two more directors on the left side of the feed element with the same gap distance. It can be seen that the total radiated power of dfr and dddfr are very close. For comparison, The power emitted at 9.3 μm is around 1.4 times larger than that at 10.5 μm. Figure 2(b) shows the maximal directivity spectra of dfr and dddfr. The directivity of dddfr has a peak value of 6.54 at 8.4 μm. It is around 5.55 at 9.3 μm for both dfr and dddfr. Since we usually compare the directivity in the x − y plane, the maximal directivity value in the x − y plane is plotted in Fig. 2(c). Because dddfr has two more directors, its directivity value is obviously larger than that of dfr in this case. Take the directivity at 9.3 μm for example, it is 2.29 for dddfr, 1.41 times larger than that of dfr at the same wavelength, which makes the unidirectionality of dddfr in the x − y plane more significant. The two extra directors change the resonance of the Yagi-Uda antenna and help to reshape the radiation pattern to increase the directivity in the x − y plane.Fig. 2 (a) The total radiated power of three-element Yagi-Uda antenna (solid blue line, director-feed-reflector, dfr) and five-element Yagi-Uda antenna (dashed red line, dddfr). (b) and (c) depict the maximal directivity of dfr and dddfr in the whole space and in the x − y plane, respectively.
Figure 3(a) shows the spacial distribution of numerically calculated D(θ, ϕ) of a single feed element on the CaF2 substrate illuminated by a laser with wavelength of 9.3 μm. When an x-polarized laser beam illuminates on the feed element, the feed element responses as a dipole antenna and emits optical energy equally perpendicular to its length and mainly into the substrate [33]. The structural parameters of the feed element are the same as in Fig. 2. The maximal directivity is calculated as 3.89. Figure 3(b) shows the directivity of the dfr as described in Fig. 2. In this case, if the incident light is x-polarized, both the reflector and director antennas cannot be excited by the incident light directly because of the perpendicular alignment. On the contrary, the feed element converts a part of the incident light into light polarized along the y-direction owing to its diagonal alignment. Then, this y-direction polarized light will induce the antenna modes of the director and the reflector through dipole-dipole coupling. Hence, besides a small lobe on the right side of the feed element, the total emission is highly directed to the left side due to the resonance between each element.
Fig. 3 (a) and (b) show the simulated directivities of a single feed element and a three-element Yagi-Uda antenna (director-feed-reflector, dfr) under 9.3 μm wavelength illumination, respectively. The emission is equally distributed on the left and right sides of a single feed element while strongly directed to the left side of the dfr. (c) and (d) depict the directivities of a single feed element, dfr and a five-element Yagi-Uda antenna (dddfr) at 9.3 μm in the x − z and x − y plane, respectively. The directivity of the dfr at 10.5 μm is plotted to present the frequency selectivity.
Figure 3(c) plots the directivity in the x − z plane of Fig. 3(a) for a single feed element (red dashed line) and Fig. 3(b) for a dfr (blue dot dashed line) at 9.3 μm. For comparison, the directivity of dddfr excited at the wavelength of 9.3 μm (magenta dotted line) and dfr excited at the wavelength of 10.5 μm (black solid line) are also plotted out, where z = 0 is the air-substrate interface. It should be noted that the directivity is related to the space angle. For instance, the maximal directivity of dfr in the x − z plane is 4.50, as a comparison of 5.55 in the whole space. The directivity of a dddfr, with a maximal value of 4.95 in the x − z plane, is 1.10 times larger than that of a dfr in the x − z plane, and is about two times larger than that for a single feed antenna at 9.3 μm in the x − z plane. Meanwhile, the maximal directivity of a dfr at 10.5 μm is only 2.65 in the x − z plane, 1.70 times smaller than that of a dfr at 9.3 μm in the x − z plane, which indicates the frequency selectivity of the Yagi-Uda antenna. This frequency selectivity originates from the strict requirement of the interference between each resonant element. Similarly, the directivity in the x − y plane at z = 0 is shown in Fig. 3(d). Because most of the optical energy penetrates into the substrate, the directivity in the x − y plane is smaller than a half of that in the x − z plane.
4. Near-field properties of Yagi-Uda antenna in the emission mode
Our Yagi-Uda antanna structures were fabricated by means of focused ion beam (FIB) in a 50 nm gold layer on a CaF2 substrate. The structures were imaged with the transmission-mode s-SNOM. We first characterize the near field feature of a single feed antenna as shown in Fig. 4. The feed antenna has the same structure that was simulated in Fig. 3 and the schematic is shown in the inset in Fig. 3(a). Two detector antennas with the same dimensions, 120 nm in width and 3 μm in length, were aligned along the y direction and positioned on the left and right sides of the feed antenna with a distance of 6 μm, respectively. The corresponding AFM topography is shown in Fig. 4(a). Figure 4(b) shows the experimental images of the real part of the vertical near-field component Re(Ez)=|Ez|cosφz, where |Ez| is the amplitude and φz is the phase. This near-field of the feed antenna shows a typical dipolar pattern, where a phase jump occurs at the center. Since the incident light was polarized along the x-axis, the detector antennas could only be excited by the emission of the feed antenna rather than the incident light. Line-profiles of |Ez| along the y-direction of two detector antennas are plotted in Fig. 4(c). It can bee seen that the distributions of |Ez| in the left and right detector antennas are very similar, which means that the optical energy emitted from the feed element is equally on both sides. The numerically calculated Re(Ez), presented in Fig. 4(d), agrees well with the experimental result.
Fig. 4 Near field of a feed antenna and two nearby detector antennas measured by a transmission-mode s-SNOM at 9.3 μm. (a) The AFM topography. (b) Experimental near-field images showing Re(Ez)=|Ez |cosφz. (c) Line-profiles of |Ez| along the detector antennas. (d) FEM calculated near-field Re(Ez).
We then extended the measurement to three element Yagi-Uda antennas, which structure is shown in the inset of Fig. 3(b). The design of the structure was optimized in terms of both directivity and radiated power at the wavelength of 9.3 μm. Like the single feed antenna, two detector antennas along the y-direction were aligned nearby to verify the unidirectional emission of the Yagi-Uda antenna. The distance between the detector antenna and the the feed is 6 μm. We first verify the the unidirectionality in Fig. 5(a)–5(d). In addition to the dipole pattern of near field on the feed antenna, the s-SNOM images of near field in Fig. 5(b) presents a clear dipole-dipole coupling between the feed element and other parasitic elements. We plotted the line profiles of |Ez| along two detector antennas in Fig. 5(c) to validate the unidirectionality. This configuration does not clearly show the preferential emission towards either direction until the separation of the detector elements is reduced to be 4 μm as in in Fig. 5(e)–5(k).
Fig. 5 Verification of the unidirectionality of three-element Yagi-Uda antennas. (a)–(d) The distance between the detector antennas and the feed is 6 μm. (a) and (e) Topography images of three-element Yagi-Uda antennas. (e)–(k) The distance between the detector antennas and the feed is 4 μm. (b), (f) and (i) s-SNOM image of the near-field. (c), (g) and (j) Line-profiles of |Ez | along the detector antennas. (d), (h) and (k) Numerically calculated near-field images.
Similar to Fig. 5(b), Fig. 5(f) exhibits obvious near field of dipole pattern on the feed element and a strong coupling between the feed and parasitic elements. The cross-section values of |Ez| are compared in Fig. 5(g) for two detector antennas. The maximal |Ez| in the left detector antenna is 1.84 times larger than that in the right side. In comparison with Fig. 5(c), by decreasing the detecting distance, the difference in |Ez| between two detector antennas are more pronounced. This is because the direction for the peak directivity is not directly towards the detector elements but much of it is leaked into the substrate. Furthermore, we illuminated the same structure at 10.5 μm to verify the frequency-selectivity. As shown in Fig. 5(i), though the near field of the dipole mode on the feed element is still clear, near-field pattern on the parasitic elements was detected with low signal-to-noise ratio. The reason is that the coupling between the feed and the other parasitic elements was weak. Maximal values of |Ez| in the left and right detector antenna are very close, which means that the unidirectionality of Yagi Uda antenna has frequency-selectivity.
All the experimental results matched well with numerical simulations in Fig. 5(d), 5(h) and 5(k). It should be noted that we observed a better match between the experimental and simulation results in the Yagi-Uda antenna than that in the detector antennas. This mismatch might result from a lack of considering the tip in our simulations. Some inevitable background noise can also cause this problem. The near field of the dipole modes in the detector are weak because they are excited by the Yagi-Uda antenna rather than the incident light directly. The signal-to-noise ratio of the near field in the detector antennas is lower than that in the Yagi-Uda antenna elements.
As we have shown in Fig. 3(d), the directivity of dddfr in the x − y plane is larger than that of dfr. In Fig. 6(a), we characterized the unidirectionality of dddfr. Two detector antennas were positioned 12 μm away from the feed antenna on both left and right side. Similar to the results of dfr, the measured near-field in Fig. 6(b) shows the dipole mode pattern on the feed element and the dipole-dipole coupling between feed and parasitic elements. Due to the constructive interference, the leftmost director is still strongly coupled and presents near field with high intensity. In order to validate the unidirectionality, Fig. 6(c) compares line-profiles of |Ez| along two detector antennas. The maximal |Ez| fields on the left and right detectors are not significantly different at this distance. When we test the dddfr that has two detector antennas located 8 μm away from the feed as shown in Fig. 6(e)–6(h), the ratio of the maximal |Ez| between the left and right detector antennas is 1.72. The ratios of |Ez| between the left and right detector antennas in the dddfr, with two detector antennas located 12 μm or 8 μm from the feed element, are larger than that in dfr with two detectors located 6 μm away, which agrees well with the simulation results in Fig. 2(c) and Fig. 3(d).
Fig. 6 Verification of the unidirectionality of dddfr. (a)–(d) The distance between the feed and detector antenna is 12 μm. (e)–(k) The distance between the feed and the detectros is 8 μm. (a) and (e) Topography images of five-element Yagi-Uda antennas. (b), (f) and (i) Experimental near-field images. (c), (g) and (j) Line-profiles of |Ez | along the detector antennas. (d), (h) and (k) Numerically calculated near-field images. .
In the end, Fig. 6(i) and 6(j) present the results when the sample was illuminated by the wavelength of 10.5 μm. The near-field intensity in the parasitic elements is weak compared to that excited with wavelength of 9.3 μm. Little difference in the maximal |Ez| between the left and right detector antenna in Fig. 6(j) reveals the frequency-selectivity of Yagi-Uda antenna as well. All the experimental results were confirmed by numerical simulations in Fig. 6(d), 6(h) and 6(k).
5. Discussion
In our experiment, a single Yagi-Uda antenna was measured for the directivity. To achieve higher directivity, an array of Yagi-Uda antennas can be used [26]. Moreover, through integrating with graphene or both polar and doped semiconductor layers (e.g., SiC, InP, GaAs and others), Yagi-Uda antenna can potentially excite high directional GPs, SPhPs and hot carriers. Besides, since most of the optical energy emitted by Yagi-Uda antenna penetrates into the substrate, which reduces the optical energy utilization efficiency and limits its further applications, those metal-like layers might act as mirrors to reflect optical energy out of the substrate, hence enhancing the directivity in the upper air side.
6. Conclusion
In this work, near field patterns of Yagi-Uda antenna were measured experimentally via transmission-mode s-SNOM. Our results presented the near field of typical dipolar patterns on the feed element and the dipole-dipole coupling between the feed and other parasitic elements of Yagi-Uda antenna in the emission mode. By comparing the difference of |Ez| between two detector antennas, the unidirectionality as well as the frequency-selectivity was confirmed. We also experimentally demonstrated that a five-element Yagi-Uda antenna had a larger directivity than that of a three-element one. Our work demonstrates that Yagi-Uda antenna has the ability to control the direction of mid-infrared radiation. It can also potentially excite high directional GPs and SPhPs with better confinement and field enhancement in the mid-infrared range, which paves the way for highly sensitive mid-infrared material analysis and bio-sensing.
Funding
National Key R&D Program of China (2017YFA0305100, 2017YFA0303800); National Natural Science Foundation of China (91750204, 11774185, 11504184, 61775106, 11711530205); Changjiang Scholars and Innovative Research Team in University (IRT13_R29); the 111 Project (B07013); Tianjin Natural Science Foundation (18JCQNJC02100); Fundamental Research Funds for the Central Universities.
Acknowledgments
Y. X. would like to thank Dr. Cuifeng Ying for insightful discussion.
Disclosures
Competing financial interests: The authors declare the following competing financial interest(s): S.A. is a senior application engineer of neaspec GmbH, a company producing scattering-type scanning near-field optical microscope systems, such as the one used in this study. All other authors declare no competing financial interests.
References
1. P. Mühlschlegel, H.-J. Eisler, O. Martin, B. Hecht, and D. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005). [CrossRef] [PubMed]
2. M. Agio and A. Alù, Optical antennas (Cambridge University Press, 2013).
3. 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, 333–337 (2011). [CrossRef] [PubMed]
4. M. W. Knight, H. Sobhani, P. Nordlander, and N. J. Halas, “Photodetection with active optical antennas,” Science 332, 702–704 (2011). [CrossRef] [PubMed]
5. M. L. Brongersma, N. J. Halas, and P. Nordlander, “Plasmon-induced hot carrier science and technology,” Nature Nanotech. 10, 25–34 (2015). [CrossRef]
6. A. Ahmed and R. Gordon, “Directivity enhanced raman spectroscopy using nanoantennas,” Nano Lett. 11, 1800–1803 (2011). [CrossRef] [PubMed]
7. T. Taminiau, F. Stefani, F. Segerink, and N. Van Hulst, “Optical antennas direct single-molecule emission,” Nature Photon. 2, 234–237 (2008). [CrossRef]
8. A. Gutberlet, G. Schwaab, Ö. Birer, M. Masia, A. Kaczmarek, H. Forbert, M. Havenith, and D. Marx, “Aggregation-induced dissociation of hcl (h2o) 4 below 1 k: the smallest droplet of acid,” Science 324, 1545–1548 (2009). [CrossRef] [PubMed]
9. Z. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, and D. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,” Nature Phys. 4, 532–535 (2008). [CrossRef]
10. P. R. Griffiths and J. A. De Haseth, Fourier transform infrared spectrometry, vol. 171 (John Wiley & Sons, 2007). [CrossRef]
11. R. Hillenbrand, T. Taubner, and F. Keilmann, “Phonon-enhanced light–matter interaction at the nanometre scale,” Nature 418, 159–162 (2002). [CrossRef] [PubMed]
12. F. Koppens, D. Chang, and F. García de Abajo, “Graphene plasmonics: a platform for strong light-matter interactions,” Nano Lett. 11, 3370–3377 (2011). [CrossRef] [PubMed]
13. A. Y. Nikitin, P. Alonso-González, and R. Hillenbrand, “Efficient coupling of light to graphene plasmons by compressing surface polaritons with tapered bulk materials,” Nano Lett. 14, 2896 (2014). [CrossRef] [PubMed]
14. D. Rodrigo, O. Limaj, D. Janner, D. Etezadi, F. J. G. de Abajo, V. Pruneri, and H. Altug, “Mid-infrared plasmonic biosensing with graphene,” Science 349, 165–168 (2015). [CrossRef] [PubMed]
15. W. Luo, W. Cai, Y. Xiang, W. Wu, B. Shi, X. Jiang, N. Zhang, M. Ren, X. Zhang, and J. Xu, “In-plane electrical connectivity and near-field concentration of isolated graphene resonators realized by ion beams,” Adv. Mater. 29, 1701083 (2017). [CrossRef]
16. X. Jiang, W. Cai, W. Luo, Y. Xiang, N. Zhang, M. Ren, X. Zhang, and J. Xu, “Near-field imaging of graphene triangles patterned by helium ion lithography,” Nanotechnology 29, 385205 (2018). [CrossRef] [PubMed]
17. A. Huber, B. Deutsch, L. Novotny, and R. Hillenbrand, “Focusing of surface phonon polaritons,” Appl. Phys. Lett. 92, 203104 (2008). [CrossRef]
18. A. Huber, N. Ocelic, and R. Hillenbrand, “Local excitation and interference of surface phonon polaritons studied by near-field infrared microscopy,” J. Microsc. 229, 389–395 (2008). [CrossRef] [PubMed]
19. P. Alonso-González, A. Y. Nikitin, F. Golmar, A. Centeno, A. Pesquera, S. Vélez, J. Chen, G. Navickaite, F. Koppens, A. Zurutuza, F. Casanova, L. Hueso, and R. Hillenbrand, “Controlling graphene plasmons with resonant metal antennas and spatial conductivity patterns,” Science 344, 1369–1373 (2014). [CrossRef] [PubMed]
20. T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Enhanced directional excitation and emission of single emitters by a nano-optical yagi-uda antenna,” Opt. Express 16, 10858–10866 (2008). [CrossRef] [PubMed]
21. T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical yagi–uda antenna,” Nature Photon. 4, 312–315 (2010). [CrossRef]
22. 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, 930–933 (2010). [CrossRef] [PubMed]
23. 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, 3779–3784 (2011). [CrossRef] [PubMed]
24. J. Dorfmuller, D. Dregely, M. Esslinger, W. Khunsin, R. Vogelgesang, K. Kern, and H. Giessen, “Near-field dynamics of optical yagi-uda nanoantennas,” Nano Lett. 11, 2819–2824 (2011). [CrossRef] [PubMed]
25. A. E. Krasnok, A. E. Miroshnichenko, P. A. Belov, and Y. S. Kivshar, “All-dielectric optical nanoantennas,” Opt. Express 20, 20599–20604 (2012). [CrossRef] [PubMed]
26. D. Dregely, R. Taubert, J. Dorfmüller, R. Vogelgesang, K. Kern, and H. Giessen, “3d optical yagi-uda nanoantenna array,” Nature Commun. 2, 267 (2011). [CrossRef]
27. J. Kim, Y. G. Roh, S. Cheon, J. H. Choe, J. Lee, J. Lee, H. Jeong, U. J. Kim, Y. Park, and I. Y. Song, “Babinet-inverted optical yagi–Uda antenna for unidirectional radiation to free space,” Nano Lett. 14, 3072–3078 (2014). [CrossRef] [PubMed]
28. M. Miscuglio, D. Spirito, R. P. Zaccaria, and R. Krahne, “Shape approaches for enhancing plasmon propagation in graphene,” ACS Photonics 3, 2170–2175 (2016). [CrossRef]
29. E. Hecht, Optics (Addison Wesley, 1997).
30. A. C. Jones, R. L. Olmon, S. E. Skrabalak, B. J. Wiley, Y. N. Xia, and M. B. Raschke, “Mid-IR plasmonics: near-field imaging of coherent plasmon modes of silver nanowires,” Nano Lett. 9, 2553–2558 (2009). [CrossRef] [PubMed]
31. A. Andryieuski, V. Zenin, R. Malureanu, V. Volkov, S. Bozhevolnyi, and A. Lavrinenko, “Direct characterization of plasmonic slot waveguides and nanocouplers,” Nano Lett. 14, 3925 (2014). [CrossRef] [PubMed]
32. E. D. Palik, Handbook of optical constants of solids, vol. 3 (Academic press, 1998).
33. L. Novotny and B. Hecht, Principles of nano-optics (Cambridge University Press, 2012). [CrossRef]
