Table of Contents Author Guidelines Submit a Manuscript
International Journal of Antennas and Propagation
Volume 2015, Article ID 589459, 10 pages
http://dx.doi.org/10.1155/2015/589459
Research Article

Equilateral Triangular Dielectric Resonator Nantenna at Optical Frequencies for Energy Harvesting

1KACST Technology Innovation Center in Radio Frequency and Photonics for the e-Society (RFTONICS), King Saud University, Riyadh 11451, Saudi Arabia
2Institute of Electronics and Telecommunications of Rennes University (IETR), University of Rennes 1, 35700 Rennes, France
3Electrical Engineering Department, King Saud University, P.O. Box 800, Riyadh 11421, Saudi Arabia

Received 7 May 2015; Revised 20 August 2015; Accepted 31 August 2015

Academic Editor: Giuseppe Mazzarella

Copyright © 2015 Waleed Tariq Sethi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The last decade has witnessed a remarkable growth in the telecommunication industry. With the introduction of smart gadgets, the demand for high data rate and bandwidth for wireless applications have increased exponentially at the cost of exponential consumption of energy. The latter is pushing the research and industry communities to devise green communication solutions that require the design of energy saving devices and techniques in one part and ambient energy harvesting techniques in the other part. With the advent of nanocomponents fabrication technology, researchers are now able to tap into the THz frequency regime and fabricate optical low profile antennas at a nanoscale. Optical antennas have proved their potential and are revolutionizing a class of novel optical detectors, interconnectors, sensors, and energy harvesting related fields. Authors in this paper propose an equilateral triangular dielectric resonator nantenna (ETDRNA) working at 193.5 THz standard optical frequency. The simulated antenna achieves an impedance bandwidth from 192.3 THz to 197.3 THz with an end-fire directivity of 8.6 dBi, covering the entire standard optical window of C-band. Numerical demonstrations prove the efficiency of the nantenna at the frequencies of interest, making it a viable candidate for future green energy harvesting and high speed optical applications.

1. Introduction

Antennas are found around us in abundance when we are in the midst of communicating either locally or globally via radio frequencies or microwave technologies. Since the inception of classical electromagnetics to the wonders of modern electromagnetism [1], antennas in any size or form have and are still working diligently to uphold their purpose, that is, to convert the electromagnetic energy available in free space into confined electric signals and vice versa. As the telecommunication industry is reaching new technological heights, the demand for energy consumption is also surging, resulting in an increase in environmental problems in the form of carbon emissions [2]. One proposed solution is the concept of “green communication,” which primarily aims at improving the energy efficiency while reducing the CO2 emissions and energy consumption of communication networks [3]. In order to realize this concept, researchers are now persuaded on designing antennas by utilizing the electromagnetic spectrum in the high frequency bands (THz), which fulfills the bandwidth hunger requirements of smart devices, provides low cost designs with high connectivity, and satisfies the consumer needs while keeping the environment clean and energy consumption to a minimum. The antennas designed in the THz regime are given the name of optical antennas.

Optical antennas are a quite new concept in physical optics. They were initially developed for optical microscopic applications. Their basic principle of operation lies in their ability to confine light to subwavelength volumes, plasmonic nanoparticles, and nanoantennas, providing a fundamental link between electronic and photonic circuits by associating the large size mismatch between the electronic and photonic wave functions [4]. Optical antennas have some similarities to their radio frequency (RF) and microwave counterparts, but major differences arise with their physical properties and scalable behaviors. The major difference among the two counterparts is in terms of interaction of electromagnetic waves with metals. This term is known as Plasmon’s at optical frequencies, where the EM waves interact with noble metals, that is, silver, gold, and aluminum, which are not perfect conductors. These noble metals are defined and solved via Drude model equations [5]. Optical antennas have now started to gain popularity among the researchers and scientists. Few years back, optical antennas were not so popular because of limited fabrication techniques and equipment. With the advent of nanoscience and nanotechnology machine fabrication, optical antennas can now be realized to solve the problem of high data rates, wide bandwidth, and environmental problems, that is, CO2 emissions. Also working with antennas at higher frequency bands (THz), the researchers are introduced to an insight to the natural and analytical properties of nanofabrication and nanoantenna designs. Figure 1 shows various fabrication techniques. Interested readers, about these techniques, are referred to the list of pioneering research publications [610]. Apart from fabrication, some of the excitation techniques for optical nantennas can be performed through a coupling of light using the so called nanotapers [11, 12]. Since nanoantennas cannot handle much power because of their small footprints, this makes them ideal candidates for being excited by micro lasers such as micro disks and photonic crystal lasers. Another method of excitation, which outperforms the former micro laser based technique by reducing the reflection induced power loss, exploits slot dielectric waveguides [13]. It is evident that the fabrication of optical antenna structures provides an emerging opportunity for realizing new optoelectronic devices with importance in applications such as photo detection, light emission, sensing, energy harvesting, and spectroscopy.

Figure 1: Various nanoantennas fabricated with different techniques. Source [610].

Analysis of traditional antenna design provides great opportunity for the research industry to design and analyze nanoantennas at optical frequencies. Apart from many designs, keeping in view of wide band characteristics at THz regime, one such design is making use of dielectric resonator antennas (DRAs), firstly proposed and realized in 1939 by Richtmyer, and their modes were first analyzed by Okaya and Barash in the 1960s [14, 15]. DRAs’ physical and electrical properties allow them to be flexible and diversely suited to any communication application. In microwaves, DRAs are nonmetallized dielectric objects normally made of ceramics with high permittivity (relative dielectric constants of the order of 10–300) which are used as resonant cavities for storage of electromagnetic (EM) energy. Compared to metallic antennas, which produce high radiation losses at higher frequencies, DRAs with low loss dielectric materials have some advantages such as high radiation efficiency due to lack of surface waves, small size proportion to wavelength, wide impedance bandwidth, many feeding arrangements, numerous geometries, and different excitation methods with several modes producing broadside or end-fire radiation patterns [1624].

In this paper, drawing inspiration from traditional radio and microwave design [24] and benefiting from DR characteristics, we propose and explore simulated design of an equilateral triangular dielectric resonating nantenna (ETDRNA), for the first time to the best of our knowledge, at optical frequencies. Apart from many applications [9, 10], in this paper, we address the nantenna design for solar energy harvesting application. Since the introduction of the preliminary concept four decades ago, very limited work has been done because of the unavailability of nanomaterial fabrication techniques [2527]. Nowadays, whether nanofabrication progressively became less challenging, the testing, measurement, and characterization of nantennas are still experimentally hard and very expensive. However, these limitations did not stop research community from continuing their work with high frequencies designs using theoretical and numerical modelling and performance investigation [2831]. Keeping with the state of the art, we propose, numerically simulate, and investigate a nantenna consisting of “Ag-SiO2-Ag” structure. The dielectric resonator is made of “Si” having an equilateral triangular shape. The nantenna is excited via a nanostrip transmission line made of a noble metal silver “Ag.” The theory of Drude model is used to analyze and examine the conductive properties of the noble metal “Ag.” It is worthy to note that the proposed nantenna can be operated as a receiving antenna for future green communication systems. The antenna exhibits a wide impedance bandwidth of 2.58% (192.3 THz–197.3 THz) at a center frequency of 193.5 THz, covering the entire standard optical C-band transmission widow. The achieved directivity of the nantenna is 8.6 dBi with end-fire radiation pattern. The obtained results make it a viable candidate for a green-field approach that takes into account the reduction of carbon footprints generated by human activity in the last decade.

2. Proposed Antenna Configuration

The proposed configuration (side view and top view) of the equilateral triangular dielectric resonator nantenna (ETDRNA), designed to operate as a receiving antenna for capturing energy in free space, in the standard optical communication band at a wavelength of 1.55 μm, is shown in Figures 2(a) and 2(b). The corresponding central frequency is 193.5 THz. The dimensions of the simulated antenna consist of a “SiO2” substrate with a thickness of μm, , and loss tangent [32]. The ground plane is on the bottom side with a partial rectangular geometry with optimized dimensions of having a thickness of μm and nanostrip on the top side with a thickness, μm. The ground and the nanostrip are made up of silver (Ag). The dimensions of the substrate are taken as μm2. The equilateral triangular dielectric is made of silicon “Si,” with and estimated loss tangent at 100 THz [33, 34]. The antenna is excited via the 50 Ω silver nanostrip feed that has a width of and optimized length of . In order to control the matching at the central frequency of 193.5 THz and to achieve a wide bandwidth with acceptable radiation patterns the same “SiO2” substrate material with thickness μm has been introduced between the equilateral triangle and the nanostrip. The dimensions of the equilateral triangular dielectric are calculated from the following [23, 24]:where “” is the side length of the equilateral triangular DRA, is the dielectric constant of the DRA, “” is two times the height of the triangular DRA to account for the image effect of the ground plane, and for the fundamental mode [24]. The three integers , , and have a relation of but are not zero simultaneously. For a low-profile triangular DRA, we have , and therefore the following demonstrates that the frequency is predominantly determined by the height of the DRA:where and are the height and dielectric constant of triangular DRA.

Figure 2: (a) Side view of ETDRNA. (b) Top view of ETDRNA with equal side lengths “.”

Since, at optical frequencies, metals appear with a negative permittivity therefore complex permittivity of silver (Ag) was calculated from (3) explained by the Drude model [32]:where  [F/m], , plasmonic frequency  rad/s, = central frequency, and collision frequency . The proposed model has taken into account the conductive and dielectric losses and has been simulated in commercially available EM simulator CST MWS 2014 based on FIT numerical technique using optical template.

3. Parametric Studies

For understanding the role of each geometric design of the proposed dielectric triangular nantenna structure, various parameters were extensively optimized. In order to study the effects on the antenna performance in terms of bandwidth and directivity, the following parameters were studied and analyzed.

3.1. Nanostrip Feed

The silver nanostrip characterized by Drude model was optimized in terms of its length and width. The traditional empirical formulas [1] were used as a starting point for the nanostrip design. The nanostrip acts like a coupling resonator that excites the triangular dielectric place on an upper SiO2 substrate with height . Traditionally at RF frequencies the length of the transmission lines is characterized to the wavelengths () of incoming and outgoing radiations. However working at the optical frequencies, the traditional RF wavelength characteristics scenario no longer applies as the incident waves are not perfectly reflected back from the metal’s surface. Instead, radiation penetrates into the metal giving rise to the excitation of the free electron gas. Hence, at optical frequencies, instead of using the traditional wavelength () we make use of shorter effective wavelength () which depends on the material properties [35, 36] given by the following equation for length of a transmission line [37]:where (4) shows the relationship between the free space wavelength and the effective wavelength and the order of resonance . Here effective wavelength is given byTypical values of have been measured to be in the range of 1.5–3 [38]. In our simulation, for the silver nanostrip design, the selected [39] resulted in the minimum resonating length of the nanostrip being 0.27 μm. The length of the nanostrip was optimized from 0.1 μm to 0.27 μm with the best optimized value producing required resonance at 193.5 THz which was at μm as shown in Figure 3(a). The effect of the width “” of the nanostrip was also examined by extensive parametric studies. Initial values were taken from the empirical formulas [1] and optimization was done from 0.02 μm to 0.28 μm. Figure 3(b) shows the best optimized value achieved at resonance of −22 dB with μm.

Figure 3: Optimized parameters. (a) Length of nanostrip. (b) Width of nanostrip.
3.2. Partial Ground Plane

Effects of the ground plane were studied on the nanoantenna design. Initially a finite ground plane was used to achieve a good radiation pattern with an acceptable bandwidth. The ground plane was then optimized and a partial ground plane was selected with dimensions . Figures 4(a) and 4(b) show the effects of varying the ground plane in terms of its length and width. The optimized results produce a wide impedance bandwidth of 2.5% (192.3 THz–197.3 THz) at a center frequency of 193.5 THz, covering all of the standard optical transmission widow (C-band), with a directivity of 8.6 dB.

Figure 4: Optimized parameters. (a) Length of partial ground. (b) Width of partial ground.
3.3. Height of Triangular DR

Since the height of the triangular DR predominately determines the resonance frequency according to (2), the height of the DR was optimized from 0.1 μm to 0.5 μm. Figure 5 shows the best optimized value of μm having a resonance at −23 dB.

Figure 5: Varied height of triangular DR.
3.4. Rotation of Triangular DR

In order to study the effects of bandwidth, frequency shift, and directivity of the nanoantenna design, the triangular DR was rotated on its axis. The rotation was from 0° to 360° with an angular spacing of 40°. Figure 6 shows the angular rotation of the triangular DR. The tip of the triangle was initially aligned at 0° shown in green color. The DR was then rotated along the counterclockwise direction with varying angles. It was observed that, with the rotation of the DR, the bandwidth remained the same at 2.5% but the resonant frequency shifted to other bands (200 THz–205 THz) in the frequency range from 180 THz to 220 THz as shown in Figure 7(a). Since the triangle is an equilateral one, the angular rotation produces the same shifts at other angles; that is, the shift will be the same at degrees as shown in Figure 7(b). The directivity was also affected with the rotation of the triangle as shown in Figure 7(b). It is clear that the effect of the rotation of the triangular DR lowers the directivity to nearly 3 dBi.

Figure 6: Angular rotation of triangular DR.
Figure 7: (a) Angular rotation effect on resonant frequency. (b) DR’s angular rotation effect on directivity.

After performing the above parametric studies, optimized geometric parameters of the proposed ETDRNA, resulting in a wide impedance bandwidth of 2.5% (192.3 THz–197.3 THz) and a directivity of 8.6 dB, are displayed in Table 1. It was also observed that while keeping the antenna with optimized parameters as listed in Table 1, the simple triangular nantenna structure can act as a tunable resonator when rotated around its axis resulting in usage of applications that work in the wavelengths in the range of 1463 nm–1500 nm. The proposed design, if facility exists, can be fabricated via the techniques mentioned in [610]. In our case, the fabrication will follow a bottom-up approach where the quartz or SiO2 substrate will have silver deposited on its surface.

Table 1: Optimized parameters of ETDRNA.

4. Results

The simulated return loss () and directivity of the nanoantenna are shown in Figure 8. The 3D radiation patterns of the nanoantenna at 192 THz, 193.5 THz, and 197 THz are shown in Figures 9(a)9(c). The ETDRNA exhibits resonance frequency at 193.5 THz (μm) with maximum dip around −22 dB. The antenna covers most part of the S-band and all the portion of the C-band in optical domain and can be used for relevant optical applications in nanonetworks, high speed optical data transfer, and harvesting energy. The directivity of the antenna is 8.6 dBi. Examining the 3D radiation patterns in Figure 9 provides the proof of the ETDRNA radiating in end-fire pattern.

Figure 8: Return loss and directivity of ETDRNA.
Figure 9: (a) 3D end-fire pattern at 192.5 THz. (b) 3D end-fire pattern at 193.5 THz. (c) 3D end-fire pattern at 197 THz.

5. Conclusion

In this paper, we have proposed an equilateral triangular dielectric resonator nantenna for next-generation green communication that could be in the form of solar energy harvesting at the infra-red range and optical wireless charging and for high speed optical communication applications. The nantenna is composed of a “Ag-SiO2-Ag” structure with a nanosilver “Ag” transmission line that excites a triangular dielectric made of “Si” material. The antenna yields a wide impedance bandwidth of 2.58% (192.3 THz–197.3 THz) with a high directive radiation pattern of 8.6 dBi at 193.5 THz (1.55 μm) with an end-fire radiation pattern. At present, the nanofabrication technology is limited and the proposed design is a theoretical one, yet we believe that our contribution in the fast growing field of nantennas, with the proposed ETDRNA design, will prove itself to be a promising candidate for next-generation energy harvesting and green sustainable solution applications based on nanotechnology designs.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgment

This research is supported by King Abdul Aziz City for Science and Technology (KACST) Technology Innovation Center in RF and Photonics for the e-Society (RFTONICS) hosted at King Saud University.

References

  1. C. Balanis, Antenna Theory: Analysis and Design, John Wiley & Sons, New York, NY, USA, 2005.
  2. M. H. Alsharif, R. Nordin, and M. Ismail, “Survey of green radio communications networks: techniques and recent advances,” Journal of Computer Networks and Communications, vol. 2013, Article ID 453893, 13 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  3. T. Kuwashima, K. Sekimoto, K. Kawai et al., “Neutralize CO2 emissions by product contributions,” in Proceedings of the Electronics Goes Green (ECG '12), Beijing, China, September 2012. View at Scopus
  4. G. N. Malheiros-Silveira, L. H. Gabrielli, C. J. Chang-Hasnain, and H. E. Hernandez-Figueroa, “Breakthroughs in photonics 2013: advances in nanoantennas,” IEEE Photonics Journal, vol. 6, no. 2, Article ID 0700706, 2014. View at Publisher · View at Google Scholar
  5. M. Dressel and M. Scheffler, “Verifying the Drude response,” Annalen der Physik, vol. 15, no. 7-8, pp. 535–544, 2006. View at Publisher · View at Google Scholar · View at Scopus
  6. S. H. Choudhury, M. I. Momtaz, and M. A. Matin, “Analytical deduction of the salient properties of a half wavelength J-pole antenna,” in Proceedings of the International Conference on Computational Intelligence and Communication Networks (C/CN '10), pp. 32–35, IEEE, Bhopal, India, November 2010. View at Publisher · View at Google Scholar
  7. A. Alù and N. Engheta, “Hertzian plasmonic nanodimer as an efficient optical nanoantenna,” Physical Review B—Condensed Matter and Materials Physics, vol. 78, no. 19, Article ID 195111, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Rosa, K. Sun, and S. Juodkazis, “Sierpinśki fractal plasmonic nanoantennas,” Physica Status Solidi—Rapid Research Letters, vol. 5, no. 5-6, pp. 175–177, 2011. View at Publisher · View at Google Scholar
  9. L. Novotny and B. Hecht, Principles of Nano-Optics, Cambridge University Press, Cambridge, UK, 2006.
  10. D. Dregely, K. Lindfors, M. Lippitz, N. Engheta, M. Totzeck, and H. Giessen, “Imaging and steering an optical wireless nanoantenna link,” Nature Communications, vol. 5, article 4354, 2014. View at Publisher · View at Google Scholar · View at Scopus
  11. H. T. Hattori, Z. Li, D. Liu, I. D. Rukhlenko, and M. Premaratne, “Coupling of light from microdisk lasers into plasmonic nano-antennas,” Optics Express, vol. 17, no. 23, pp. 20878–20884, 2009. View at Publisher · View at Google Scholar · View at Scopus
  12. Z. Li, H. T. Hattori, L. Fu, H. H. Tan, and C. Jagadish, “Merging photonic wire lasers and nanoantennas,” Journal of Lightwave Technology, vol. 29, no. 18, Article ID 5892863, pp. 2690–2697, 2011. View at Publisher · View at Google Scholar · View at Scopus
  13. H. T. Hattori, Z. Li, and D. Liu, “Driving plasmonic nanoantennas with triangular lasers and slot waveguides,” Applied Optics, vol. 50, no. 16, pp. 2391–2400, 2011. View at Publisher · View at Google Scholar · View at Scopus
  14. R. D. Richtmyer, “Dielectric resonators,” Journal of Applied Physics, vol. 10, no. 6, pp. 391–398, 1939. View at Publisher · View at Google Scholar · View at Scopus
  15. A. Okaya and L. F. Barash, “The dielectric microwave resonator,” Proceedings of the IRE, vol. 50, no. 10, pp. 2081–2092, 1962. View at Publisher · View at Google Scholar
  16. A. Petosa, A. Ittipiboon, Y. M. M. Antar, D. Roscoe, and M. Cuhaci, “Recent advances in dielectric-resonator antenna technology,” IEEE Antennas and Propagation Magazine, vol. 40, no. 3, pp. 35–48, 1998. View at Publisher · View at Google Scholar · View at Scopus
  17. K. M. Luk and K. W. Leung, Dielectric Resonator Antennas, Research Studies Press, Hertfordshire, UK, 2002.
  18. R. K. Mongia and P. Bhartia, “Dielectric resonator antennas—a review and general design relations for resonant frequency and bandwidth,” International Journal of Microwave and Millimeter-Wave Computer-Aided Engineering, vol. 4, no. 3, pp. 230–247, 1994. View at Publisher · View at Google Scholar · View at Scopus
  19. I. E. Hashem, N. H. Rafat, and E. A. Soliman, “Nanocrescent antenna as a transceiver for optical communication systems,” in Proceedings of the IEEE International Symposium on Electromagnetic Compatibility (EMC '14), pp. 39–45, IEEE, Raleigh, NC, USA, August 2014. View at Publisher · View at Google Scholar
  20. M. W. McAllister, S. A. Long, and G. L. Conway, “Rectangular dielectric resonator antenna,” Electronics Letters, vol. 19, no. 6, pp. 218–219, 1983. View at Publisher · View at Google Scholar · View at Scopus
  21. R. K. Mongia, A. Ittipiboon, Y. M. M. Antar, P. Bhartia, and M. Cuhaci, “Half-split cylindrical dielectric resonator antenna using slot-coupling,” IEEE Microwave and Guided Wave Letters, vol. 3, no. 2, pp. 38–39, 1993. View at Publisher · View at Google Scholar · View at Scopus
  22. A. A. Kishk, G. Zhou, and A. W. Glisson, “Analysis of dielectric resonator antennas with emphasis on hemispherical structures,” IEEE Antennas and Propagation Magazine, vol. 36, no. 2, pp. 20–30, 1994. View at Publisher · View at Google Scholar · View at Scopus
  23. H. Y. Lo, K. W. Leung, K. M. Luk, and E. K. N. Yung, “Low profile equilateral-triangular dielectric resonator antenna of very high permittivity,” Electronics Letters, vol. 35, no. 25, pp. 2164–2166, 1999. View at Publisher · View at Google Scholar · View at Scopus
  24. A. A. Kishk, “A triangular dielectric resonator antenna excited by a coaxial probe,” Microwave and Optical Technology Letters, vol. 30, no. 5, pp. 340–341, 2001. View at Publisher · View at Google Scholar · View at Scopus
  25. R. L. Bailey, “A proposed new concept for a solar-energy converter,” Journal of Engineering for Power, vol. 94, no. 2, pp. 73–77, 1972. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Midrio, S. Boscolo, A. Locatelli, D. Modotto, C. De Angelis, and A.-D. Capobianco, “Flared monopole antennas for 10 μm energy harvesting,” in Proceedings of the 13th European Microwave Conference (EuMC '10), pp. 1496–1499, September 2010. View at Scopus
  27. I. Kocakarin and K. Yegin, “Glass superstrate nanoantennas for infrared energy harvesting applications,” International Journal of Antennas and Propagation, vol. 2013, Article ID 245960, 7 pages, 2013. View at Publisher · View at Google Scholar · View at Scopus
  28. D. Sikdar, W. Cheng, and M. Premaratne, “Optically resonant magneto-electric cubic nanoantennas for ultra-directional light scattering,” Journal of Applied Physics, vol. 117, no. 8, Article ID 083101, 2015. View at Publisher · View at Google Scholar
  29. E. Rusak, I. Staude, M. Decker et al., “Hybrid nanoantennas for directional emission enhancement,” Applied Physics Letters, vol. 105, no. 22, Article ID 221109, 2014. View at Publisher · View at Google Scholar · View at Scopus
  30. S.-W. Qu and Z.-P. Nie, “Plasmonic nanopatch array for optical integrated circuit applications,” Scientific Reports, vol. 3, article 3172, 2013. View at Publisher · View at Google Scholar · View at Scopus
  31. F. J. Rodríguez-Fortuño, D. Puerto, A. Griol, L. Bellieres, J. Martí, and A. Martínez, “Sorting linearly polarized photons with a single scatterer,” Optics Letters, vol. 39, no. 6, pp. 1394–1397, 2014. View at Publisher · View at Google Scholar · View at Scopus
  32. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Physical Review B, vol. 6, no. 12, pp. 4370–4379, 1972. View at Publisher · View at Google Scholar · View at Scopus
  33. R. Sinha, M. Karabiyik, C. Al-Amin, P. K. Vabbina, D. Ö. Güney, and N. Pala, “Tunable room temperature THz sources based on nonlinear mixing in a hybrid optical and THz micro-ring resonator,” Scientific Reports, vol. 5, article 9422, 2015. View at Publisher · View at Google Scholar
  34. P. H. Bolivar, M. Brucherseifer, J. G. Rivas et al., “Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies,” IEEE Transactions on Microwave Theory and Techniques, vol. 51, no. 4, pp. 1062–1066, 2003. View at Publisher · View at Google Scholar · View at Scopus
  35. C. Fumeaux, M. A. Gritz, I. Codreanu, W. L. Schaich, F. J. González, and G. D. Boreman, “Measurement of the resonant lengths of infrared dipole antennas,” Infrared Physics & Technology, vol. 41, no. 5, pp. 271–281, 2000. View at Publisher · View at Google Scholar
  36. F. Neubrech, T. Kolb, R. Lovrincic et al., “Resonances of individual metal nanowires in the infrared,” Applied Physics Letters, vol. 89, Article ID 253104, 2006. View at Publisher · View at Google Scholar
  37. R. L. Olmon and M. B. Raschke, “Antenna-load interactions at optical frequencies: impedance matching to quantum systems,” Nanotechnology, vol. 23, no. 44, Article ID 444001, 2012. View at Publisher · View at Google Scholar
  38. F. Neubrech, D. Weber, R. Lovrincic et al., “Resonances of individual lithographic gold nanowires in the infrared,” Applied Physics Letters, vol. 93, no. 16, Article ID 163105, 2008. View at Publisher · View at Google Scholar · View at Scopus
  39. L. Yousefi and A. C. Foster, “Waveguide-fed optical hybrid plasmonic patch nano-antenna,” Optics Express, vol. 20, no. 16, pp. 18326–18335, 2012. View at Publisher · View at Google Scholar · View at Scopus