IEEE TRANSACTIONS ON NANOTECHNOLOGY, VOL. 13, NO. 4, JULY 2014 767 Dipole Nantennas Terminated by Traveling Wave Rectiﬁers for Ambient Thermal Energy Harvesting Islam E. Hashem, Student Member, IEEE, Nadia H. Rafat, Senior Member, IEEE, and Ezzeldin A. Soliman, Senior Member, IEEE Abstract—In this paper, rectennas formed from nanodipole an- tennas terminated by plasmonic metal–insulator–metal (MIM) travelling wave transmission line rectiﬁers are developed for ambient thermal energy harvesting at 30 THz. The transmission lines are formed from two strips coupled either vertically or lat- erally. A systematic design approach is presented, that shows how different components can be integrated with each other with max- imum radiation receiving nantenna efﬁciency, maximum coupling efﬁciency between nantenna and rectiﬁer, and maximum MIM diode rectiﬁer efﬁciency. The tunneling current of the rectiﬁer is calculated using the transfer matrix method and the nonequilib- rium Green’s function. A detailed parametric study of the coupled strips plasmonic transmission lines is presented and thoroughly discussed. The overall efﬁciencies of the proposed travelling wave rectennas are fully expressed and compared. Index Terms—MIM, nantennas, plasmonics, rectennas, trans- mission lines, tunneling. I. INTRODUCTION T HE spectrum of the Sun that reaches the Earth can be divided into three main parts [1], [2]: ultraviolet (9%), vis- ible (39%), and infrared (52%), where the bracketed quantities represent the approximate percentage of each frequency range from the power density received. Part of the power density of the solar radiation that reaches the atmosphere is absorbed or reﬂected back and the remaining is reradiated in the long wave- length infrared range (LWIR), 7 μm < λ < 14 μm, with peak at 10 μm (30 THz). Recent advances in the fabrication technology permit the fab- rication of nanoscale devices with reasonable precision due to the development of fabrication tools like electron beam lithogra- phy (EBL) and atomic layer deposition (ALD). Hence, the idea Manuscript received August 15, 2013; revised April 8, 2014; accepted April 21, 2014. Date of publication April 29, 2014; date of current version July 2, 2014. The review of this paper was arranged by Associate Editor M. De Vittorio. I. E. Hashem is with the Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza 12613, Egypt, and also with the Youssef Jameeel Science and Technology Research Center, The American Uni- versity of Cairo, Cairo 11835, Egypt (e-mail: eemm_hashem@ieee.org). N. H. Rafat is with the Department of Engineering Mathematics and Physics, Faculty of Engineering, Cairo University, Giza 12613, Egypt (e-mail: nhrafat@ieee.org). E. A. Soliman is with the Department of Physics, School of Sciences and Engineering, American University of Cairo, Cairo 11835, Egypt (e-mail: esoliman@aucegypt.edu). Color versions of one or more of the ﬁgures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identiﬁer 10.1109/TNANO.2014.2320513 proposed by Bailey in 1972 to harvest energy using rectennas, rectifying antennas, becomes applicable [3], [4]. The rectenna is made up of a nanoantenna, nantenna, coupled to a rectiﬁer. Research in nantennas is still in the exploration phase. Various nantenna conﬁgurations have been proposed in the literature re- cently, such as monopoles [5], dipoles [6]–[11], bowties [6]–[8], [12], fractal bowties [13], [14], spirals [15]–[18], Yagi-Uda [19]–[22], nanoring [23], nanowires [24], [25], and nanocre- scents [26]–[29], [30]. For the rectiﬁer, extensive research has been done recently in order to explore the ﬁgures of merit of the metal–insulator–metal (MIM) diodes and the parameters affect- ing them [31]–[33]. The thickness of the insulator layer in the MIM diode should be kept less than 4 nm in order to ensure that the tunneling current is the main transport phenomenon [34]. Unfortunately, the ﬁgures of merit of this device are unaccept- able if a single insulator layer is used. These merits can be slightly improved by adding another insulator layer [31], [33]. The research in integrating the MIM rectiﬁer to the nantenna in order to maximize the coupling efﬁciency between them is still under development [2], [35], [36]. In order to maximize the total efﬁciency of the rectenna, the coupling, or matching, efﬁciency between the nantenna and the rectiﬁer has to be maximized. Mainly, there are two alter- natives for the MIM rectenna: the localized [37] and the dis- tributed [38] ones. The localized rectiﬁer can be modeled as a parallel combination of a resistance and a capacitance, while a transmission line characteristic impedance can represent the distributed rectiﬁer. Hence, the distributed rectiﬁer is often re- ferred to as the traveling wave rectiﬁer (TWR). The localized rectiﬁer shows poor coupling efﬁciency due to the high diode resistance, which makes its conjugate matching with the nan- tenna input impedance very difﬁcult [39]. On the other hand, the characteristic impedance of the TWR is in the same order of magnitude as the nantenna input resistance, which leads to a much better matching [38]. In this paper, we focus on developing a rectenna operating in the LWIR range and on how to maximize the coupling ef- ﬁciency between the nantenna and rectiﬁer. The focus is on nanodipoles integrated with MIM plasmonic waveguides. Two traveling wave MIM plasmonic waveguides are considered, namely; vertical coupled strips (VCS) and lateral coupled strips (LCS) transmission lines. Due to the fabrication technology limitations, big difference is expected between the vertical and lateral dielectric spacing that isolates the two metallic sides of the transmission line. This spacing can go down to 2 nm for the VCS case, while a 20-nm spacing is possible for the LCS case. This results in huge difference between the overall efﬁciency of 1536-125X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information.