# THz Rectennas and Their Design Rules
## 2 Historical Notes
### Targeting Higher Frequencies  
The aforementioned efficiencies in Section 2.2 provide a good reason as to why rectennas might be favored over p-n junction solar cells. The experimentally-achievable efficiency is at least two-times that of the widespread solar cells. Moreover, their fabrication costs are generally less expensive. However, increasing the frequency into the THz range leads to many limitations. It is well known that the AC signal wavelength \(\lambda\) is inversely proportional to the oscillation frequency \(f\) such that  
Figure 2: Generic circuit diagram for a rectenna system (Adapted with permission from [16], [PERSON], 2013). fabricating the circuit components, be it antennas, filters, transmission lines or rectifiers, can be very challenging with dimensions in the \(\upmu\)m range or even less. In addition to that is the onset of the lossy nature of metals and insulators, equally, at frequencies close to the visible range when their plasmonic features are not exploited [21]. To the authors' best of knowledge, there has been no attempt to implement a matching circuit for a rectenna system in the THz range. It might be beneficial at this point to consider that THz rectennas are made up of two main parts as shown in Figure 2, that is the micro- or nano-scale antenna, often referred to in the literature as a nantenna [22] and the rectifier diode. This separation is helpful in terms of tracking the research progress of both parts. **Antennas** used with rectennas have witnessed major progress thanks to computer modeling that facilitated the prototyping and analyzing process. Today, many free and licensed computer-aided design (CAD) packages are available and provide in-depth analysis of antenna models. Many prototypes have been built and tested in a real environment at 1-THz frequencies and above [23; 24]; [PERSON] et al. [25] have modeled a 84-THz antenna array. **Rectifiers**, on the other hand, still have many challenges to efficiently function as energy harvesting devices in the THz range. Power efficiency figures are still very low to compete with those of regular solar cells. In 2003, [PERSON] [5] noted in his technical report many reasons for not achieving high efficiency. He attributes the poor figures to weak antenna-wave coupling, mismatch between the diode and the antenna, the semi linear \(I(V)\) curve of the rectifying diode and the difficulty to accurately reproduce the diode prototype, which would lead to unpredictable results. Interestingly, many researchers are working to optimize the design of the rectenna system using different diode types without much detail about the difference between them. Moreover, there is more than one theory to explain the output of rectenna devices. For example, while tunneling is assumed to be the reason for the resulting current response of a rectenna diode in the [PERSON] and [PERSON] model [26], [PERSON] et al. [27] try to explain the behavior of the rectenna device based on thermocoupling between both antenna branches. [PERSON] et al. [28] attempted a rigorous approach trying to explain the studied diode behavior assuming a composite behavior of thermal and tunneling effects [28]. In order to address and prioritize the factors for not reaching an efficient THz rectenna system, [PERSON] and [PERSON] [26] proposed the following efficiency Equation (1), such that the overall rectenna system efficiency is formed by four terms. While it is a conceptual equation, it helps having an in-depth understanding of the possible reasons of the poor efficiency figures of the recent rectenna trials:  
\[\eta=\eta_{a}.\eta_{s}.\eta_{c}.\eta_{j}, \tag{1}\]  
where \(\eta_{a}\) represents the coupling efficiency of the antenna with the impinging electromagnetic wave. \(\eta_{s}\) stands for the antenna efficiency. In other words, it represents the ratio of the delivered energy to the successive parts with respect to the energy already captured by the antenna. The ratio \(\eta_{c}\) represents the coupling efficiency between the antenna and the diode.