# THz Rectennas and Their Design Rules
## 3 Frequency  
Based on their generic structure, rectennas are assumed to collect the radiation energy from the ambient environment. As for the microwave range up to a few hundreds of GHz, there has been tangible progress in many fields. Theoretically, the problem here is usually approached from the antenna theory point of view such that the objective is to optimize the received microwave power and focus the transmitted power when possible. For frequencies above this range, there is usually little control over the radiating object such that the radiation may come out from any object around the rectenna device, be it walls, floor, hot surfaces or maybe visible light. Additionally, the reason for this radiation is just because the object has a temperature above 0 K where the matter particles are agitated, and so, they radiate energy at very high frequencies. It is, therefore, convenient to assume all surrounding objects to follow the black body radiation law. It is out of the scope of this paper to discuss the theoretical details of this physical phenomenon, and the reader may consult [38] for further information about its equation. Figure 4 shows the radiation intensity functionality regardless of the values with respect to wavelength \(\lambda\). As the root locus of the intensity peak shows, when the radiating body temperature rises, the intensity peaks rise in amplitude and shift to the left, which represents an increase in the corresponding frequency \(f\). For a radiating body whose temperature is 7000 K, the intensity has a sharp peak at the highest visible wavelength violet color. Conversely, a 3000 K body has a much lower intensity peak and much wider spectrum, and the peak occurs within the invisible infrared range. While harvesting energy from the sun can be very rewarding based on its high intensity, attempting frequencies as high as 800 THz is quite challenging with the available technology. On the other hand, there are many other sources that provide a good deal of energy at lower temperatures, hence lower radiation frequencies, and have more realistic designs to attempt. For example, the radiated heat from hot surfaces such as those of hot engines, motors, chimneys, etc., is better harvested than being wasted into space, and they are quite abundant. This energy source is usually referred to in the literature as waste heat energy source [16]. Figure 4: Black body radiation law curves for different temperatures. For the highest temperature 7000 K, the intensity peak is high and sharp, while it tends to level out for lower temperatures as for the case of 2000 K.  
Having said that, there have been some challenges such as their wideband nature, as seen in Figure 4, a very low power level that requires very low voltage drop for rectifying diodes, as well as their proximity to the harvesting rectenna in any future design, which in turn may lead to diminishing returns as will be shown in Section 5.2.1. In practical terms, if waste heat sources are assumed to have temperatures around 373 K, their radiation intensity peak will be around 30 THz according to [PERSON]'s radiation formula [38] and the corresponding wave length \(\lambda=10\,\upmu\)m.  
Although increasing the operation frequency opens up a new range for applications, the process is hampered by many challenges. Most importantly, the classical physics approach used for describing charge transition in semiconducting material fails to explain their behavior at extremely high frequencies when the radiation wave oscillates at much higher speeds than those of charge carriers. At these speeds, quantum approaches extend to explain the behavior based on Schrodinger's equation. Equally important is the effect of photo-assisted tunneling [39], which explains the behavior of electrons crossing a potential barrier illuminated by a radiation with frequency \(f\). This effect starts to get noticed even before reaching the 1 THz frequency as stated by [PERSON] et al. [40].