## 2 Quasi-optical Design of the MMW Channel, Calculations and Alignment
The focal lengths of both dishes are also fixed and can't be altered and are equal to \(F_{dish}=600\) mm. The approximate beam waist can be calculated for a given position in the quasi optical setup shown in Figure 1, using the transformation of the complex beam parameter q\({}_{1}\) at the output of the MMW source (\(W=6.2\) mm and \(R=\infty\)) by the ABCD transfer matrix for paraxial rays. The complex beam parameter q\({}_{2}\) can then be calculated at that given position using Equation (4). Knowing the complex beam parameter q\({}_{2}\) can allow the calculation of the beam waist W and the beam radius of curvature \(R\) at that given position using Equation (5). The parameters in Equation (3) are as follows:  
\[\left[ \begin{array}{cc}A&B\\ C&D\end{array} \right]=\left[ \begin{array}{cc}1&d_{3}\\ 0&1\end{array} \right]\left[ \begin{array}{cc}1&0\\ -1/F_{dish}&1\end{array} \right]\left[ \begin{array}{cc}1&d_{2}\\ 0&1\end{array} \right]\left[ \begin{array}{cc}1&0\\ -1/F_{dish}&1\end{array} \right]\left[ \begin{array}{cc}1&d_{1}\\ 0&1\end{array} \right] \tag{3}\]  
\[q_{2}=\frac{\text{Aq}_{1}+\text{B}}{\text{Cq}_{1}+\text{D}} \tag{4}\]  
\[\frac{1}{q_{2}}=\frac{1}{R}-\frac{i\lambda}{\pi\text{W}^{2}} \tag{5}\]  
\(d_{1}\) is the distance between the transmitter and the projecting dish, \(F_{dish}\) is the focal length of both of the dishes, \(d_{2}\) is the distance between the projecting and receiving dishes and \(d_{3}\) is the distance between the receiving dish and the detector plane which is identical to the focal length of the receiving dish and equal to (600 mm). The MMW losses that are shown in Table 1 were calculated using Equation (2) with the aperture diameter D of 800 mm for the transmitting and receiving dishes and a diameter of 1 mm for the effective detector aperture. To generate the final ABCD matrix shown in Equation (3), the individual matrices representing each section of the system shown in Figure 1 have to be multiplied together. The beam waist at a given point can be calculated by using the individual matrices representing each section up to that point to produce the total ABCD matrix, and then Equations (4) and (5) can be used to calculate the beam waist at that point. From Table 1 it can be noticed that for up to 50 m, the suggested concept can produce a strong signal. For larger distance communication the MMW source needs to be relocated slightly further from the focal point of the dish antenna, in order to obtain greater spot size at the transmitting dish and consequently a smaller spot size at the receiving dish. In the set-up of Figure 1, the emitted MMW radiation was collimated using a dish antenna and directed to the second dish antenna that focused the beam on the effective detection area of the GDD. The current MMW technology can produce MMW power of more than 600 mW and also detect signals lower than 1 uW. Under such conditions it will be theoretically possible to transmit MMW power with the quasi-optical shown in Figure 1 for distances longer than 10 km. The dishes used here have a diameter of 800 mm. Better results can be achieved with dishes that have larger diameters, which increase the power collected by the receiving dish.