# Free Space Optical Communication: An Enabling Backhaul Technology for 6G Non-Terrestrial Networks
## 2 Fundamentals of FSO Signal Transmission
### Atmospheric Attenuation  
Light propagation through any medium is affected by three interactions, known as absorption, scattering, and emission. Radiative transfer functions describe these interactions [77; 78], where light intensity during propagation is affected by losses caused by extinction (i.e., absorption and scattering) and gains caused by emission. Absorption describes the fact that by interacting with the particles and molecules in the medium, part of the energy in the light beam can be converted into another form of energy, such as heat. Scattering describes the fact that light beams deviate from their straight paths due to particles in the media they pass through. It should also be considered that a particle may emit radiation when it interacts with the light beam. This phenomenon is known as  
Figure 4: Geometrical loss versus transmission distance for different wavelengths. Figure 3: Geometrical loss under the assumption of plane wave approximation. emission and describes this gain. In addition, emission may refer to the radiation radiated back after absorption. In the event of no or negligible gains from emission, the light intensity during its propagation in a particular medium is only subject to losses due to absorption and scattering. If so, the radiative transfer function can be expressed as a simple First-Order Linear Ordinary Differential Equation (FOLODE). The Beer-Lambert law provides a solution to the FOLODE and, accordingly, the attenuation coefficient, also referred to as transmittance, can be written as [79; 80; 81]  
\[h_{a}\approx\exp(-\gamma(\lambda)\ z_{\mathrm{km}}), \tag{5}\]  
where \(\gamma(\lambda)\) is the extinction coefficient per km and \(z_{\mathrm{km}}\) is the propagation distance in km. The Beer-Lambert law is commonly used in the literature to model path loss in FSO communication systems [82]. A critical issue is the selection of a proper extinction coefficient to accurately model given atmospheric conditions. As listed in Table 4, there are some well-known models, such as [PERSON] [79], [PERSON] [80], and [PERSON] [81] used to describe the fog extinction coefficient. Fog models are also used for cloud attenuation, based on the argument that fog is a type of cloud [83; 84]. Additionally, extinction coefficients for rain and drizzle are obtained based on data fitting to experimental results at different geographical locations [85; 86]. Before presenting the results of attenuation loss, we need to emphasize that, while both attenuation and geometric loss contribute to signal degradation, they may operate over different distances. For example, in a satellite-ground link, geometric loss affects the signal strength over the entire link distance. On the other hand, the attenuation caused by atmospheric factors primarily influences the signal strength within relatively short distances, typically over the transmission range where rain, fog, clouds, etc. exist. In Figure 5, we first present the attenuation loss versus distance for clear weather conditions using Equation (5), where the visibility takes very large values. The extinction coefficient is computed utilizing [PERSON]'s model and a visibility of \(V=50\) km [80] is assumed. We consider a propagation distance of up to \(z_{\mathrm{km}}\)= 20 km, aligning with the understanding that losses with clear weather conditions typically occur within the troposphere. We can observe that the attenuation losses are 1.07 dB, 2.14 dB, 3.21 dB, and 4.28 dB for \(z_{\mathrm{km}}\)= 5 km, 10 km, 15 km, and 20 km assuming \(\lambda=785\) nm, respectively. These drop, respectively, to 0.44 dB, 0.88 dB, 1.32 dB, and 1.76 dB for \(\lambda=1550\) nm. This indicates that higher wavelengths bring lower attenuations. Compared to geometrical loss (see Figure 4), the losses in clear weather conditions are observed to be very small and can therefore be neglected in most cases. To investigate the impact of fog on signal propagation, it is crucial to consider the orientation of the connections, whether they are vertical or horizontal.