## 2 Fundamentals of Terahertz Communication
### The Terahertz Spectrum
#### 2.1.1 High Bandwidth  
The high bandwidth that can be achieved from the THz spectrum is one of the biggest strengths attributed to this spectrum. Microwave frequencies, which operate only in 1-10 GHz frequencies, cannot support the data intensity required by modern applications [23; 24]. On the other hand, the THz spectrum has a bandwidth that is more than 100 GHz and up to 10 THz in some scenarios, with data rates of 1-10 Tbps. Such a bandwidth is essential for solutions like ultra-HD streaming, which requires data rates of at least 25 Mbps per stream, and 6G networks, which are expected to require at least 1 Tbps per user in peak scenarios [25]. Figure 2 shows a data rate and stability comparison. Furthermore, photonic-assisted technologies have been demonstrated to operate effectively in this bandwidth by attaining data rates of 1.03 Tbps per meter for the free-space optical link method in laboratory prototypes [26]. Metamaterial-based modulators and filters also play an important role in achieving great bandwidth characteristic improvements in usability in dense urban areas in terms of spectral efficiency [27; 28]. Figure 3 illustrates the bandwidth capacities of different communication technologies, highlighting the significant increase in available bandwidth as we move from microwave to millimeter-wave (mmWave) and terahertz (THz) frequencies. The figure presents a comparative analysis of the bandwidth ranges for microwave (300 MHz-30 GHz), mmWave (30 GHz-300 GHz), and THz (300 GHz-10 THz) frequencies, demonstrating the exponential growth in spectral availability. Microwave technologies, which include conventional wireless and satellite communications, offer limited bandwidths (typically 1-10 GHz) but provide robust long-range capabilities. In contrast, mmWave communication, widely used in 5G backhaul and automotive radar, offers a 10-100 GHz bandwidth range, enabling high-speed short-range applications. The THz spectrum (300 GHz-10 THz), which is the focus for emerging 6G and ultra-high-speed wireless communication technologies, delivers from 100 GHz to several THz of bandwidth, making it an ideal candidate for next-generation holographic telepresence, inter-satellite links, and ultra-low latency applications. However, despite its vast bandwidth potential, THz communication faces challenges such as atmospheric attenuation, hardware limitations, and dispersion effects, which must be addressed to ensure practical deployment. The channel capacity for a communication system can be determined using the Shannon-Hartley theorem, as shown below:  
\[\mathrm{C}=\mathrm{B}\cdot\mathrm{log}_{2}(1+\mathrm{SNR}) \tag{1}\]  
where C is the channel capacity in bits per second (bps), \(B\) is the bandwidth in Hz, and SNR is the signal-to-noise ratio [29]. In the context of THz systems, the bandwidth \(B\) can reach up to 1 THz in practical implementations, leading to unprecedented capacities exceeding 1 Tbps. However, in ideal scenarios, the theoretical bandwidth can extend up to 10 THz, although extreme absorption and device limitations significantly constrain the system's usability at this rate [30]. For multi-antenna systems like MIMO, the channel capacity scales with the number of transmit (Nt) and receive (Nr) antennas:  
\[\mathrm{C}_{\mathrm{MIMO}}=\mathrm{N}_{\mathrm{t}}\cdot\mathrm{N}_{\mathrm{r} }\cdot\mathrm{B}\cdot\mathrm{log}_{2}(1+\mathrm{SNR}) \tag{2}\]Equation (2) models THz signal transmission, accounting for the power loss due to free-space path loss (FSPL) and atmospheric absorption. The received power (Pr) depends on the transmitted power (Pt), propagation distance (d), antenna gains (Gt, Gr), and wavelength (\(\lambda\)). As the distance increases, THz signals suffer from severe attenuation; thus, they require high-gain directional antennas and beamforming to achieve efficient transmission. Atmospheric absorption loss (L\({}_{\text{atm}}\)) is frequency-dependent, and THz-FSO systems experience significant losses above 500 GHz, making long-range THz communication challenging.