## 2 Principle  
### Photonics-Assisted MIMO Terahertz Technology  
Figure 1 illustrates the principle of photonic-assisted terahertz signal generation based on heterodyne beat frequency. Two independent continuous-wave lasers are employed, one serving as the signal laser and the other as the local oscillator (local oscillator, LO) laser. These lasers emit light waves with distinct frequencies. The output of the signal laser is modulated by the optical modulator (Opt. Mod), which is used to encode information onto the optical carrier. The modulated signal light wave is then coupled with the unmodulated local oscillator light wave using an optical coupler (OC). The coupled light waves are transmitted through single mode fibers (SMFs) before reaching the photodetector (PD). Within the PD, the interaction between the signal light wave and the local oscillator light wave, because of the PD's quadratic-law characteristic, generates a beat frequency signal, whose frequency is equal to the difference between the two light wave frequencies. If this difference falls within the terahertz frequency range, the resulting beat frequency signal is a terahertz wave. In this manner, a terahertz signal can be directly generated within the PD without the need for additional electrical terahertz wave generation devices. The high-gain antenna (HA) is used to transmit the generated terahertz signal, ensuring efficient signal propagation. Within the photodetector (PD), the phenomenon of beat frequency can be described by the following formulas. Suppose two light waves are heterodyne beat after the PD, their optical fields can be expressed as follows:  
\[E_{i}(t)=E_{i0}\text{cos}\left(\omega_{i}t+\Phi_{i}\right)\ \left(i=1,2\right) \tag{1}\]  
where \(E_{i}(t)\) represents the optical field of the \(i\)-th light wave, \(E_{i0}\) is its amplitude, \(\omega_{i}\) is its angular frequency, and \(\phi_{i}\) is its phase. When these two light waves are coupled into the PD, the output current \(I(t)\) of the PD is proportional to the square of the incident light power, that is,  
\[I(t)\propto(E_{1}(t)+E_{2}(t))^{2} \tag{2}\]  
\[I(t)\propto E_{1}^{2}(t)+2E_{1}(t)E_{2}(t)+E_{2}^{2}(t) \tag{3}\]  
Figure 1: Photonics-assisted terahertz technology based on heterodyne beat frequency. Among these terms, the intermediate term can be expanded into the following:  
\[2E_{1}(t)E_{2}(t)=E_{10}E_{20}(\cos((\omega_{1}-\omega_{2})t+(\Phi_{1}-\Phi_{2}))+ \cos((\omega_{1}+\omega_{2})t+(\Phi_{1}+\Phi_{2}))) \tag{4}\]  
where the first term represents the beat frequency component and the second term represents the sum frequency component. If the difference between \(\omega_{1}\) and \(\omega_{2}\) falls within the terahertz frequency range, then the beat frequency component is a signal of terahertz frequency. This is the principle by which the PD generates a beat frequency. The photonic-assisted terahertz signal generation technology based on the heterodyne beat frequency scheme boasts high flexibility and tunability, capable of generating both broadband terahertz waves, suitable for a variety of application scenarios. The advantages of this technology include high efficiency, ease of integration and control, as well as the ability to operate at room temperature. Polarization multiplexing is a technology that utilizes the polarization characteristics of electromagnetic waves to increase the capacity of communication systems. In polarization multiplexing, two or more signals with different polarization directions can be transmitted simultaneously within the same frequency band without interfering with each other, thereby enhancing spectral efficiency. MIMO technology is a technique that employs multiple antennas for both transmission and reception, improving the performance of wireless communication systems through spatial diversity and spatial multiplexing. In our system, we utilize photonic-assisted terahertz technology combined with polarization multiplexing MIMO technology to establish a 2 \(\times\) 2 MIMO wireless link with two transmitters and two receivers.