## 2 System Model  
Figure 1 shows the mixed RF/FSO system based on RIS reflection interference to the eavesdropper. The system comprised of an RF source (S) with a single antenna, a single antenna relay (R) and a destination node (D), a wireless-powered multi-antenna jammer (J), and an RIS (\(R^{\prime}\)) with \(N\) reflection elements. The RF and FSO links followed Nakagami-m and M fading distribution, respectively. A single antenna eavesdropper (E) in the RF link,  
attempts to eavesdrop on information sent from S to R but is interfered by the jamming signals. These signals are emitted by the jammer via RIS reflection and guarantee secure communication throughout the system. We assumed that the channel state information for each node is known.  
We considered two-phase communication where the jammer considered fixed-rate transmission. The two phases are the energy-harvested phase and the information transmission phase. The SWIPT adopts a time-switching protocol in the whole process, meaning that during each time cycle \(T\), energy collection is performed over \(\lambda T\), and information transmission is performed over \((1-\lambda)T\)[10]. Multiple receive antennas \(M_{j}\) (j = 1, 2,...) were used at the jammer that receives the transmitted signal from the source node, and thus the signal received at J can be expressed as follows:  
\[y_{J}=\frac{1}{\sqrt{d_{SJ}^{\tau}}}\sqrt{P_{S}}h_{SJ}x_{S}+n_{J} \tag{1}\]  
where \(P_{S}\) refers to the transmission signal power of the S, \(x_{S}\) indicates the signal sent by the S, and \(h_{SJ},d_{SJ}\) denotes the channel coefficients between the S and the J, and the distance between them, respectively. \(\tau\) represent path loss index, and \(n_{J}\) is the additive Gaussian white noise with zero mean and variance \(\sigma_{J}^{2}\) at the jammer. The energy harvested by the J can be expressed as:  
\[W_{J}=\lambda\rho\left(\frac{1}{\sqrt{d_{SJ}^{\tau}}}\sqrt{P_{J}}h_{SJ}\right) ^{2}T \tag{2}\]  
where the time switching factor is represented by \(\lambda\) and \(\rho\) denotes the J energy conversion efficiency in converting the RF signal into direct current. In the information transmission phase, the energy consumed by the jammer to transmit signals cannot exceed the energy collected and stored in the previous phase. According to (2), the transmission power of the jammer \(P_{J}\) satisfies:  
\[P_{J}(1-\lambda)T\leq W_{J} \tag{3}\]  
Using the N number of reflectors, the RIS redirects the incoming interference signal to the eavesdropper with an appropriate phase change, where \(h_{i}=d_{JR^{\prime}}^{\tau}\alpha_{i}e^{-i\theta_{i}}\) and \(g_{i}=d_{RE}^{\tau}\beta_{i}e^{-j\varphi_{i}}\) for \(J-R^{\prime}\) and \(R^{\prime}-E\) links, respectively. Here, \(\alpha_{i},\theta_{i}\) represent the ampli  
Figure 1: Mixed RF/FSO system based on RIS reflection interference eavesdropper.  
tude and phase of the \(h_{i}\) channel, respectively. Similarly, \(\beta_{i}\), \(\varphi_{i}\) denotes the amplitude and phase of the \(g_{i}\) channel, respectively. Therefore, the signal received by E can be expressed as:  
\[y_{E}=\sum_{i=1}^{N}\sqrt{P_{I}}h_{i}v_{i}g_{i}x_{J}+\frac{1}{\sqrt{d_{SE}^{ \ast}}}\sqrt{P_{S}}h_{SE}x_{S}+n_{E} \tag{4}\]  
where \(x_{J}\) is the signal transmitted by the J, and \(h_{SE}\) and \(d_{JR^{\prime}},d_{R^{\prime}E},d_{SE}\) indicate the channel coefficient and distances of the corresponding links, respectively. The RIS reflection coefficient of the \(i\)th reflection module is \(v_{i}=\rho_{i}(\phi_{i})e^{\phi_{i}}\), the phase shift is \(\phi_{i}\in[-\pi,\pi)\), and \(\rho_{i}(\phi_{i})\in[0,1]\) represents the corresponding amplitude. The additive Gaussian white noise with zero mean and variance \(\sigma_{E}^{2}\) at the eavesdropper is represented by \(n_{E}\), respectively.