## 1 Introduction
However, compared to the relay technology, the RIS consumes less power, is not affected by the receiver noise at the relay, and does not require complex processing at the relay. The RIS is a planar array composed of multiple mirrors or optical phased array structures, which can intelligently control the amplitude, phase, and polarization of the incident signal through integrated electronics [14]. Based on the aforementioned features, it can effectively customize the wireless environment to enhance the intelligence of the wireless communication channel, thus improving the capacity, spectrum, and energy efficiency of the communication network [15]. RIS has been proposed in recent years in RF communications to solve the dead zone problem in RF networks and to create smarter communication channels [16; 17]. In the physical-layer security scheme, RIS-assisted secure communication has also attracted wide attention [18]. The RIS concept had also been expanded to include optical and hybrid systems. [PERSON] et al. combined RIS and a Light Fidelity (LiFi) transmitter in visible light communication, so as to realize the dynamic tunability of the LiFi transceiver [19]. [PERSON] et al. used RIS with an RF signal generator as a terminal for signal enhancement in a hybrid RF/FSO unmanned aerial vehicle (UAV) communication system [20]. In the first study on RIS technology in a terrestrial free-space optical (FSO) communication system, [PERSON] et al. proposed an RIS-assisted FSO system using phase-shift profiles. The geometric and misalignment losses (GML) were modeled to characterize the effect of different RIS physical parameters on the channel. The probability density function (PDF) of the GML was derived for two-dimensional and three-dimensional scenarios, and finally the outage performance of the RIS-assisted FSO system was studied, considering GML and atmospheric turbulence [21]. Different techniques for designing reflective surfaces at optical frequencies were reviewed by [PERSON] et al. and compared optical IRS with RF IRSand optical relaying [22]. In [23], the authors analyzed the performance of RIS-assisted terrestrial FSO subjected to turbulence and pointing errors, considering the link distance and RIS jitter ratios at the RIS position. In [24], the authors unified the Fisher-Snedecor (F), Gamma-Gamma (GG) and Malaga (M) distribution atmospheric turbulence models. Closed expressions for the outage probability, BER and channel capacity of the RIS-FSO system are derived considering the effects of atmospheric turbulence, pointing errors, and random fog. In [25], considering the imperfect channel state information (CSI) and pointing errors, the authors derived closed expressions for the PDF and CDF of the RIS-assisted FSO system under the F distribution. The study of RIS in the above article was conducted in a horizontal link FSO system, where the purpose of using the RIS was to relax the line-of-sight requirements of the FSO system. The RIS technology can also be used to improve system performance by using RIS modules with multiple RIS elements to reflect the incident beam. This results in the formation of multiple independent channels to mitigate the effects of atmospheric turbulence, and intelligently control the direction of the reflected beam to reduce the pointing errors. To the best of our knowledge, the use of RIS technology to enhance the performance of vertical link satellite-terrestrial laser communication systems has not been reported in existing literature. In short, the differences between this article and related articles are shown in Table 1.  
Based on the above analysis, this paper introduces RIS technology into the satellite-HAP-terrestrial laser communication system. The M distribution is used to characterize the atmospheric channel model, and the SIMO technology is used to improve the system performance in the satellite-to-HAP system.