# Prediction of Power Fluctuations of Gaussian Beams After Transmission Through Turbulent Atmosphere
###### Abstract  
As laser beams propagate through free space, power fluctuation occurs due to atmospheric turbulence, which significantly increases the bit error rate of free-space optical communication. If the precise prediction of power fluctuations can be achieved, it will be of great benefit for improving communication efficiency. To achieve this goal, this paper proposes a novel Time Series Long Short-Term Memory Fully Connected Processing Network (TSLSTM/RFCPN), which consists of two long short-term memory (LSTM) network layers and a fully connected layer, for predicting the power fluctuations of laser beams caused by atmospheric turbulence. The experimental results show that the mean absolute percentage error of the TSLSTM/RFCPN in predicting laser power fluctuations is only 1.2%. This result indicates that this model can accurately predict the laser power fluctuations caused by atmospheric turbulence. Our results are expected to be applied in free-space optical communication systems and imaging laser radar system. os 2024 11108 11 11 11 11 11 11 11 11 11 11 11 11 11  
can be accurately predicted, a precise evaluation of the error rate of free-space optical communication systems can be obtained. As is well known, the intensity of atmospheric turbulence is closely dependent on meteorological conditions, and this intensity directly determines the amplitude of power fluctuations in laser beams propagated through the atmosphere [14; 15; 16]. Given the relatively straightforward and feasible acquisition of meteorological data, investigating how to utilize these routine meteorological data to predict laser power fluctuations undoubtedly represents a research topic of great significance. Apart from being influenced by meteorological data such as temperature, pressure, and humidity, the effect of atmospheric turbulence on laser beams is also significantly constrained by the wavelength and mode of the beams themselves [17; 18; 19]. As a result, a complex nonlinear relationship exists between fluctuations in laser power and meteorological conditions, which renders research on optical turbulence based on traditional physical models often unsatisfactory [20; 21; 22; 23]. In the past few years, the rapid development of artificial intelligence and computing power has enabled deep learning to be widely applied in various fields. For instance, in 2016, [PERSON] et al. pioneered the introduction of artificial neural networks at the Mauna Kea Observatories, conducting a month-long study on estimating atmospheric optical turbulence intensity, thereby opening a new chapter in this field [24]. Subsequently, in 2017, [PERSON] et al. collected three key meteorological parameters--temperature, wind speed, and relative humidity--over four consecutive days in Sanya, and leveraged a Back-Propagation Neural Network (BPNN) to accurately estimate the atmospheric refractive index structure constant (e.g., \(C_{n}^{2}\)) [25]. Following this, [PERSON] et al. further innovated by integrating neural networks with a Genetic Algorithm (GA) to optimize and upgrade the neural network models of [PERSON] and [PERSON], ultimately achieving effective prediction of \(C_{n}^{2}\) using actual meteorological observation data from the northwest plateau of China [26]. These research achievements demonstrate the remarkable feasibility and potential of deep learning methods in establishing complex nonlinear relationships between meteorological data and atmospheric turbulence intensity. Based on this, to achieve the accurate prediction of power fluctuations in laser beams propagating through a turbulent atmosphere with the aid of meteorological parameters, this study designs and constructs a model named the Time Series Long Short-Term Memory Fully Connected Processing Network (TSLSTMFCPN). This model, meticulously constructed with two LSTM layers and a fully connected layer, aims to deeply mine information from measured meteorological data, thereby enabling the precise prediction of power fluctuations in laser beams propagating through a turbulent atmosphere.