Robustness analysis of the phase-conjugation algorithm in weak and medium atmospheric turbulence for free-space optical laser communications

Modeling the phase conjugation algorithm in atmospheric turbulence is a cornerstone for advancing free-space optical communication systems. The primary challenge lies in mitigating the severe wavefront distortions that degrade signal quality as a laser beam propagates through an inhomogeneous medium. This process, often referred to as generating a "time-reversed" or "phase-conjugate" wave, aims to precisely undo these aberrations. The simulation of this algorithm typically involves several key stages. First, a realistic model of atmospheric turbulence must be generated. Next, a sensor, such as a Shack-Hartmann wavefront sensor, measures the distorted wavefront, capturing its local slopes across a grid of sub-apertures. The core of the phase conjugation algorithm then takes this measured phase profile and mathematically inverts it by multiplying the complex field by its complex conjugate (E*). The entire system was modeled in MathWorks Simulink R2024b utilizing the Phased Array System Toolbox for field propagation and custom MATLAB Function blocks for low-level matrix operations. This signal contains pronounced high-frequency components associated with rapid changes in atmospheric inhomogeneities. The oscillation amplitude in the provided example reaches 0.6–0.8 radians, which corresponds to a moderate level of phase distortions. The assessment of the algorithm's stability was performed by varying two key parameters: the intensity of atmospheric disturbances (the Gain coefficient in the Atmosphere subsystem) and the negative feedback coefficient from the deformable mirror controller. The numerical experiment revealed the following patterns: At low Gain values (0.2–0.3), the algorithm is fully stable, and the system response smoothly converges to the compensating signal At Gain values of 0.5–0.6, an increase in disturbance amplitude is observed; however, the controller maintains stability provided that the feedback coefficient remains within the range of –0.8 to –1.1 At Gain values above 0.7, oscillations of the compensation signal may occur in the system, indicating a transition into a high-frequency saturation mode.