Phase Simulation of Intensity in Laguerre-Gaussian Beam Propagation

The phase screen method serves as a powerful computational technique for simulating both atmospheric turbulence effects and the intensity-phase characteristics of Laguerre-Gaussian beam propagation. In atmospheric turbulence simulations, this method models wavefront distortions caused by random refractive index fluctuations in the atmosphere. Implementation typically involves generating phase screens using Kolmogorov or von Kármán turbulence models through Fast Fourier Transform (FFT) algorithms, where the phase structure function is calculated using parameters like Fried's coherence length (r0). This simulation approach is crucial for optimizing optical systems in long-range communication, astronomical observation, and remote sensing applications. For Laguerre-Gaussian beam propagation, the phase screen method enables analysis of complex beam behavior in optical fibers, lasers, and waveguide systems. Code implementation involves numerically solving the paraxial wave equation using split-step Fourier methods, where propagation is divided into phase screen segments. Key computational steps include: 1. Generating Laguerre-Gaussian modes using orthogonal polynomials with radial (p) and azimuthal (l) indices 2. Applying phase screens to simulate medium interactions 3. Propagating through Fourier domain transformations 4. Accumulating intensity and phase data at each propagation step Researchers can investigate modal interference, vortex dynamics, and beam degradation effects by simulating different Laguerre-Gaussian modes (LG_pl) through turbulent media. The numerical approach typically employs Python/MATLAB with specialized toolboxes like Optical Propagation Toolbox or custom FFT-based propagation algorithms. This methodology provides valuable insights into light-medium interactions for advanced photonics applications.