Hollow Gaussian Beam Propagation Simulation in Free Space

The propagation of Hollow Gaussian Beams through free space represents a significant research subject in optical physics. During this propagation process, variations in atmospheric refractive index substantially influence beam transmission characteristics. To accurately simulate Hollow Gaussian Beam propagation in free space, computational models must incorporate refractive index fluctuations. The propagation distance serves as another critical parameter since it directly determines beam attenuation levels. In transmission simulations, these factors require careful consideration and appropriate adjustments to achieve precise predictions of beam propagation behavior. From a coding perspective, the simulation typically involves solving the paraxial wave equation using numerical methods like the Split-Step Fourier Algorithm. Key implementation aspects include modeling the initial hollow Gaussian beam profile using Bessel functions or Laguerre-Gaussian modes, then propagating it through discrete steps while applying phase modifications based on refractive index variations. The code structure generally consists of three main components: beam initialization, propagation kernel with phase correction, and intensity profile analysis at different distances. Important functions would handle refractive index modeling (possibly using atmospheric turbulence models), diffraction calculations via Fourier transforms, and beam parameter tracking throughout propagation.