Revealing the propagation dynamic of Laguerre-Gaussian beam with two Bohm-like theories

TL;DR

This paper uses Bohm-like theories to analyze the propagation and formation of Laguerre-Gaussian beams, revealing their subluminal behavior and visualizing their complex intensity patterns through particle and wave trajectories.

Contribution

It introduces a novel approach to visualize LG beam propagation using x-Bohm and p-Bohm theories, linking particle trajectories with wave interference.

Findings

LG beams exhibit subluminal propagation effects.

The petal-shaped intensity distribution results from combined particle and wave dynamics.

Trajectory analysis clarifies the formation of complex beam patterns.

Abstract

By employing x-Bohm theory and p-Bohm theory, we construct the position and momentum trajectories of single-mode and superposed-mode Laguerre-Gaussian (LG) beams. The dependence of divergence velocity and rotation velocity on the initial position and propagation distance is quantified, indicating that LG beams exhibit subluminal effects, even in free space. Additionally, we clarify the formation of the petal-shaped intensity distribution of the superposed-mode LG beam in terms of motion trajectory, where the particle-like trajectory and wave-like interference are ``simultaneously" observed. Our work provides an intuitive way to visualize the propagation characteristics of LG beams and deepen the comprehension of Bohm-like theory.