Related Experiment Video
Updated: Feb 20, 2026

Femtosecond Laser Filaments for Use in Sub-Diffraction-Limited Imaging and Remote Sensing
Published on: April 25, 2019
Self-focusing effect of annular beams propagating in the atmosphere
Abstract:
The self-focusing effect of annular beams propagating in the atmosphere to assist delivering powerful laser beams from orbit to the ground is studied in detail. It is found the annular beam is compressed more strongly due to the self-focusing effect as the beam obscure ratio increases. On the other hand, the self-focusing effect between annular, flat-topped and Gaussian beams is compared. It is shown that the self-focusing effect on the annular beam is stronger than that on flat-topped and Gaussian beams. However, the threshold critical power values of annular, flat-topped and Gaussian beams should be in sequence from small to large. Furthermore, the expression of the B integral of annular beams propagating from orbit to the ground in the atmosphere is derived, and the fitting equation related to the B integral of annular beams for maximal compression without filamentation is presented.
Related Concept Videos
Influence of Earth's Curvature and Atmospheric Refraction on Leveling
Deflection of a Beam
Singularity functions, described in an earlier lesson, are powerful mathematical tools that represent discontinuities within a function commonly encountered in structural loading...
Shear on the Horizontal Face of a Beam Element
Beams with Symmetric Loadings
The M/EI...
Interference and Diffraction
Beams with Unsymmetric Loadings
The first moment-area theorem determines the slope at any point on the beam. This theorem indicates that the change in slope between two points on a beam...

