Engineering equations for characterizing non-linear laser intensity propagation in air with loss
Related Experiment Video
Updated: Feb 14, 2026

Custom Engineered Tissue Culture Molds from Laser-etched Masters
Published on: May 21, 2018
Abstract:
The propagation of high peak-power laser beams in real atmospheres will be affected at long range by both linear and nonlinear effects contained therein. Arguably, J. H. Marburger is associated with the mathematical characterization of this phenomenon. This paper provides a validated set of engineering equations for characterizing the self-focusing distance from a laser beam propagating through non-turbulent air with, and without, loss as well as three source configurations: (1) no lens, (2) converging lens and (3) diverging lens. The validation was done against wave-optics simulation results. Some validated equations follow Marburger completely, but others do not, requiring modification of the original theory. Our results can provide a guide for numerical simulations and field experiments.
Related Concept Videos
Linear Equations
Linear Differential Equations
Application of the Linear Momentum Equation
The goal is to determine the force components in the x and y directions to hold the pipe in place. Since...
Systems of Linear Equations in Two Variables
Balancing Redox Equations
Clausius-Clapeyron Equation

