Engineering equations for characterizing non-linear laser intensity propagation in air with loss

Area of Science:

• Optics and Photonics
• Atmospheric Physics

Background:

• High peak-power laser beams experience linear and nonlinear effects during long-range atmospheric propagation.
• J. H. Marburger's work is foundational in the mathematical characterization of laser beam self-focusing.

Purpose of the Study:

• To provide validated engineering equations for calculating the self-focusing distance of laser beams in non-turbulent air.
• To account for propagation with and without loss, and for three different source configurations (no lens, converging lens, diverging lens).

Main Methods:

• Development of engineering equations for self-focusing distance.
• Validation of these equations against wave-optics simulation results.
• Comparison of derived equations with Marburger's original theory.

Main Results:

• A validated set of engineering equations for laser beam self-focusing distance was established.
• Some derived equations align with Marburger's theory, while others necessitate modifications to it.
• The study considered atmospheric loss and various optical configurations.

Conclusions:

• The developed equations offer a practical tool for predicting laser self-focusing in atmospheric conditions.
• The findings provide guidance for refining numerical simulations and planning field experiments.
• This work contributes to a more accurate understanding of laser beam propagation physics.