Mathematic model analysis of Gaussian beam propagation through an arbitrary thickness random phase screen

Area of Science:

• Optics and Photonics
• Laser Physics
• Statistical Optics

Background:

• Gaussian beam propagation is crucial for laser communication and adaptive optics.
• Existing models often simplify phase screens as thin, limiting accuracy for thicker screens.
• Understanding statistical properties of beam propagation through random media is essential.

Purpose of the Study:

• To develop mathematical models for statistical quantities of Gaussian beam propagation through arbitrary thickness random phase screens.
• To provide analytic results for thick phase screens using the Kolmogorov power spectrum.
• To compare thick and thin phase screen models and highlight the advantages of the generalized approach.

Main Methods:

• Application of the Rytov method for wave propagation analysis.
• Development of a thin phase screen model as a basis.
• Derivation of analytic results for an arbitrary thickness phase screen.
• Utilizing the Kolmogorov power spectrum to characterize the random phase screen.

Main Results:

• Established mathematical models for statistical quantities in Gaussian beam propagation.
• Derived analytic results applicable to arbitrary thickness phase screens.
• Demonstrated that the generalized model is more suitable than the thin screen model, particularly for scintillation index.
• Showcased improved accuracy in predicting scintillation index.

Conclusions:

• The developed models accurately describe Gaussian beam propagation through thick random phase screens.
• The generalized model offers superior performance over the thin screen approximation, especially for scintillation.
• This research provides a more robust framework for adaptive optics and laser communication systems.