A phase-space Gaussian beam summation representation of rough surface scattering

Area of Science:

• Electromagnetics and Optics
• Wave Propagation
• Computational Physics

Background:

• Modeling electromagnetic wave scattering from rough surfaces is crucial for understanding wave propagation in complex environments.
• Existing methods often face challenges in accuracy and computational efficiency when dealing with inhomogeneous media and intricate boundary conditions.

Purpose of the Study:

• To introduce a novel Gaussian beam (GB) summation representation for analyzing rough surface scattering.
• To provide a framework that combines the accuracy of deterministic propagators with the flexibility of stochastic scattering matrices.

Main Methods:

• The proposed method represents coherent and incoherent scattered fields as a phase-space summation of Gaussian beams.
• It utilizes stochastic Gaussian beam to Gaussian beam (GB2GB) scattering matrices and deterministic Gaussian beam propagators.
• GB2GB matrices are derived from statistical moments of the scattering amplitude, which can be determined analytically or empirically.

Main Results:

• An analytical and numerical example for weakly rough surfaces is presented, demonstrating the method's validity.
• The GB summation approach offers a balance of simplicity and accuracy for scattering problems.
• The framework is suitable for wave propagation in complex scenarios, including inhomogeneous media with rough surface boundaries.

Conclusions:

• The developed Gaussian beam summation representation provides an effective tool for modeling rough surface scattering.
• This method facilitates the analysis of wave propagation in complex systems with rough interfaces.
• Future work will extend the application to more complex scenarios like doubly rough surface waveguides.