Generalized Stokes parameters of three-dimensional stochastic electromagnetic beams

Area of Science:

• Optics and Photonics
• Electromagnetism
• Mathematical Physics

Background:

• Stochastic electromagnetic beams are crucial in various optical applications.
• Existing 2D generalized Stokes parameters offer limited descriptions for complex beam propagation.
• A need exists for a more comprehensive framework to analyze 3D beam characteristics.

Purpose of the Study:

• To develop and investigate 3D generalized Stokes parameters for stochastic electromagnetic beams.
• To analyze the propagation laws of coherence and polarization properties in three dimensions.
• To compare the 3D model with existing 2D approaches for accuracy.

Main Methods:

• Extension of 2D generalized Stokes parameters to the 3D case.
• Utilizing the 3x3 cross-spectral density matrix and Gell-Mann matrices.
• Employing the electromagnetic Gaussian Shell-model source for analysis.
• Numerical simulations to demonstrate propagation laws and comparisons.

Main Results:

• The 3D generalized Stokes parameters are defined as linear combinations of the 3x3 cross-spectral density matrix.
• Precise propagation laws for coherence and polarization properties in 3D were investigated.
• Numerical examples validated the theoretical framework and highlighted differences from the 2D case.

Conclusions:

• 3D generalized Stokes parameters are necessary for an exact description of stochastic electromagnetic beams.
• The developed framework provides a more accurate representation of beam behavior in three dimensions.
• This advancement is vital for understanding and manipulating complex light fields.