Overall degree of coherence for vectorial electromagnetic fields and the Wigner function

Area of Science:

• Optics and Photonics
• Quantum Optics
• Mathematical Physics

Background:

• Coherence is a fundamental property of electromagnetic waves, crucial for understanding wave phenomena.
• Vectorial electromagnetic waves exhibit complex polarization states that influence their coherence.
• Existing methods for coherence quantification may not fully capture the vectorial nature of light.

Purpose of the Study:

• To elaborate the overall degree of coherence for vectorial electromagnetic waves.
• To express this coherence in terms of novel mathematical frameworks.
• To provide a comprehensive understanding of light coherence in paraxial systems.

Main Methods:

• Development of a theoretical framework for vectorial wave coherence.
• Utilizing the polarization Wigner function for coherence description.
• Employing spatial-angular Stokes parameters to characterize wave properties.

Main Results:

• The study successfully expresses the degree of coherence for vectorial electromagnetic waves.
• A direct link is established between the polarization Wigner function and spatial-angular Stokes parameters.
• The proposed method offers a unified approach to coherence quantification.

Conclusions:

• The polarization Wigner function provides a powerful tool for analyzing vectorial wave coherence.
• Spatial-angular Stokes parameters offer new insights into the interplay of polarization and spatial properties.
• This work advances the understanding of coherence in paraxial optical systems.