Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices

Area of Science:

• Optics and Photonics
• Electromagnetism
• Wave Physics

Background:

• Coherence is a fundamental property of light, crucial for applications like interferometry and imaging.
• Existing measures of coherence often focus on scalar fields or specific experimental setups.
• Quantifying coherence in vectorial electromagnetic fields requires robust theoretical frameworks.

Purpose of the Study:

• To define and assess the degree of coherence for vectorial electromagnetic fields in the space-frequency domain.
• To compare the proposed definition with existing coherence measures.
• To establish a new metric for quantifying field incoherence.

Main Methods:

• Assessing coherence by calculating the distance between the cross-spectral density matrix and the identity matrix.
• Comparing the proposed distance-based metric with previous definitions of coherence.
• Analyzing the behavior of the metric in a Young interferometer setup.

Main Results:

• The proposed distance serves as a robust measure of vectorial field coherence in the space-frequency domain.
• This distance provides an upper bound for the degree of coherence and visibility of derived scalar waves.
• The approach aligns with previous definitions of global coherence when applied to interferometric measurements.

Conclusions:

• The developed metric offers a unified and comprehensive way to quantify the coherence of vectorial electromagnetic fields.
• This work advances the understanding of light coherence, with potential implications for advanced optical systems.
• The distance-based approach provides a valuable tool for characterizing and manipulating light fields.