Optical cross-purity

Area of Science:

• Quantum optics
• Classical optics
• Information optics

Background:

• Cross-spectral purity, defined by Mandel in 1961, applies to optical fields with identical spectra at two superposition points.
• Generalizing this concept is essential for broader applications in optical science.

Purpose of the Study:

• To generalize the concept of cross-spectral purity beyond its original definition.
• To investigate the role of coherence matrix properties in determining cross-purity across various optical degrees-of-freedom.

Main Methods:

• Discretizing the modal structure of optical fields.
• Utilizing two binary degrees-of-freedom: polarization and two spatial modes.
• Analyzing the separability of the 4x4 coherence matrix.

Main Results:

• Cross-purity is achieved when the coherence matrix is separable.
• The rank of the coherence matrix is critical: rank-1 and rank-2 fields are always cross-pure.
• Rank-3 fields are never cross-pure, and only a subset of rank-4 fields exhibit cross-purity.

Conclusions:

• The rank of the coherence matrix fundamentally dictates optical cross-purity.
• This generalized framework enables the analysis of cross-purity in diverse optical systems.
• The findings provide new insights into the structure and properties of optical fields.