Cross-spectral purity: a generalization of spatiotemporal separability

Area of Science:

• Optics and Photonics
• Quantum Optics
• Classical Field Theory

Background:

• Nonstationary (pulsed) scalar fields exhibit complex spatiotemporal characteristics.
• Cross-spectral purity is a key metric for describing coherence properties of optical fields.
• Spatiotemporal separability defines whether a field's properties can be independently analyzed in space and time.

Purpose of the Study:

• To investigate the relationship between cross-spectral purity and spatiotemporal separability.
• To determine if cross-spectral purity can generalize separability concepts to partially coherent fields.
• To explore practical measurement techniques for assessing cross-spectral purity.

Main Methods:

• Theoretical analysis of the connection between cross-spectral purity and spatiotemporal separability.
• Examination of correlation functions for partially coherent fields.
• Discussion of self-referencing linear measurement schemes.

Main Results:

• A two-way relationship exists between global cross-spectral purity and spatiotemporal separability for fully coherent fields.
• Cross-spectral purity serves as a generalization of spatiotemporal separability for partially coherent fields.
• The separability of correlation functions underpins this generalization.

Conclusions:

• Cross-spectral purity is a fundamental property linking coherence and spatiotemporal structure in optical fields.
• The findings extend the understanding of coherence and separability to a broader class of fields.
• Simple measurement methods can be employed to quantify cross-spectral purity.