Coherence current, coherence vortex, and the conservation law of coherence

Area of Science:

• Optics
• Wave Physics
• Mathematical Physics

Background:

• Optical coherence is fundamental to understanding wave propagation.
• Topological phenomena in wave fields are of significant interest.
• Existing frameworks lack a comprehensive coherence conservation law.

Purpose of the Study:

• To introduce a new conservation law for optical coherence in scalar wave fields.
• To explore topological phenomena using a novel coherence framework.
• To investigate the properties of a newly defined coherence vector density.

Main Methods:

• Formulation of scalar and vector densities for the mutual coherence function.
• Derivation of a continuity equation representing the coherence conservation law.
• Theoretical analysis and experimental investigation of coherence properties.

Main Results:

• A novel coherence conservation law in the form of a continuity equation was established.
• New insights into topological phenomena of the complex coherence function were gained.
• The existence of a circulating coherence current associated with a coherence vortex was demonstrated.

Conclusions:

• The new coherence conservation law provides a deeper understanding of optical coherence.
• The study reveals novel topological properties related to coherence vortices.
• This work establishes a foundation for future research in optical coherence and topology.