Abstract
Introducing scalar and vector densities for a mutual coherence function, we present a new conservation law for optical coherence of scalar wave fields in the form of continuity equation. This coherence conservation law provides new insights into topological phenomena for the complex coherence function. Some properties related to the newly introduced coherence vector density, such as a circulating coherence current associated with a coherence vortex, are investigated both theoretically and experimentally for the first time.
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