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Effective degree of coherence: a second look
Summary
We identified scaled unitary transformations as key for preserving electromagnetic field coherence. The effective degree of coherence is the only additive functional invariant under these transformations, generalizing coherence measures.
Area of Science:
- Quantum Optics
- Mathematical Physics
Background:
- Understanding the transformations of electromagnetic fields is crucial for analyzing their coherence properties.
- Previous research established coherence functionals invariant to scaled unitary transformations.
Purpose of the Study:
- To identify the most general transformations preserving global second-order coherence properties of electromagnetic fields.
- To prove the unique additive nature of the effective degree of coherence under these transformations.
- To generalize scalar coherence measures to systems involving orthogonal Hilbert spaces.
Main Methods:
- Analysis of scaled unitary transformations on electromagnetic fields.
- Development and application of coherence functionals.
- Generalization of the scalar two-point degree-of-coherence function.
Main Results:
- Scaled unitary transformations are the most general transformations preserving global second-order coherence.
- The effective degree of coherence is the sole additive coherence functional invariant under these transformations.
- This invariance ensures the effective degree of coherence yields consistent values across various field representations.
Conclusions:
- The effective degree of coherence offers a robust measure of field coherence, invariant to significant transformations.
- A generalized coherence function is introduced, encompassing common coherence and polarization measures as special cases.
- This work provides a unified framework for understanding coherence in complex electromagnetic field systems.
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