Twisting partially coherent light

Area of Science:

• Optics and Photonics
• Wave Phenomena
• Statistical Optics

Background:

• Twisted Gaussian Schell-model beams are a notable class of partially coherent wavefields.
• The precise effect of twist phase on arbitrary cross-spectral density remains an open question.

Purpose of the Study:

• To establish the necessary and sufficient conditions for mapping a typical axially symmetric Schell-model cross-spectral density (CSD) to a twisted CSD.
• To determine the criteria for a shift-invariant degree of coherence to be successfully 'twistable'.

Main Methods:

• Analysis of the mathematical conditions for transforming a Schell-model CSD into a twisted CSD.
• Investigation of the properties of the zeroth-order Hankel transform of a modified radial coherence function.

Main Results:

• A definitive condition is derived for a typical axially symmetric Schell-model CSD to be considered a twisted CSD.
• It is proven that any shift-invariant degree of coherence of the form μ(|r1-r2|) is twistable if and only if a specific Hankel transform yields a well-defined, non-negative function.

Conclusions:

• The study provides a clear mathematical criterion for the 'twistability' of partially coherent beams.
• This work clarifies the relationship between coherence properties and the introduction of twist phase in optical wavefields.