Partially coherent conical refraction

TL;DR

This paper extends the paraxial conical refraction model to partially coherent light using optical coherence theory, deriving analytical expressions and predicting new phenomena such as ring narrowing and spot shifts.

Contribution

It introduces a simplified, rigorous model for partially coherent conical refraction, enabling exact analysis similar to the coherent case and predicting novel effects.

Findings

Analytical expressions for conical refraction intensity in focal and far fields.

Prediction of ring narrowing and dark ring disappearance.

Universal power-law relation between coherence degree and input correlation length.

Abstract

In this paper, we extend the paraxial conical refraction model to the case of the partially coherent light using the unified optical coherence theory. We demonstrate the decomposition of conical refraction correlation functions into well-known conical refraction coherent modes for a Gaussian Schell-model source. Assuming randomness of the electrical field phase of the input beam, we reformulated and significantly simplified the rigorous conical refraction theory. This approach allows us to consider the propagation of light through a conical refraction crystal in exactly the same way as in the classical case of coherent radiation. Having this in hand, we derive analytically the conical refraction intensity both in the focal plane and in the far field, which allows us to explain and rigorously justify earlier experimental findings and predict new phenomena. The last include the counterintuitive effect of narrowing of the conical refraction ring width, disappearance of the dark Poggendorff's ring in the Lloyd's plane, and shift of Raman spots for the low-coherent conical refraction light. We also demonstrate a universal power-law dependence of conical refraction cones coherence degree on the input correlation length and diffraction-free propagation of the low-coherent conical refraction light in the far field.