Shimony-Wolf states and hidden coherences in classical light

The classical theory of polarisation coherence is briefly summarised and then extended. The extension is motivated by the recognition that the traditional theory of two-point coherence provides only what we identify as ` diagonal' correlation functions and their associated two-point coherence matrices. It is pointed out that a wider focus is possible when taking account of the three-sector vector space underlying all two-point coherences in classical optics. This reveals the possibility of observing a new type of ` off-diagonal' correlations that arise when the correlation functions under investigation are associated with points in two distinct vector spaces, pairs of points that are not analogous to the pairs of space points or time points that underlie traditional measures of spatial and temporal coherence. Quantum theory has experience with correlations engaging such ` cross-sector' coherences, for example in tests of Bell inequalities, and the quantum formulations are shown to be easily adopted by classical theory without incorporating quantum features in the optical signals. The familiar theory of classical coherence that is associated with the pioneering work of EmilWolf is extended in conformance with three criteria advanced by Abner Shimony to obtain formulas for correlation functions and for the Bell measure S of coherence. Values of S greater than the standard upper limit S = 2 are predicted for certain classical Shimony-Wolf fields, indicating strong cross-sector coherence, but only when standard measures of coherence such as degree of polarisation P are minimised. Experimental results confirming the predictions for cross-sector coherence are exhibited.