Mesoscopic correlation in electromagnetic wave polarization

Abstract

We have measure the correlation of microwave field and intensity versus polarization of the source and detector in a ensemble of randomly positioned alumina spheres. Unlike correlation functions in space, frequency, and time, for which the corresponding parameter may be unbounded and the field correlation function vanishes asymptotically with increasing parameter shift, the polarization variable is of finite range and the field correlation function vanishes when either the source or detector is rotated by 90 degrees. This facilitates an unambiguous experimental separation of the intensity correlation function into three components, with a form that is independent of the closeness to the localization threshold. The polarization correlation function depends upon the underlying field correlation function in a manner analogous to that found for the intensity correlation function with displacement [1]. The first component of the intensity correlation function is the product of the square of the field correlation function with shift of either source or detector and dominates intensity fluctuations. The field correlation function is simply the cosine of the angular shift of the polarization of the electromagnetic field. The second component is associated with long-range intensity correlation. It is proportional to the sum of the square of the field correlation function with respect to variation of the source and detector. The third component of the polarization correlation function gives rise to universal conductance fluctuations. It is the sum of a multiplicative and additive term involved in the short and long-range contributions to the correlation function and also includes a constant term, which is independent of polarization. Thus, the functional form of the intensity correlation function with polarization is remarkably simple. It is determined exclusively by the cosine of the angular shift of the polarization of the electric field at the source and detector.