Experimental study on degree of coherence for stochastic electromagnetic fields

Abstract

All optical fields undergo random fluctuation and the degree of coherence defined as the normalized correlation function of optical fields has played a fundamental role as an important manifestation of the underlying random fluctuations. For randomly varying electromagnetic waves, the usual treatment of polarization based on the well-known Stokes parameters or polarization matrices is not adequate and a unified theory of coherence and polarization of random electromagnetic beams has been proposed by Wolf to elucidate the changes of polarization and coherence as the beam propagate. In this paper, a novel optical geometry is proposed based on the polar-interference law of electromagnetic beams with its unique capability to visualize the mutual coherence tensor directly. Note the fact that wave equations govern the propagation of mutual coherence tensor, which can be regarded as a tensor wave. After retrieval of the complex functions for all the elements of coherence tensor from the recorded interferograms, we obtain the magnitude and the unit direction tensor for the coherence tensor wave and demonstrate the degree of coherence for stochastic electromagnetic fields with partial polarization and partial coherence experimentally for the first time.