Electromagnetic Theory of Optical Coherence

Almost half a century has passed since the polarization of light beams and the theory of optical coherence, in classical and quantized forms, were formulated in a systematic manner. In a classic paper published in 1955, Emil Wolf introduced the two-point space-time correlation function, now known as the mutual function, and showed that in free space this function obeys two wave equations (see Fig. 1). This demonstrated the fundamental phenomenon that not only the field but also the spatial coherence propagates in the form of waves. In another pioneering work,Wolf analyzed the state of polarization of a light beam in terms of its "coherency matrix" and the now well-familiar Stokes parameters. Using the properties of the 2 × 2 coherence matrix, the degree of polarization could be introduced in an unambiguous manner. The formal theory of space-time coherence of arbitrary stationary electromagnetic fields was put forward in twin papers in 1960 by Roman and Wolf. In these works the four general 3×3 correlation tensors (electric, magnetic, and mixed coherence matrices) were introduced and their properties were analyzed. This research, which took place before or around the time the first lasers were produced, has become the cornerstone of most of the subsequent studies on polarization and electromagnetic coherence. The quantum theory of coherence was formulated soon afterwards.