Statistical similarity and cross-spectral purity of stationary stochastic fields

In practical situations, one often generates a beam by superposition of two or more light beams. The beam generated by superposition displays, in general, different spectral properties than do the original beams. However, there are some optical beams, called cross-spectrally pure beams, which can generate a light beam of identical spectral distribution on superposition. The relationship between cross-spectral purity and spatial coherence has been the subject of investigations for some time. Recently, a concept of so-called statistical similarity has been introduced which provides a new way to elucidate complete spatial coherence. In this Letter, we discuss some implications of statistical similarity of an optical field on its cross-spectral purity.