Generation of cross-spectrally pure electromagnetic fields using a pair of moving diffusers

In this paper, we demonstrate that the vector light field is cross-spectrally pure if it passes through two diffusers (having similar correlation properties) moving with identical linear speeds in opposite directions. To determine the spatio-temporal coherence function of cross-spectrally pure light, a double slit is placed just after the second diffuser. We show that the normalized space-time coherence Stokes parameters of emerging light can be described in the form of a reduction formula, whereas the absolute values of the normalized space-frequency coherence Stokes parameters are the same for every frequency component of the light field. These are the conditions of cross-spectral purity of Stokes parameters. We further prove that at zero time delay, the condition of strict cross-spectral purity is validated. Furthermore, we establish the conditions for cross-spectral purity for a vector light field passing through the aforesaid diffusers, when they rotate with identical angular speeds in opposite directions, offering a possibility to optimize the scheme using only a single diffuser. For the first time, to our knowledge, an additional condition for equality of the degree of cross-polarization in space-time and space-frequency domains for strict cross-spectrally pure light beams is also introduced.