Propagation of mutual intensity expressed in terms of the fractional Fourier transform

The propagation of mutual intensity through quadratic graded-index media or free space can be expressed in terms of two-dimensional fractional Fourier transforms for one-dimensional systems and in terms of fourdimensional fractional Fourier transforms for two-dimensional systems. As light propagates, its mutual intensity distribution is continually fractional Fourier transformed. These results can also be generalized to arbitrary first-order optical systems. Furthermore, the Wigner distribution associated with a partially coherent field rotates in the same manner as the Wigner distribution associated with a deterministic field.