Unified matrix approach to the description of phase-space rotators

In optics, the rotation of a phase-space can be realized via light propagation through both an inhomogeneous medium with a radial gradient of refractive index and two special kinds of mirror-symmetrical optical systems suggested by Lohmann. Although light propagation through Lohmann's systems is described in terms of matrix optics, light propagation through the gradient-index medium is traditionally described as a solution of the wave equation. The difference in these descriptions hinders the understanding of the phase-space rotators. Fortunately, there is a matrix description of light propagation through a gradient-index medium too. A general description of the phase-space rotators is presented, which can be used to treat light propagation through both Lohmann's systems and the gradient-index medium in a unified matrix manner.