The photon vortex beam in rotating medium

In this paper, we demonstrate that there are vortex beam solutions for the photon in the rotating medium. By constructing the photon wave function with Riemann-Silberstein vector, we derive the dynamic equation of the photon in moving medium from the Maxwell equations and the non-relativistic Minkowski relations. In case of the stationary state, the dynamic equation of the photon can be written as a Dirac-like equation, where the velocity of the medium plays the role of a vector potential. By giving the medium different forms of rotating velocity fields, we obtain different vortex beam solutions of the photon, such as the diffracting and non-diffracting Laguerre-Gaussian (LG) beam solutions via proper approximations. For the diffracting LG beam solution, we acquire a new term arising from the medium rotation that can change the Gouy phase, and then accordingly predict the rotation behavior of the photon interference pattern. In addition, the rotation of the medium can lead to the change of the relative intensity distribution of the interference pattern. Furthermore, our theory predicts the existence of the Landau levels of transverse photon energy in the nondiffracting LG beam solution.