Amplification of OAM radiation by astrophysical masers

We extend the theory of astrophysical maser propagation through a medium with a Zeemansplit molecular response to the case of a non-uniform magnetic field, and allow a component of the electric field of the radiation in the direction of propagation: a characteristic of radiationwith orbital angular momentum. A classical reduction of the governing equations leads to a set of nine differential equations for the evolution of intensity-like parameters for each Fourier component of the radiation. Four of these parameters correspond to the standard Stokes parameters, whilst the other five represent the z-component of the electric field, and its coupling to the conventional components in the x-y-plane. A restricted analytical solution of the governing equations demonstrates a non-trivial coupling of the Stokes parameters to those representing orbital angular momentum: the z-component of the electric field can grow from a background in which only Stokes-I is non-zero. A numerical solution of the governing equations reveals radiation patterns with a radial and angular structure for the case of an ideal quadrupole magnetic field perpendicular to the propagation direction. In this ideal case, generation of radiation orbital angular momentum, like polarization, can approach 100 per cent.