New Transition to Ray Optics

It is shown that it is possible to make a transition from the vector wave equation to ray optics. However, because of the possibility of polarization of the waves, it is no longer true that the rays will be normal to a given wave surface, $\varphi \mathrm{}\left(x\right)=\mathrm{constant}$. In place of the usual curl-free velocity field that is defined by a scalar wave equation we find that the new velocity field depends upon parameters that express its vorticity. The expression for the velocity, and thus the direction of the rays, agrees in magnitude and direction with the time-averaged Poynting vector, except for a term that is the curl of a vector, and which can be interpreted as the intrinsic vorticity of the medium.