What is the linear momentum of an EM wave in a medium?

Question

In free space, the linear momentum density of an EM wave is given by the Poynting vector $\vec S$ over the speed of light squared, $\vec g=\frac{\vec S}{c^2}$.

In a medium, $S$ is generally not directed along the wave vector $\vec k$. If $v_g$ is the group velocity and $W$ is the density of EM wave energy, then $S = v_g W$. On the other hand, it is often assumed that the momentum of a photon is still $\hbar\vec k$. What is the macroscopic momentum density of EM wave in an anisotropic medium such as magnetized plasma ?

Answer 1

Best description of the problem of those I found is given by Nobel winner Vitaly Ginzburg. See, e.g.

http://ufn.ru/en/articles/1973/3/k/

or (even better)

VL Ginzburg, Theoretical Physics and Astrophysics (Pergamon, Oxford, 1979); other editions with somewhat different titles also available.