Shining massive light through a wall

A massive photon possesses a longitudinal polarization mode absent in its massless counterpart. Transverse and longitudinal modes follow different dispersion relations, the latter being much less attenuated than the former when passing through a conductor, suggesting the possibility of isolating longitudinal modes by shining intense light on a conducting wall. We calculate the transmission rates for normal incidence upon a semi-infinite medium and passage through a slab. For the second case we compare the expected photon fluxes with those measurable in current and future light-shining-through-a-wall experiments. Using a 1-MW microwave source as envisaged by the STAX project, a sensitivity at the level of $m_\gamma < 9.6 \times 10^{-11} \, {\rm eV/c^2}$ could be reached after a run time of an year, with a potential improvement by a factor of $\sim 10^4$ if radio waves of similar power are used.