  Many theories beyond the Standard Model contain hidden photons. A light
hidden photon will generically couple to the Standard Model through a kinetic
mixing term, giving a powerful avenue for detection using
"Light-Shining-Through-A-Wall"-type transmission experiments with resonant
cavities. We demonstrate a parametric enhancement of the signal in such
experiments, resulting from transmission of the longitudinal mode of the hidden
photon. While previous literature has focused on the production and detection
of transverse modes, the longitudinal mode allows a significant improvement in
experimental sensitivity. Although optical experiments such as ALPS are unable
to take useful advantage of this enhancement, the reach of existing microwave
cavity experiments such as CROWS is significantly enhanced beyond their
published results. Future microwave cavity experiments, designed with
appropriate geometry to take full advantage of the longitudinal mode, will
provide a powerful probe of hidden-photon parameter space extending many orders
of magnitude beyond current limits, including significant regions where the
hidden photon can be dark matter.
