Microwave cavity light shining through a wall optimization and experiment

It has been proposed that microwave cavities can be used in a photon regeneration experiment to search for hidden sector photons. Using two isolated cavities, the presence of hidden sector photons could be inferred from a 'light shining through a wall' phenomenon. The sensitivity of the experiment has strong a dependence on the geometric construction and electromagnetic mode properties of the two cavities. In this paper we perform an in depth investigation to determine the optimal setup for such an experiment. We also describe the results of our first microwave cavity experiment to search for hidden sector photons. The experiment consisted of two cylindrical copper cavities stacked axially inside a single vacuum chamber. At a hidden sector photon mass of 37.78 micro eV we place an upper limit on the kinetic mixing parameter chi = 2.9 * 10^(-5). Whilst this result lies within already established limits our experiment validates the microwave cavity `light shining through a wall' concept. We also show that the experiment has great scope for improvement, potentially able to reduce the current upper limit on the mixing parameter chi by several orders of magnitude.