Motion-Induced Radiation from a Dynamically Deforming Mirror

A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the height function. For a harmonic traveling wave on the surface, we find many different regimes in which the radiation is restricted to certain directions. It is shown that high frequency photons are emitted in a beam with relatively low angular dispersion whose direction can be controlled by the mechanical deformations of the plate.