Electromagnetic fields in a 3D cavity and in a waveguide with oscillating walls

We consider classical and quantum electromagnetic fields in a three-dimensional (3D) cavity and in a waveguide with oscillating boundaries of the frequency $\Omega $. The photons created by the parametric resonance are distributed in the wave number space around $\Omega/2 $ along the axis of the oscillation. When classical waves propagate along the waveguide in the one direction, we observe the amplification of the original waves and another wave generation in the opposite direction by the oscillation of side walls. This can be understood as the classical counterpart of the photon production. In the case of two opposite walls oscillating with the same frequency but with a phase difference, the interferences are shown to occur due to the phase difference in the photon numbers and in the intensity of the generated waves.