Electromagnetic fields in a three-dimensional cavity and in a waveguide with oscillating walls

We consider classical and quantum electromagnetic fields in a three-dimensional cavity and in a waveguide with oscillating boundaries of the frequency Omega. The photons created by the parametric resonance are distributed in the wavenumber 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. In the case of two opposite walls oscillating with the same frequency but with a phase difference, the interferences are shown to occur because of the phase difference in the photon numbers and in the intensity of the generated waves.