Motion-induced radiation from a dynamically deforming mirror: Neumann boundary condition

We study the dynamical Casimir effect for a scalar field satisfying the (generalized) Neumann boundary condition on a deforming mirror. The angular distribution and the spectrum of radiation is calculated to second order in the deformation amplitude. For a harmonic traveling wave on the surface, we find two cusps in the radiation spectrum. There are several regimes in which the radiation is restricted to particular directions. The position of the cusps and the radiation window at a certain frequency can be tuned by the mechanical deformation. The number of emitted photons is much larger than for the Dirichlet boundary condition