Perturbative approach to Dynamical Casimir effect in an interface of   dielectric mediums
  Electromagnetic field quantization in the presence of two semi-infinite dielectrics with moving interface is investigated in $1+1$-dimensional space-time. The moving interface is modeled for small displacements and the field equation is solved perturbatively. Input-output relations and spectral distribution of emitted photons are obtained and the effect of small transitions trough the interface discussed. 
Vahid Ameri, Mohammad Eghbali-Arani, and Morteza Soltani
quant-ph