Reply to Comment on "System-environment coupling derived by Maxwell's boundary conditions from the weak to the ultrastrong light-matter-coupling regime"

As mentioned by Simone De Liberato [arXiv:1307.5615], when we suppose the metallic thin mirror and perform the renormalization additionally to the approach starting from the frequently-used system-environment coupling Hamiltonian, we can certainly resolve the discrepancy of its result from that obtained by the reliable approach in the main discussion of our paper [Phys. Rev. A 88, 013814 (2013), arXiv:1301.3960]. Although the suggested approach is currently applicable to the specific situation after checking its validity by our reliable but cumbersome approach, we instead propose to start from the system-environment coupling Hamiltonian determined properly by the mechanism of the confinement and loss of the cavity fields. This approach is applicable to any cavity structures in principle, and we do not face the renormalization problem appearing in the comment.