  In the standard theory of cavity quantum electrodynamics (QED), coupling
between photons inside and outside a cavity (cavity system and photonic
reservoir) is given conserving the total number of photons. However, when the
cavity photons (ultra)strongly interact with atoms or excitations in matters,
the system-reservoir coupling must be determined from a more fundamental
viewpoint. Based on the Maxwell's boundary conditions in the QED theory for
dielectric media, we derive the quantum Langevin equation and input-output
relation, in which the total number of polaritons (not photons) inside the
cavity and photons outside is conserved.
