Strongly coupled matter field and nonanalytic decay rate of dipole molecules in a waveguide

The decay rate gamma of an excited dipole molecule inside a waveguide is evaluated for the strongly coupled matter-field case near a cutoff frequency omega(c) without using perturbation analysis. Because of the singularity in the density of photon states at the cutoff frequency, we find that gamma depends nonanalytically on the coupling constant g as g(4/3), which leads to a vast increase in the decay rate.