Purcell effect and Lamb shift as interference phenomena

The Purcell effect and Lamb shift are two well-known physical phenomena which are usually discussed in the context of quantum electrodynamics, with the zero-point vibrations as a driving force of those effects in the quantum approach. Here we discuss the classical counterparts of these quantum effects in photonics, and explain their physics trough interference wave phenomena. As an example, we consider a waveguide in a planar photonic crystal with a side-coupled defect, and demonstrate a perfect agreement between the results obtained on the basis of quantum and classic approaches and reveal their link to the Fano resonance. We find that in such a waveguide-cavity geometry the Purcell effect can modify the lifetime by at least 25 times, and the Lamb shift can exceed 3 half-widths of the cavity spectral line.