Off-diagonal photonic Lamb shift in reactively coupled waveguide-resonator system

We report on a joint theoretical and experimental study of an analogue of the Lamb shift in the photonic framework. The platform is an integrated photonic device consisting of a single mode waveguide vertically coupled to a disk-shaped microresonator. The presence of a neighboring waveguide induces a reactive inter-mode coupling in the resonator, an effect analogous to an off-diagonal Lamb shift from atomic physics. Waveguide mediated coupling of different radial families results in peculiar Fano lineshapes in the waveguide transmission spectra, which manifests for different relative frequency shifts of the modes at different azimuthal numbers. Finally, a non-linear model for the dinamic tuning of the Fano lineshape under continuous wave pumping conditions is proposed.