Hermitian and Non-Hermitian mode coupling in a micro-disk resonator due to stochastic surface roughness scattering

We make use of a phase-sensitive set-up to study the light transmission through a coupled waveguide-microdisk system. We observe a splitting of the transmission resonance leading to an unbalanced doublet of dips. The experimental data are analysed by using a phasor diagram which correlates the real and the imaginary parts of the complex transmission. In addition, detailed features are evidenced by a complex inverse representation of the data which maps ideal resonances into straight lines and splitted resonances into complicated curves. Modelling with finite element method simulations suggests that the splitting and the unbalance is caused by an induced chirality in the propagation of the optical fields in the microdisk due to the interplay between the stochastic roughness and the inter-modal dissipative coupling which yield an asymmetric behavior. An analytical model based on the temporal coupled mode theory shows that both a reactive and a dissipative coupling of the counter-propagating modes by the surface roughness of the ring resonator are required to quantitatively reproduce the experimental observations and the numerical simulations.