| A structure consisting of N coupled optical resonators exhibits resonances that split into N higher-Q modes due to coherent coupling between resonators. This has a direct analogy with other types of oscillators. In particular, for two (or any even number of) coupled optical resonators, this mode splitting leads to a cancellation of absorption on resonance as a result of classical destructive interference of the symmetric and antisymmetric modes of the system. An analogy between this effect and electromagnetically-induced transparency in an atomic system is explored. Furthermore, a variety of photonic coherence phenomena in passive and active coupled optical resonators is investigated. Specifically, the effective dispersive and absorptive steady-state response of coupled resonators is derived and used to determine the conditions for coupled-resonator-induced transparency and absorption, lasing without gain, and cooperative cavity emission. These effects rely on coherent photon trapping, in direct analogy with coherent population trapping phenomena in atomic systems. It is also demonstrated that the coupled-mode equations are formally identical to the two-level atom Schrodinger equation in the rotating-wave approximation. The impulse response of coupled resonators is also derived. It is found that the coupled-resonator photon dynamics display damped Rabi oscillations, which facilitates adiabatic coherent photon transfer techniques such as stimulated Raman adiabatic passage. These effects are predicted directly from coupled-mode theory, and thus are not unique to atoms, but rather are fundamental to systems of coherently coupled resonators. It is also theoretically predicted that in coupled optical resonators slow and fast light can propagate without attenuation. In systems of coupled resonators, slow light can propagate without attenuation by a cancellation of absorption as a result of mode splitting and destructive interference, whereas transparent fast light propagation can be achieved with the assistance of gain and splitting of the intracavity resonances, which consequently switches the dispersion from normal to anomalous. |
