Resonantly enhanced second and third harmonic generation in microfibre loop resonators

Due to their strong modal confinement, optical microfibres (OMs) provide an excellent opportunity for studying nonlinear effects and in particular intermodally phase matched second (SHG) and third (THG) harmonic generation with predicted efficiencies up to 10^-1 over several cm in an ideal uniform silica OM for both cases. Experimentally however, fabricating the required phase matching diameter uniformly over such lengths remains challenging. A simple solution is to reconfigure the OM as a resonator, such that pump recirculation near resonance increases conversion without the need for higher power sources or OM lengths greater than a few mm. Here, we theoretically study surface-SHG and THG in OM loop resonators by numerically solving the underlying coupled mode equations to determine the dependence of the enhancement on the resonance properties.