Maximization of the optical intra-cavity power of whispering-gallery mode resonators via coupling prism

In this paper, a detailed description of the optical coupling into a Whispering Gallery Mode (WGM) resonator through a prism via frustrated total internal reflection (FTIR) is presented. The problem is modeled as three media with planar interfaces and closed expressions for FTIR are given. Then, the curvature of the resonator is taken into account and the mode overlap is theoretically studied. A new analytical expression giving the optimal geometry of a disc-shaped or ring-shaped resonator for maximizing the intra-cavity circulating power is presented. Such expression takes into consideration the spatial distribution of the WGM at the surface of the resonator, thus being more accurate than the currently used expressions. It also takes into account the geometry of the prism. It is shown an improvement in the geometry values used with the current expressions of about 30%. The reason why the pump laser signal can be seen in experiments under critical coupling is explained on this basis. Then, the conditions required for exciting the highest possible optical power inside the resonator are obtained. The aim is to achieve a highly-efficient up-conversion of a THz signal into the optical domain via the second-order nonlinearity of the resonator material.