Complex polarization in non z-cut whispering gallery mode resonators

Birefringent crystals like lithium niobate show a very strong χ⁽²⁾ non-linear response and have thus been used in a whispering galley mode (WGM) supporting geometry to achieve extremely high conversion efficiencies[1,2]. In a uniaxial crystal, light is split into two different eigenpolarizations showing different phase velocities. Usually the WGM resonators are fabricated such that the optic axis is parallel to the symmetry axis, such that there are still two mode families of parallel (perpendicular) polarization with respect to the optic axis, namely TE (TM) modes, which “feel” the extraordinary (ordinary) index of refraction of the material respectively. The dispersion between these two types of modes can be exploited to achieve phasematching in nonlinear processes.