Nonlinear optics in spheres: from second harmonic scattering to quasi-phase matched generation in whispering gallery modes

Over the last fifteen years, a series of theoretical and experimental investigations have demonstrated the usefulness of circular geometries to tailor second-order nonlinear optical effects. However, until recently, such effects have remained rather weak, calling for their enhancement. In parallel, developments in the field of high quality factor spherical or ring resonators have shown that many different types of light-matter interactions can be dramatically amplified when light is coupled in the whispering gallery modes of such resonators. In high-quality spherical micro-resonators, close to one million interactions can occur between a nonlinear molecule and a circulating light pulse. Recent research on nonlinear optics in spherical geometry is reviewed, from micrometer-size spheres to whispering gallery mode resonators.