Optical microresonators can provide miniature dimensions, flexibility, and the control needed to deliver breakthrough capabilities in optical computing, communications, and fundamental science. I will first introduce surface nanoscale axial photonic (SNAP) fiber resonators, which properties can be tailored through modulation along the axial dimension. We show how to realize reflectionless potentials to achieve pure phase control of propagating signals, which is important for nonlinear processes. We also derive mode equations for nonlinear SNAP fiber resonators and predict generation of frequency combs with an ultra-fine spacing of hundreds MHz compared to a tens GHz for conventional microscale ring resonators.
I then discuss photonic structures with gain and loss possessing parity-time (PT) symmetry, and present results on light amplification and filtering. PT symmetric SNAP fiber resonators are of great interest for further research.