Phase-Array Approach to Optical Whispering Gallery Modulators

Abstract

This technology leverages the well-defined orbital number of a whispering gallery modulator (WGM) to expand the range of applications for such resonators. This property rigidly connects the phase variation of the field in this mode with the azimuthal angle between the coupling locations. A WGM with orbital momentum L has exactly L instant nodes around the circumference of the WGM resonator supporting such a mode. Therefore, in two locations separated by the arc alpha, the phase difference of such a field will be equal to phi= alpha L. Coupling the field out of such locations, and into a balanced interferometer, once can observe a complete constructive or distractive interference (or have any situation in between) depending on the angle alpha. Similarly, a mode L + delta L will pick up the phase phi + alpha delta L. In all applications of a WGM resonator as a modulator, the orbital numbers for the carrier and sidebands are different, and their differences delta L are known (usually, but not necessarily, delta L = 1). Therefore, the choice of the angle alpha, and of the interferometer arms difference, allows one to control the relative phase between different modes and to perform the conversion, separation, and filtering tasks necessary.