Quantitative phase imaging for surface roughness measurements to demonstrate variation of quality factor in crystalline whispering-gallery mode resonators

An experimental study of the variation of quality factor (Q-factor) of mm-size whispering-gallery mode (WGM) resonators manufactured with fluoride crystals as a function of surface roughness is proposed. Q-factors of the order of 1 billion are measured at 1550 nm. The experimental procedure needs repeated polishing steps, after which the surface roughness is measured by quantitative phase imaging, based on a white-light phase-shifting interferometry approach, while the Q-factors are determined using the cavity-ring-down method. This process allows us to reach an explicit curve linking the Q-factor of the disk-resonator to the surface roughness of the rim. The variations of Q-factor as a function of surface roughness is universal, in the sense that it is globally independent of the bulk material under consideration. We used a white-light interferometer to investigate the dependency of Q-factors considering three different difluoride crystals as bulk materials; in all cases, we have found that a billion Q-factors at 1550 nm are achieved when the rms surface roughness has a nanometer order of magnitude. We have also compared our experimental data with theoretical estimations. This comparison enabled us to highlight a mismatch, which can be explained by the many physical constraints imposed by the mechanical grinding and polishing protocol. We expect that our work will contribute to a better understanding of the Q-factor limitations for mm-size WGM resonators, which are finding applications in a broad range of areas