Dependence of quality factor on surface roughness in crystalline whispering-gallery mode resonators

We present an experimental study of the variation of quality factor (Q-factor) of WGM resonators as a function of surface roughness. We consider mm-size whispering-gallery mode resonators manufactured with fluoride crystals, featuring Q-factors of the order of 1 billion at 1550 nm. The experimental procedure consists of repeated polishing steps, after which the surface roughness is evaluated using profilometry by white-light phase-shifting interferometry, while the Q-factors are determined using the cavity-ring-down method. This protocol permits us to establish an explicit curve linking the Q-factor of the disk-resonator to the surface roughness of the rim. We have performed measurements with four different crystals, namely, magnesium, calcium, strontium, and lithium fluoride. We have thereby found that 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 also discuss our experimental results in the light of theoretical estimates of surface scattering Q-factors already published in the literature.