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Optical whispering gallery mode (WGM) resonators have been very attractingplatforms for versatile Kerr frequency comb generations. We report a systematicstudy on the material dispersion of various optical materials that are capableof supporting quality factors above $10^9$. Using an analytical approximationof WGM resonant frequencies in disk resonators, we investigate the effect ofthe geometry and transverse mode order on the total group-velocity dispersion($GVD$). We demonstrate that the major radii and the radial mode indices playan important role in tailoring the $GVD$ of WGM resonators. In particular, ourstudy shows that in WGM disk-resonators, the polar families of modes have verysimilar $GVD$, while the radial families of modes feature dispersion valuesthat can differ by up to several orders of magnitude. The effect of these giantdispersion shifts are experimentally evidenced in Kerr comb generation withmagnesium fluoride. From a more general perspective, this critical featureenables to push the zero-dispersion wavelength of fluorite crystals towards themid-infrared (mid-IR) range, thereby allowing for efficient Kerr combgeneration in that spectral range. We show that barium fluoride is the mostinteresting crystal in this regard, due to its zero dispersion wavelength($ZDW$) at $1.93 \rm{\mu m}$ and an optimal dispersion profile in the mid-IRregime. We expect our results to facilitate the design of different platformsfor Kerr frequency comb generations in both telecommunication and mid-IRspectral ranges.

optics express

On the dispersion management of fluorite whispering-gallery mode  resonators for Kerr optical frequency comb generation in the telecom and  mid-infrared range