Designing and engineering microresonator dispersion are essential for generating microresonator frequency comb. Microresonator frequency combs (microcombs, Kerr frequency combs) offer the potential for various attractive applications as a new type of coherent light source that is power efficient and compact and has a high repetition rate and a broad bandwidth. They are easily driven with a continuous-wave pump laser with adequate frequency tuning; however, the resonators must have a high quality (Q) factor and suitable dispersion. The emergence of cavity enhanced four-wave mixing, which is based on third-order susceptibility in the host material, results in the generation of broadband and coherent optical frequency combs in the frequency domain equivalent to an optical pulse in the time domain. The platforms on which Kerr frequency combs can be observed have been developed, thanks to intensive efforts by many researchers over a few decades. Ultrahigh-Q whispering gallery mode (WGM) microresonators are one of the major platforms since they can be made of a wide range of material including silica glass, fluoride crystals and semiconductors. In this review, we focus on the dispersion engineering of WGM microresonators by designing the geometry of the resonators based on numerical simulation. In addition, we discuss experimental methods for measuring resonator dispersion. Finally, we describe experimental results for Kerr frequency combs where second- and higher-order dispersions influence their optical spectra.
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