We precisely determine the dispersion of an optical cavity over a large spectral bandwidth using a broadband optical comb generated by a femtosecond laser. This approach permits the effective characterization of the next generation of mirrors that will offer high reflectivity, minimal absorption/scattering loss, and well-defined dispersion characteristics. Such mirrors are essential for constructing passive, high-finesse cavities capable of storing and enhancing ultrashort pulses and for exploring novel intracavity-based experiments in atomic and molecular spectroscopy and extreme nonlinear optics. We characterize both zero and negative group-delay-dispersion mirrors and compare their performance against the targeted coating design. The high sensitivity of this approach is demonstrated with a precise determination of the group-delay dispersion of air inside a 40-cm long optical cavity, demonstrating an accuracy better than 1 fs2.
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