Sensitive and broadband measurement of dispersion in a cavity using a Fourier transform spectrometer with kHz...

Optical cavities provide high sensitivity to dispersion since their resonance frequencies depend on the index of refraction. We present a direct, broadband, and accurate measurement of the modes of a high finesse cavity using an optical frequency comb and a mechanical Fourier transform spectrometer with a kHz-level resolution. We characterize 16000 longitudinal cavity modes spanning 16 THz of bandwidth in terms of center frequency, linewidth, and amplitude. Using the center frequencies we retrieve the group delay dispersion of the cavity mirror coatings and pure N₂ with 0.1 fs² precision and 1 fs² accuracy, as well as the refractivity of the 3ν₁ + ν₃ absorption band of CO₂ with 5 × 10^-12 precision. This opens up for broadband refractive index metrology and calibration-free spectroscopy of entire molecular bands.