High-accuracy absolute rotation rate measurements with a large ring laser gyro: establishing the scale factor

Large ring lasers have exceeded the performance of navigational gyroscopes by several orders of magnitude and have become useful tools for geodesy. In order to apply them to tests in fundamental physics, remaining systematic errors have to be significantly reduced. We derive a modified expression for the Sagnac frequency of a square ring laser gyro under Earth rotation. The modifications include corrections for dispersion (of both the gain medium and the mirrors), for the Goos-Hänchen effect in the mirrors, and for refractive index of the gas filling the cavity. The corrections were measured and calculated for the 16  m² Grossring laser located at the Geodetic Observatory Wettzell. The optical frequency and the free spectral range of this laser were measured, allowing unique determination of the longitudinal mode number, and measurement of the dispersion. Ultimately we find that the absolute scale factor of the gyroscope can be estimated to an accuracy of approximately 1 part in 10⁸.