Stabilizing the free spectral range of a large ring laser

A ring laser is defined by its perimeter, which directly enters the conversion factor between measured Sagnac frequency and the actual rotation rate. Large ring lasers employed in geodesy and fundamental physics require stability of the perimeter at or below the parts-per-billion level. We present two complementary approaches to actively control the perimeter length of such ring lasers, reaching a relative length stability of $4\times 10^{-10}$. One of these approaches is based on a phase detection between the beat of two resonances of different longitudinal mode index and a stable local oscillator. The other approach employs a highly stable wavelength meter to measure the absolute frequency of the laser light. These methods can readily be implemented and bring the stability of heterolithic devices on par with monolithic designs.