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.

💡 Research Summary

The paper addresses a critical limitation in large heterolithic ring lasers used for high‑precision rotation sensing: the long‑term stability of the resonator perimeter, which directly determines the free spectral range (FSR) and thus the scale factor of the Sagnac frequency measurement. The authors present two complementary active control schemes that reduce perimeter fluctuations to the few‑nanometre level, corresponding to relative stabilities of 4 × 10⁻¹⁰ and better.

The experimental platform is a square helium‑neon ring laser with 3.5 m sides (≈ 14 m total perimeter), a finesse of ~40 000, and an FSR of 21.423 199 Hz. About 3.5 ppm of the counter‑propagating beams is extracted and used for feedback. One feedback loop, termed the “absolute frequency lock,” sends ~40 nW of light to a HighFinesse WS8 wavelength meter. The meter provides a 0.1 MHz resolution and 2 MHz absolute accuracy, but requires a 4 s integration time, limiting the loop bandwidth to 0.25 Hz. The measured absolute frequency f_L is compared to a set point in a digital PID controller, which drives a high‑voltage amplifier and a piezo actuator attached to one cavity mirror. This scheme compensates slow drifts of the laser frequency (≈ 1 MHz h⁻¹) and suppresses perimeter changes to about 9.9 nm (≈ 7.1 × 10⁻¹⁰ relative).

The second loop, the “FSR phase lock,” exploits the fact that the He‑Ne gain bandwidth (~1.8 GHz) allows simultaneous lasing on several longitudinal modes. By slightly over‑driving the discharge, a weak secondary mode appears exactly four FSRs away from the main carrier (4 · f_FSR ≈ 85.69 MHz). This beat note is detected with a 400 MHz bandwidth avalanche photodiode, filtered, and amplified to achieve a signal‑to‑noise ratio > 25 dB. The beat is mixed with a low‑phase‑noise RF reference derived from a Stanford FS725 atomic clock, and the resulting phase error (±0.8 V rad⁻¹) is fed to a PID controller that drives the same piezo actuator. The loop stabilizes the FSR to better than 1 Hz, which translates to a perimeter stability of 5.8 nm (≈ 4.1 × 10⁻¹⁰ relative). The bandwidth is limited to ~17 Hz by the mass of the 10 kg mirror mount; the authors note that a lighter, mirror‑only piezo could raise this to the acoustic regime (~2 kHz).

Performance is evaluated over four‑hour night‑time runs. Without any lock, the absolute laser frequency drifts linearly at ~25 MHz h⁻¹ and exhibits frequent mode hops (often by one or two FSRs), causing large, non‑stationary fluctuations in the Sagnac beat frequency (≈ 311 Hz). Both locking schemes eliminate mode hops and reduce frequency fluctuations: the absolute‑frequency lock yields a standard deviation of 334 kHz (≈ 9.9 nm perimeter change), while the FSR phase lock achieves 196 kHz (≈ 5.8 nm). Allan deviation analysis of the Sagnac signal shows that the FSR phase lock reaches a minimum of 280 prad s⁻¹ at 250 s integration (≈ 5 × 10⁻⁶ Ω_E), whereas the unlocked system’s optimum occurs already at ~80 s. Both active schemes improve the rotation‑sensing sensitivity to 5.5 nrad s⁻¹ Hz⁻¹ᐟ², still above the quantum‑shot‑noise limit of 0.16 nrad s⁻¹ Hz⁻¹ᐟ², mainly due to detector inefficiency and electronic white noise.

The authors conclude that inexpensive, readily implementable control methods can bring heterolithic ring lasers to the same perimeter stability as monolithic devices, removing perimeter drift as a limiting factor for state‑of‑the‑art rotation sensors. Future work will focus on reducing the piezo‑actuated mass to increase control bandwidth, and on actively stabilizing the beam path and mirror angles using position‑sensitive detectors, aiming to approach the quantum‑limited sensitivity. This advancement opens the way for more reliable geodetic, seismological, and fundamental‑physics measurements with large ring lasers.