Stabilizing the free spectral range of a large ring laser

TL;DR

This paper addresses the need for stable ring-laser perimeters to ensure accurate Sagnac-rotation measurements in large interferometers. It presents two complementary perimeter-stabilization strategies: an absolute frequency lock that tracks the laser’s absolute frequency $f_L$ via a wavemeter, and an FSR phase lock that stabilizes the perimeter by locking a beat at $4 f_{FSR}$ against a stable RF reference. Both approaches achieve a relative length stability of $4\times 10^{-10}$ and significantly improve Sagnac stability, with Allan deviations reaching about $5.5$ nrad s$^{-1}$ sqrt(Hz) at 250 s. The methods are cost-effective, compatible with heterolithic designs, and pave the way for high-precision rotation sensing in geodesy and fundamental physics without requiring fully monolithic construction.

Abstract

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.

Figures (4)

• Figure 1: Schematic view of the setup to stabilize the perimeter of the ring laser cavity using either the absolute frequency lock or FSR phase lock method (left-hand side corner) and to measure the Sagnac frequency (right-hand side corner). Abbreviations: AMP radio frequency amplifier, APD avalanche photodetector, BS beamsplitter, DIC directional coupler, FC fiber coupler, PHD phase detector, PID proportional-integral-derivative controller, PZT piezo actuator, RFG radio frequency generator, WLM wavelength meter.
• Figure 2: a) Absolute frequency of the ring laser $f_{\text{L}}$, shifted by $f_{\text{L}_{0}} =$ 473.612T Hz, as measured by the wavelength meter with a rate of 0.25Hz for unlocked operation, for the absolute frequency lock (in-loop) and for the FSR phase lock (out-of-loop). b) Beat of the free spectral range $f_{\text{FSR}}$, shifted by $f_{\text{FSR}_{0}} =$ 21.4232M Hz, for unlocked operation, for the absolute frequency lock (out-of-loop) and for the FSR phase lock (in-loop).
• Figure 3: Sagnac frequency $\delta f$, plotted with a running mean average of 100s interval length.
• Figure 4: Classic Allan deviations of the measured Sagnac frequency time series shown in Fig. \ref{['fig:sagnac']}. The data is normalized to Earth's rotation rate $\Omega_{\text{E}}$ according to Eq. \ref{['align:sag']}. The sensitivity of $\sigma_{\delta f} =\mathrm{5.5n rad \per s \per \sqrt{Hz}}$ is marked with a dashed line.