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Stabilizing the free spectral range of a large ring laser

The paper presents two complementary active control methods—phase detection between longitudinal mode beats and absolute frequency measurement via a stable wavelength meter—that achieve a relative perimeter stability of $4\times 10^{-10}$ in large ring lasers, thereby matching the performance of monolithic designs.

Original authors: Jannik Zenner, Karl Ulrich Schreiber, Simon Stellmer

Published 2026-03-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jannik Zenner, Karl Ulrich Schreiber, Simon Stellmer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to measure the rotation of the Earth with a giant, high-tech hula hoop made of light. This is essentially what a ring laser does. It sends two beams of light racing around a square track in opposite directions. Because the Earth is spinning, one beam has to run a tiny bit further than the other to catch up, creating a "beat" or a wobble in the sound of the light. By measuring this wobble, scientists can calculate exactly how fast the Earth is turning.

However, there's a catch: The track itself is wobbly.

Just like a rubber band stretches when the temperature changes or the ground shifts, the physical size of this laser's square track (its perimeter) changes by a few nanometers (billionths of a meter). If the track stretches, the math gets messed up, and the measurement of Earth's spin becomes inaccurate.

This paper, written by researchers from the University of Bonn and others, is about building a super-stable "shrink-wrap" for this giant light-hula-hoop to keep its size perfectly constant.

Here is how they did it, explained with everyday analogies:

The Problem: A Stretchy Rubber Band

Think of the ring laser as a giant rubber band track. If the rubber band stretches even a tiny bit, the time it takes for the runners (the light beams) to finish a lap changes. In the world of precision physics, a stretch of a few nanometers is like a runner tripping over a pebble—it ruins the race time.

The scientists wanted to keep the track size stable to within 4 parts per billion. To put that in perspective: if the track were the size of the Earth, they wanted to keep its size stable to within the width of a human hair.

The Solution: Two Different "GPS" Systems

The team built two different ways to constantly check the track size and fix it instantly. They used a giant, invisible robotic arm (called a piezo actuator) attached to the mirrors that hold the track together. If the track gets too long, the arm pushes the mirrors closer; if it gets too short, it pulls them apart.

Here are the two "GPS" systems they used to tell the robotic arm what to do:

1. The "Ruler" Method (Absolute Frequency Lock)

Imagine you have a magical ruler that measures the color of the light.

How it works: The scientists take a tiny bit of the laser light and run it through a device called a wavelength meter (the magical ruler). This ruler tells them the exact "color" (frequency) of the light.
The Logic: If the track stretches, the light's color changes slightly. The ruler sees this change and yells, "Hey! The track got longer! Push the mirrors in!"
The Flaw: This ruler is a bit slow. It takes a few seconds to get a good reading, so the corrections happen slowly. It's like checking your GPS every 30 seconds while driving; you might overshoot a turn before you realize you need to correct.

2. The "Echo" Method (FSR Phase Lock)

Imagine you are in a canyon and you clap your hands. You hear an echo. The time it takes for the echo to return depends on the size of the canyon.

How it works: Inside the laser, the light bounces around the track. The scientists listen to the "echo" of the light waves. Specifically, they listen to the "beat" between two different notes of light. This beat frequency is directly tied to the size of the track.
The Logic: They compare this "echo beat" to a super-stable, perfect clock (an atomic clock). If the beat gets out of sync with the clock, it means the track has changed size.
The Advantage: This method is much faster. It's like having a GPS that updates every millisecond. The robotic arm can make tiny, instant adjustments to keep the track perfectly sized.

The Results: A Rock-Solid Track

When they tested these methods, the results were amazing:

Without the fix: The track size drifted, and the measurements of Earth's rotation were shaky and full of "jumps" (glitches).
With the fix: The track became incredibly stable. The "jumps" disappeared, and the measurements became smooth and precise.

They managed to stabilize the track so well that the laser is now as stable as the best, most expensive, single-piece (monolithic) lasers in the world, but built from separate parts (heterolithic).

Why Does This Matter?

Think of this technology as upgrading from a paper map to a live, high-definition satellite view of the Earth's rotation.

For Geologists: It helps them "see" earthquakes and volcanic shifts in real-time by detecting the tiny wobbles in Earth's spin caused by these events.
For Physicists: It allows them to test the fundamental laws of the universe with extreme precision.

In short, the scientists built a "smart shrink-wrap" for a giant light-ring. By using two clever ways to measure the ring's size and a robotic arm to fix it instantly, they turned a wobbly, stretchy track into a perfectly rigid ruler for measuring the spinning Earth.

1. Problem Statement

Large ring lasers are critical instruments for geodesy, seismology, and fundamental physics, utilizing the Sagnac effect to measure Earth's rotation and other geophysical signals with extreme precision. The accuracy of these measurements depends directly on the scale factor, which is determined by the ring's perimeter ( $P$ ) and enclosed area ( $A$ ).

The Challenge: For heterolithic ring lasers (constructed from separate components rather than a single monolithic block), mechanical instabilities cause the perimeter to drift. To achieve the required sensitivity for modern applications, the perimeter must be stable at the parts-per-billion (ppb) level or better.
Current Limitations: While active stabilization of the perimeter has been demonstrated for passive ring resonators, it has not been successfully applied to active ring lasers (where the gain medium is inside the cavity). Without stabilization, drifts in the perimeter lead to fluctuations in the Free Spectral Range (FSR) and the Sagnac frequency, causing mode hops and limiting measurement sensitivity.

2. Methodology

The authors developed and tested two complementary active stabilization methods on a square ring laser with a side length of approximately 3.5 meters (total perimeter $P \approx 14$ m). The setup uses a piezoelectric transducer (PZT) attached to a cavity mirror holder to adjust the perimeter dynamically.

The two stabilization approaches are:

A. Absolute Frequency Lock

Principle: Stabilizes the absolute frequency of the laser light ( $f_L$ ).
Implementation:
- A fraction of the transmitted light is coupled into a HighFinesse WS8 wavelength meter (WLM).
- The WLM measures the absolute frequency with a resolution of 0.1 MHz and an accuracy of ~2 MHz.
- A digital PID (Proportional-Integral-Derivative) controller compares the measured frequency to a reference and drives a high-voltage amplifier to adjust the PZT.
Limitations: The integration time required for the WLM (4 seconds per data point) limits the control loop bandwidth to 0.25 Hz. This makes the system susceptible to faster drifts and limits the resolution due to the WLM's inherent noise.

B. FSR Phase Lock

Principle: Stabilizes the Free Spectral Range ( $f_{FSR} = c/P$ ) directly, which inherently stabilizes the perimeter.
Implementation:
- The laser is operated in a regime where a secondary longitudinal mode exists at $4 \times f_{FSR}$ (approx. 85.7 MHz) alongside the main carrier.
- This beat signal is detected by a high-bandwidth Avalanche Photodetector (APD), filtered, and amplified.
- The signal is compared against a highly stable RF reference (derived from an atomic clock) using a phase detector.
- The resulting error signal (proportional to the phase difference) is fed to a PID controller to steer the PZT.
Advantages: This method offers a much faster response. The bandwidth is limited by the mechanical inertia of the mirror mount (~17 Hz) rather than the measurement integration time, allowing for the suppression of faster drifts.

3. Key Contributions

First Active Stabilization of Ring Lasers: This work presents the first demonstration of active perimeter stabilization specifically for a ring laser (as opposed to passive resonators).
Dual-Approach Validation: The authors provide a comparative analysis of two distinct locking strategies, demonstrating that both can achieve sub-nanometer stability.
Performance Benchmarking: The study quantifies the improvement in stability and sensitivity, showing that heterolithic devices can now match the stability of quasi-monolithic designs (like the C-II and G ring lasers).

4. Results

The authors conducted four-hour measurement intervals comparing three states: unlocked, absolute frequency locked, and FSR phase locked.

Perimeter Stability:
- Unlocked: The laser frequency drifted linearly at 25 MHz/h, causing mode hops.
- Absolute Frequency Lock: Reduced frequency fluctuations to a standard deviation of 334 kHz, corresponding to a perimeter stability of $\Delta P \approx 9.9$ nm ( $7.1 \times 10^{-10}$ relative stability).
- FSR Phase Lock: Achieved superior performance with frequency fluctuations of 196 kHz, corresponding to $\Delta P \approx 5.8$ nm ( $4.1 \times 10^{-10}$ relative stability).
Sagnac Frequency ( $\delta f$ ) Stability:
- Unlocked: Characterized by large drifts and discontinuous jumps caused by mode hopping and backscatter coupling changes.
- Locked: Both methods eliminated mode hops. The FSR phase lock was most effective at reducing residual drifts in the Sagnac frequency.
Allan Deviation (Sensitivity):
- The sensitivity of the ring laser improved significantly with stabilization.
- FSR Phase Lock: Achieved the best stability with an Allan deviation minimum at 250 s integration time, reaching a sensitivity of 5.5 nrad/s/ $\sqrt{\text{Hz}}$ (or 280 prad/s at 250 s).
- This represents a factor of two improvement in sensitivity compared to the unlocked state.
- The theoretical limit (shot noise) is 0.16 nrad/s/ $\sqrt{\text{Hz}}$ ; the experimental limit is currently constrained by photodetector efficiency and electronic white noise.

5. Significance

Enabling Heterolithic Designs: This research proves that large, cost-effective heterolithic ring lasers can achieve stability levels comparable to expensive, quasi-monolithic designs. This opens the door for deploying high-precision ring lasers in more locations for global geophysical monitoring.
Geodesy and Seismology: By stabilizing the scale factor, these instruments can reliably detect low-frequency geophysical signals (such as Earth tides and seismic rotations) without being obscured by instrumental drift.
Future Roadmap: The authors note that while perimeter stability is now sufficient, future work will focus on stabilizing the beam path (using position-sensitive detectors) and correcting for local tilt and beam wander to push sensitivity closer to the quantum shot-noise limit.

In conclusion, the paper demonstrates that active stabilization of the Free Spectral Range is a robust and effective method for maintaining the integrity of large ring lasers, enabling them to reach the $10^{-10}$ stability regime required for next-generation fundamental physics and geodesy experiments.