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Hänsch-Couillaud locking of a large Sagnac interferometer: advancing below the flicker floor

This paper presents the first Hänsch-Couillaud locked passive laser gyroscope, introducing a cost-effective lock-in scheme to overcome flicker noise limitations and achieve a sensitivity of 3.1 nrad/s, which represents a significant advancement for large Sagnac interferometers in geophysical sensing.

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

Published 2026-02-12

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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 incredible precision. To do this, scientists use a giant, square-shaped "race track" for light, called a Sagnac interferometer. Think of this track as a 3.5-meter square loop made of mirrors.

In this experiment, scientists shoot two beams of light around this track in opposite directions: one clockwise and one counter-clockwise. If the Earth (and the track) is spinning, one beam has to travel a tiny bit farther than the other to complete the lap. This difference creates a "beat" or a wobble when the two beams meet again. By measuring this wobble, they can calculate exactly how fast the Earth is spinning.

The Problem: The "Static" in the Radio

For years, scientists have tried to keep these light beams perfectly locked to the track using a method called Pound-Drever-Hall (PDH). Imagine trying to tune a radio to a specific station. The PDH method is like turning the dial while listening for static. However, this method has a flaw: it introduces a type of "static" called Residual Amplitude Modulation (RAM). It's like trying to hear a whisper in a room where the lights are flickering; the flickering makes it hard to hear the true signal.

The New Idea: The "Polarized" Lock

In this paper, the researchers tried a different tuning method called Hänsch-Couillaud (HC) locking.

Instead of using the "flickering lights" (frequency modulation) of the old method, they used polarization.

The Analogy: Imagine the light beam is a person trying to walk through a doorway. The doorway (the laser cavity) only lets people wearing a specific color shirt (polarization) through easily.
The scientists send in a beam that is slightly the "wrong" color. If the beam is perfectly aligned with the doorway, it passes through. If it's slightly off, it bounces back.
By watching how much light bounces back, they can tell if they are perfectly aligned. This method is cleaner because it doesn't introduce the "flickering lights" (RAM) that plagued the old method.

The New Problem: The "Flicker Floor"

When they first tried this new method, they hit a different wall. They found that at low frequencies (slow changes), their measurements were stuck on a "flicker floor."

The Analogy: Imagine you are trying to weigh a feather on a scale. Even if the scale is perfect, the air currents in the room (flicker noise) make the needle jitter back and forth. No matter how steady your hand is, you can't get a reading better than that jitter. In their experiment, this jitter came from tiny electronic imperfections in the sensors, making the measurement "fuzzy" at slow speeds.

The Solution: The "Lock-In" Trick

To fix the jitter, the researchers added a clever trick called a Lock-in scheme.

The Analogy: Imagine you are at a noisy party trying to hear a friend speak. The background noise (flicker noise) is constant and annoying. Suddenly, your friend starts tapping a specific rhythm on the table while speaking. You can now ignore all the other noise and focus only on that rhythm.
How they did it: They took the signal controlling the light and made it pulse (tap) at a very fast, specific speed (10,000 times a second).
Then, they told their computer: "Ignore everything that isn't pulsing at this exact speed."
Because the annoying "flicker noise" doesn't pulse at that speed, the computer filters it out completely. The result? The "jitter" disappears, and they can hear the "whisper" of the Earth's rotation clearly.

The Result: A Super-Sensitive Spin Detector

By using this new "Lock-in" trick with the polarization method, they achieved a sensitivity of 3.1 nanoradians per second.

What does that mean? It means they can detect a change in the Earth's rotation that is 0.000077% of the Earth's normal spin speed.
To put it in perspective: If the Earth's rotation were a giant clock hand, they could detect if that hand moved the width of a single human hair over the course of a year.

Why This Matters

This is a big deal because:

It's cheaper and simpler: The new method avoids the complex electronics of the old method.
It opens new doors: This technique can be used in other fields, like detecting earthquakes (seismology) or measuring gravity waves, without needing the expensive, high-maintenance equipment of the past.
It proves a concept: They showed that you can build a world-class rotation sensor using a "passive" system (just mirrors and an external laser) rather than a complex "active" laser inside the box.

In short, the team built a better "tuning fork" for light, realized it still had a little shake, and then invented a way to filter out the shake, allowing them to listen to the Earth spin with unprecedented clarity.

1. Problem Statement

Large Sagnac interferometers (ring lasers) are critical tools in geodesy and seismology for detecting Earth's rotation and seismic signals. While active ring lasers (with an internal gain medium) are highly sensitive, they suffer from intrinsic limitations like lock-in effects and plasma dynamics. Passive laser gyroscopes, which use an external laser to probe a high-finesse cavity, offer a solution to these issues but face their own stabilization challenges.

Currently, passive gyroscopes rely on the Pound-Drever-Hall (PDH) stabilization technique. However, PDH is limited by Residual Amplitude Modulation (RAM). RAM arises from asymmetries in the phase of frequency-modulated sidebands caused by optical components, creating a non-zero error signal baseline that fluctuates and degrades sensitivity. Despite various mitigation strategies, RAM remains a fundamental bottleneck. The authors sought an alternative stabilization method that avoids frequency modulation entirely to eliminate the root cause of RAM.

2. Methodology

The researchers developed and tested a Hänisch-Couillaud (HC) locking scheme on a large, square passive ring laser cavity (3.5 m side length, perimeter $P \approx 14$ m, finesse $\approx 36,000$ ).

A. The HC Locking Principle

Unlike PDH, which uses frequency modulation, HC locking utilizes polarization.

Setup: A linearly polarized external diode laser (473.6 THz) is injected into the birefringent ring cavity at a 45° angle relative to the cavity plane.
Mechanism: The cavity supports two orthogonal polarization modes ( $s$ and $p$ ) with slightly different resonance frequencies due to the Goos-Hänchen shift. The laser is tuned to the $s$ -polarized mode.
Error Signal Generation: The reflected beam passes through wave plates and a Wollaston prism, separating the $s$ and $p$ components. Differential detection of these two beams generates an error signal. When the laser is on resonance, the error signal crosses zero; deviations create a linear error signal proportional to the frequency detuning.
Advantage: Since no frequency modulation is used, the primary source of RAM in PDH systems is completely avoided.

B. The Lock-in Enhancement (Sub-Flicker Floor)

Initial tests revealed that the standard DC-coupled HC detection was limited by $1/f$ flicker noise (dominant below 2 Hz), likely originating from photodiode dark currents and laser power fluctuations. To overcome this, the authors introduced a lock-in detection scheme:

Modulation: The radio frequency signal driving the Acousto-Optic Modulator (AOM) is amplitude-modulated at $f_m = 10$ kHz.
Demodulation: The photodiode signal is mixed with a phase-shifted reference signal at 10 kHz.
Filtering: A low-pass filter (2.2 kHz cutoff) removes residual modulation, leaving a clean error signal shifted to the modulation frequency.
Result: This shifts the detection bandwidth away from the low-frequency flicker noise region, effectively suppressing the $1/f$ noise floor.

3. Key Contributions

First HC-Locked Passive Gyroscope: This work presents the first implementation of the Hänisch-Couillaud locking scheme for a large-scale passive laser gyroscope, offering a viable alternative to the dominant PDH technique.
Elimination of RAM: By avoiding frequency modulation, the method inherently sidesteps the Residual Amplitude Modulation problem that plagues PDH systems.
Flicker Noise Suppression: The authors successfully demonstrated a cost-effective lock-in enhancement that pushes the noise floor below the intrinsic flicker limit of standard DC detection, achieving a purely shot-noise-limited performance in the low-frequency regime.
High Sensitivity Achievement: The system achieved a rotation sensitivity of 3.1 nrad/s, corresponding to a fraction of $7.7 \times 10^{-5}$ of the Earth's rotation rate ( $\Omega_E$ ).

4. Results

Noise Spectral Density (PSD):
- Standard HC Lock: Dominated by flicker noise ( $1/f$ ) below 2 Hz, limiting the Allan deviation.
- Lock-in Enhanced HC: The flicker noise was suppressed, revealing a shot-noise limited PSD at a level of $\approx 1.2 \times 10^{-8}$ rad/s/ $\sqrt{\text{Hz}}$ .
Allan Deviation:
- The lock-in method achieved a minimum Allan deviation at an averaging time of 6 seconds.
- Sensitivity: $3.1$ nrad/s ( $7.7 \times 10^{-5} \Omega_E$ ).
- Frequency Stability: This corresponds to a Sagnac frequency deviation of 24 mHz, with each counter-propagating lock stabilized to 17 mHz (a fraction of $3.6 \times 10^{-17}$ of the absolute laser frequency).
Comparison: The performance is comparable to similar-sized passive gyroscopes using PDH locking but achieved without the complexity of managing RAM.
Limitations: For integration times longer than 200 seconds, both methods exhibit similar drift (random walk), attributed to environmental factors (temperature/pressure) affecting the wave plates and optomechanics, causing polarization baseline drifts.

5. Significance

This research is significant for the field of precision metrology and geophysics for several reasons:

Alternative Stabilization: It validates the HC scheme as a robust, RAM-free alternative to PDH for high-finesse ring cavities, expanding the toolkit for building next-generation rotation sensors.
Cost-Effectiveness: The lock-in enhancement required to beat the flicker floor is described as simple and cost-effective, making it accessible for other research groups.
Geophysical Applications: Achieving sub-nanoradian per second sensitivity allows these passive gyroscopes to detect subtle geodetic and seismological signals (such as Earth tides and seismic rotations) without the noise floor limitations previously imposed by RAM and flicker noise.
Future Outlook: The authors note that while short-term sensitivity is now shot-noise limited, long-term stability is currently limited by environmental drifts. Future improvements in environmental control (temperature/pressure) could further enhance the sensitivity of these sensors.