Special Report: Pound–Drever–Hall Feedforward Technique: Laser Phase Noise Suppression Beyond Feedback

Authors: Yu-Xin Chao, Zhen-Xing Hua, Xin-Hui Liang, Zong-Pei Yue, Li You, Meng Khoon Tey
Institution: State Key Laboratory of Low-Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing, China
Journal: Optica
Publication Date: July 9, 2024
DOI Link: Click here

1. Research Background

Over the past few decades, the emergence of narrow-linewidth lasers frequency-locked to ultra-stable optical reference cavities has pioneered revolutionary technologies such as gravitational wave detection, optical clocks, ultra-low noise photonic microwave generation, high-fidelity atomic quantum bit control, ultra-cold molecule coherent synthesis, and the search for dark matter and fundamental constant variations. At the core of all these applications is the frequency discrimination and locking method called Pound–Drever–Hall (PDH) technique. This technique converts the deviation between the laser and cavity resonance frequency into an electrical signal suitable for high-speed feedback. Combined with high-quality factor ultra-stable optical cavities, PDH feedback technology has now been routinely used to achieve laser systems with ultra-narrow linewidths.

However, any feedback mechanism inherently introduces a time delay, which limits its feedback bandwidth. Noise beyond the feedback bandwidth not only cannot be suppressed but may also be amplified, forming so-called servo bumps. In optical clock applications, the common method to solve this problem is to use an optical cavity for spectral filtering, but this method has power limitations and other issues. It is even more sensitive for applications like photonic microwave generation and high-fidelity quantum gates in quantum computing.

To address these issues, this research team proposed a new feedforward method by re-utilizing the residual PDH signal when the laser is locked to the cavity and feedforwarding it to the laser output field to achieve high-frequency phase noise suppression. Through this simple and direct method, this study demonstrates noise suppression performance in a range of several MHz bands, surpassing traditional PDH feedback methods by four orders of magnitude.

2. Paper Source

This paper was jointly completed by Yu-Xin Chao, Zhen-Xing Hua, Xin-Hui Liang, Zong-Pei Yue, Li You, and Meng Khoon Tey from the State Key Laboratory of Low-Dimensional Quantum Physics at Tsinghua University and was published in the journal Optica on July 9, 2024. It is noteworthy that in the research and writing process of the paper, the first authors Yu-Xin Chao and Zhen-Xing Hua made equal contributions.

3. Experimental Methods

1. Experimental Procedure

In PDH technology, the traditional feedback setup includes: - Using a Local Oscillator (LO) and an Electro-Optic Modulator (EOM1) for phase modulation to generate frequency sidebands. - Utilizing the optical cavity to reflect the sidebands far from the resonance frequency and the near-resonant carrier differently. - Using an Avalanche Photodiode (APD) to detect the beat frequency between the reflected sidebands and the carrier. - Converting the deviation between the laser and cavity resonance frequency into a dispersive “error signal” suitable for frequency locking through a mixer and Low-Pass Filter (LP).

In traditional feedback control, this error signal would go through a loop filter (PID filter) and then be applied to the laser to achieve frequency locking. In the feedforward control method, this study re-utilizes the residual PDH error signal and feeds it forward to the laser.

2. Experimental Design and Implementation

In the experiment, the research team used a 1013 nm band External Cavity Diode Laser (ECDL), an ultra-low expansion cavity (ULE cavity) with a full width at half maximum linewidth of 14.5 kHz, a 20-meter-long delay optical fiber, and two custom loop filters (PID and P filters). Through the experiment, the research team compared the heterodyne beat signal power spectrum between the laser output through EOM2 and the laser filtered by the cavity. The results show that in a certain frequency range (several hundred kHz to several MHz), the phase noise suppressed using the feedforward signal was significantly lower.

4. Research Results

1. High-Frequency Phase Noise Suppression

Through a series of experiments, the research team demonstrated the significant phase noise suppression capability of the PDH feedforward method. In the frequency band above 500 kHz, the phase noise level after feedforward processing was much lower than the detection noise, indicating the excellent performance of the feedforward method in suppressing high-frequency phase noise.

2. Noise Attenuation Performance

To verify the effectiveness of the feedforward method, the research team artificially introduced a weak sinusoidal phase modulation signal and experimented with different modulation frequencies (fin). The experimental results showed that in the frequency range of 10 kHz to 4 MHz, the noise suppression exceeded 30 dB, with a maximum of 43 dB. Although there was some attenuation at high frequencies, this performance was still significantly better than previous feedforward techniques.

5. Working Principle

The theoretical basis of the feedforward method lies in that the residual PDH error signal at different frequencies contains the entire spectrum information of the laser’s phase noise. Therefore, a loop filter with constant gain can be used to feed it forward to the laser to achieve phase noise compensation. By fixing the feedforward gain in the experiment, the feedforward signal interferes with the laser, thus achieving high-frequency phase noise suppression.

6. Performance Limitations and Improvement Directions

The research team pointed out that factors such as delay fiber length, loop gain, and system stability all affect the feedforward performance. To achieve better suppression effects, it is recommended to stabilize the light cavity transmission power, use faster feedforward circuits to reduce delay, and avoid using excessively long optical fibers. Additionally, the research team proposed some potential improvement directions, such as further optimizing the experimental setup to enhance high-frequency noise suppression capability.

7. Conclusion

Through experiments, the research team validated that using the PDH signal for feedforward can effectively suppress laser phase noise at higher frequencies. Combining feedback and feedforward control, the PDH method has now achieved unparalleled suppression of laser phase noise from DC to several tens of MHz. Compared to previous feedforward schemes, the PDH feedforward method does not require additional in-phase or quadrature-phase detection to detect phase noise, making it more robust to optical path changes and intensity noise. Additionally, since the PDH feedforward scheme is not limited by cavity transmission power, it can use narrow linewidth optical cavities to achieve optimal low-frequency noise suppression. The research team stated that this new method has great potential for high stability laser applications requiring high power output and low phase noise within tens of MHz.