Pound-Drever-Hall frequency stabilisation technique

  • I
  • Thread starter epsilon
  • Start date
  • Tags
    Frequency
In summary, the Pound-Drever-Hall frequency stabilisation technique involves emitting a laser frequency, f0, which is modulated with sideband frequencies, ±fm, and firing it towards a Fabry-Perot cavity with a resonant frequency, fc. The resulting signal is then mixed with the modulation frequency, and the output error signal from the mixer is used to correct the emitted frequency to match the resonant frequency of the cavity. The key component in this technique is the square law detector, which contains all the necessary information at the modulation frequency. This allows for precise frequency locking and control.
  • #1
epsilon
29
1
I am having some difficulty understanding the Pound-Drever-Hall frequency stabilisation technique, when locking a laser to a stable cavity.

As far as I understand:
  • We emit the laser frequency, f0.
  • This signal is modulated with sideband frequencies, ± fm.
  • This is fired towards the Fabry-Perot cavity, which has a resonant frequency fc.
  • As f0fc, some of the light is reflected at the entrance to the Fabry-Perot cavity, known as the "promptly reflected beam", picking up a phase shift of π/2 like any standard mirror reflection.
  • The rest of the f0 signal is transmitted into the cavity (sidebands are never transmitted).
  • As f0 is close to fc, the light is able to somewhat resonate in the cavity, with a phase shift of almost 2π picked up on each complete transit of the cavity (it would be exactly 2π at perfect resonance).
  • Small amounts of the light periodically escape the cavity, called the "leakage beam".
  • There is therefore a phase difference between the promptly reflected beam and the leakage beam, which is just under π (if it were π, such as at perfect resonance, these two beams would cancel exactly).
  • Hence the two beams interfere - very close to antiphase - to produce a wave with the two sidebands unchanged and the f0 peak reduced in amplitude and phase-shifted sideways (does the shift directly depend on being above or below resonance?).
  • This signal is now incident on a photodetector.
  • This signal is now mixed with the modulation frequency.
This is where my understanding breaks down. Why mix this signal with the modulation frequency? I would have expected you to mix the output signal with the initial laser signal, such that the shift in phase could be determined and hence accounted for.

From what I've read, the two different frequency signals produce the beats phenomenon in the mixer, with an internal frequency (f0 + fm) and the envelope/amplitude frequency (f0 - fm). This is low-pass filtered to keep the (f0 - fm) component, and this is the error signal needed to correct the frequency emitted to correctly match the resonant frequency of the Fabry-Perot cavity.

But we want the error signal to be the difference between the resonant frequency and input frequency. I don't understand why we have used the modulation frequency/sidebands at all! Please answer using similar level of language as I have used here. I have attached a schematic of the Pound-Drever-Hall system from Wikipedia below.

Many thanks in advance! :oldsmile:

PDHBasicLayout.png
 
Physics news on Phys.org
  • #2
I don't think there is a good way to explain this without using a bunch of equations and plots and even then it gets complicated. Have you e..g looked at any of the review articles from LIGO? There are several, but at least one is a very good article aimed at "beginners".

Anyway, I believe the key point you are missing is that the photodetector is a square law detector. This means that the output signal from the detector contains products with all the necessary "information" at the modulation frequency. The square law detector is the key component here, the only function of the mixer is to down-convert the signal.
The mixer (which in some schemes can be a RF lock-in amplifier) will then output the error signal (which I would encourage you to plot, it can also be measured experimentally) which is zero when f0=fc and has a nice steep slope, meaning it is ideal for e.g. a P-I servo.
 

1. What is the Pound-Drever-Hall frequency stabilisation technique?

The Pound-Drever-Hall (PDH) frequency stabilisation technique is a method used to lock the frequency of a laser to a reference cavity. It was developed in the 1980s by R.W.P. Drever, J.L. Hall, and F.V. Kowalski, and is widely used in precision measurements and experiments in fields such as physics, astronomy, and engineering.

2. How does the PDH technique work?

The PDH technique works by using a reference cavity, which is a highly stable optical cavity with a known resonance frequency. A phase modulator is used to modulate the frequency of the laser beam, and the light reflected from the reference cavity is then detected and demodulated. The error signal generated from this process is used to adjust the laser frequency and keep it locked to the reference cavity.

3. What are the advantages of using the PDH technique?

The PDH technique offers several advantages over other frequency stabilisation methods. It is relatively simple and inexpensive to implement, and it provides a high level of stability and accuracy. It is also able to correct for frequency drifts and noise in the laser, making it suitable for long-term experiments and applications.

4. What types of lasers can be stabilised using the PDH technique?

The PDH technique can be used to stabilise a wide range of lasers, including continuous-wave (CW) lasers, mode-locked lasers, and pulsed lasers. It is particularly useful for stabilising lasers with high optical power, as it can handle large amounts of reflected light from the reference cavity without causing damage or instability.

5. Are there any limitations to the PDH technique?

While the PDH technique is a highly effective method for frequency stabilisation, it does have some limitations. It requires a stable reference cavity with a known resonance frequency, which can be challenging to construct and maintain. It is also sensitive to environmental factors such as temperature and vibrations, which can affect the stability of the reference cavity and the laser frequency lock.

Similar threads

Replies
2
Views
1K
  • STEM Academic Advising
Replies
2
Views
2K
Replies
6
Views
17K
  • General Engineering
Replies
4
Views
3K
  • Science and Math Textbooks
Replies
19
Views
17K
Back
Top