Talk:Pound–Drever–Hall technique

I think that this:

$\mathbf {E} (\mathbf {r} ,t)\approx e^{i\omega t}[1+{\frac {\beta }{2}}e^{i\omega _{m}t}-{\frac {\beta }{2}}e^{-i\omega _{m}t}]$

was meant to be this:

$\mathbf {E} (\mathbf {r} ,t)\approx E_{0}e^{i\omega t}[1+{\frac {\beta }{2}}e^{i\omega _{m}t}-{\frac {\beta }{2}}e^{-i\omega _{m}t}]$

based on the $E_{0}$ in the third equation...will fix.

OK, the equations should be looked over by someone who knows exactly what they should be and has a little more time than me. I believe they are correct, but have not worked out any algebra to verify this. They seem to have been put up in a hurry though, with quantities like $P_{0}$ unexplained. It's obvious what these quantities are to a knowledgeable reader, but that shouldn't be taken for granted...will add some things —Preceding unsigned comment added by 198.129.209.197 (talk) 18:58, 30 June 2009 (UTC)

Also, I believe $\beta$ is the amplitude of the modulation applied to the carrier light, but I'm not certain enough of this to change it in the actual article. —Preceding unsigned comment added by 198.129.209.197 (talk) 19:13, 30 June 2009 (UTC)

$\beta$ is indeed the amplitude modulation depth, $P_{0}$ is the power given when you absolute square the electric field. Fincle (talk) 07:00, 28 April 2010 (UTC)

Even more important is that:

${\begin{aligned}E_{\text{i}}&=E_{0}e^{i\omega t+\beta \sin(\omega _{m}t)}\\\end{aligned}}$

Should be:

${\begin{aligned}E_{\text{i}}&=E_{0}e^{i(\omega t+\beta \sin(\omega _{m}t))}\\\end{aligned}}$

Or else series expansion approximation shown is incorrect. I have made those changes. --Varneyphd (talk) 16:12, 25 August 2011 (UTC)

PDH readout function

There is a line that reads:

"Additionally, it is sensitive only to intensity fluctuations due to the frequency of light in the cavity and insensitive to intensity fluctuations from the laser itself.[2]"

This is incorrect, the PDH readout error signal does fluctuate with intensity of the imputed light. The point here is that its zero point remains zeroed. The technique is most commonly applied to laser frequency stabilization. In that case a control system uses the error signal to readout resonance condition and drive the laser or cavity to resonance. The slope of the error function will fluctuated with incident light but remain zeroed. Thus small fluctuations in laser power don't transmitted to incorrect readout of resonant frequency (such as in fringe locking techniques) although the gain of the control loop may fluctuate.--Fincle (talk) 06:24, 7 November 2011 (UTC)

Section on Servo/PID control

Shouldn't there be a section, or at least a paragraph describing how the error signal is used in a feedback loop so actually achieve the PDH lock? All that the article mentions about a feedback loop is the word "servo" in the caption of the schematic experimental setup. I'm adding a sentence about this in the article, but it would be nice to have a detailed description. Quantumavik (talk) 01:06, 30 July 2014 (UTC)

The mention of PID controller:

"The feedback is typically carried out using a PID Controller which takes the PDH error signal readout and converts it into a voltage that can be fed back to the laser"

This is typically not true. The servo is a piece of electronics or digital signal processing that reshapes the frequency response of the feedback to make the loop stable. It is usual to not be very specific because the implementation varies from application to application: it depends on the frequency response of the device under control (laser/cavity length) and the loop bandwidth requirements. PID is definitely not the norm/typical, it is a very limited tool for shaping the frequency response. Some typical servo features are a low pass filter at low (10 Hz) frequency to provide some basic shape to the loop that is inherently stable, integrator or boost at low frequencies, notch filtering to remove known mechanical resonances or lines etc. But that is maybe getting too much into the weeds for a wikipedia article. Its enough to say that the servo is a gain stage with some shaping of the frequency response of the the loop. We should also remove mention of PID from the figure. --Fincle (talk) 07:11, 17 March 2018 (UTC)

Frequency (or wavelength)

1st time contributing to this page. Does anyone care if I remove the "or wavelength" in the intro? It seems out of place, as wavelength is inversely proportional to index of refraction. Thus, a stable wavelength would require stabilization of the index (and a constant medium).

I'm also thinking of adding more secondary sources in accordance to wiki guidelines. Any suggestions? Az7997 (talk) 02:34, 18 March 2014 (UTC)

Final formula for error signal $V(\omega )$

Quite at the end, the article states that from demodulation of $P_{r}$ with the local oscillator $\cos(\omega _{m}t+\phi )$, you get

$V(\omega )\propto {\textrm {Re}}[\chi (\omega )]\cos \varphi +{\textrm {Im}}[\chi (\omega )]\sin \varphi .$

However if I do the calculation (using only the term of $P_{r}$ that leads to coherent interference with the local oscillator), I get a minus sign in between, instead of the plus. Could someone verify this?

$\cos(\omega _{m}t+\phi )(A\cos(\omega _{m}t)+B\sin(\omega _{m}t))$ // TrigExpand

-> Average over infinite time such that oscillating terms vanish:

${\frac {1}{2}}A\cos(\phi )-{\frac {1}{2}}B\sin(\phi )+{\frac {1}{4}}B\sin(\phi )-{\frac {1}{4}}B\sin(\phi )$

$={\frac {1}{2}}A\cos(\phi )-{\frac {1}{2}}B\sin(\phi )$