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The unclear part is the details of how the frequency comb is hooked together with the radio frequency domain in a feedback loop to control the comb. I.e. where
by CamperBob2 2y ago
The unclear part is the details of how the frequency comb is hooked together with the radio frequency domain in a feedback loop to control the comb. I.e. where in the RF domain we have the precise frequency reference we'd like to convey to the optical domain.
As I understand it, two effects are involved. One is the laser's pulse repetition rate that determines the frequency spacing between adjacent comb lines. This is on the order of hundreds of MHz, so it can be measured with a photodiode detector and phase-locked like any other RF signal.
The other effect is the carrier (light) phase shift that occurs from one pulse to the next. Assuming the pulse rate has been stabilized, nulling out this carrier phase shift is equivalent to stabilizing the laser's frequency. The photodiode can't see the carrier cycles, of course, but if the comb spans at least one octave in frequency, there will be a detectable beatnote between the second harmonic of the fundamental F (which like you say is always present to some extent given various nonlinearities in any real-world system) and the comb line at the beginning of the next octave. Driving this difference frequency to zero stabilizes the actual lightwave carrier.
As far as stabilizing the signal from the photodiode is concerned, that's just a matter of mixing it with a signal from the desired frequency standard to get the difference frequency that you steer to zero by tuning the laser. Some systems care about locking at a specific phase, others are OK with just getting the frequency right.
Disclaimer: treat the above with healthy skepticism, as IANAPhysicist and have never actually had my hands on this sort of hardware. Corrections actively solicited.
(Edit: Actually I like o1-pro's explanation better than mine: https://i.imgur.com/L3b7S8v.png https://i.imgur.com/L3b7S8v.png -- although the same disclaimer obviously applies.)
- kazinator 2y agoHow the pulse rate of the laser determines the frequency between comb lines is unclear. Frequencies are in hundreds of THz; pulsing is way, way slower. Plus don't you need the fundamental frequency of the comb to follow the radio-frequency references, not just the spacing. What is clear is that this may indeed be beyond an optical comb appreciation video produced by the NIST for the general public.
- cycomanic 2y agoRegarding the spacing of the comb lines that's simply a fundamental property of the time and frequency domains. If you take the Fourier transform of a pulse train you will have comb of lines in the frequency domain where the spacing is the inverse of the pulse period. This depends on the size of the optical cavity. The carrier frequency oscillates underneath (at >100 THz frequency as you correctly point out). You can stabilise the offset frequency i.e. the position of the first line, by f-2f sabilization as described by the other poster. We still need to relate this to an absolute frequency and we do that using accurately known gas absorption lines. That way we have a comb of frequency lines at > 100 THz and more than an octave wide, where we know the absolute frequency with very high accuracy.
- CamperBob2 2y agoThe fundamental lightwave carrier frequency F is locked by means of the F-2F beatnote. But if I understand it correctly, they normally stabilize the PRF first (which, again, is in the hundreds of MHz). Otherwise, the frequency separation between the second harmonic of F and the comb tooth at 2F will be noisier/driftier. The business about the PRF determining the comb spacing comes straight out of Fourier. A train of narrow pulses in the time domain is a series of comb lines in the frequency domain, with spacing equal to the PRF. Lots of applications in traditional RF work for this, but femtosecond lasers made it relevant in the optical field as well. To measure the absolute frequency of the light, as mentioned by cycomanic, one or more well-known quantum transitions is certain to be within range of any octave-bandwidth laser comb. Some of those transitions have line widths in the hundreds of hertz, which gives serious levels of precision if you're working with a THz or PHz carrier. Then you say goodbye to Mr. Fourier and hello to Mssrs Zeeman and Stark.
- kazinator 2y agoOK. It seems that the key is the femtosecond capability in the lasers. Even if the pulses are relatively far apart compared to the target frequencies for the comb, if those pulses are super crisp, that will drive energy into that frequency band?