Well, I did get an idea about what the thing actually is: basically a signal consisting of a mixture of frequencies, precisely spaced. Techniques to generate some of the bands include nonlinear mixing. Turns out, light can undergo distortion, so you can get intermodulation distortion to generate colors not present in the inputs.

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 -- although the same disclaimer obviously applies.)

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.

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.

Being able to go from IR to UV in one comb spectrum was considered a very worthwhile advance when it happened. Now you can apparently buy a single box that does it, such as the one mentioned in https://news.ycombinator.com/item?id=42890578 . But you have to ask for the price, and usually I find that if I have to ask, I needn't have bothered. :-P

The frequency of the pulses must be low enough so that they can be counted with digital counters, while the frequency of the sinusoidal signal may be as high as to reach the ultraviolet light range.

The fixed frequency ratio is achieved by a control loop with feedback, which works in a similar way, but more complex, with a PLL (phase-locked loop).

The control loop of a PLL controls a single variable. For example, a PLL can be made with a VCO (voltage-controlled oscillator), where a voltage determines the frequency of the oscillator, together with a device that provides means to detect whether the ratio between an input frequency and an output frequency deviates from the desired fixed ratio. If a deviation is detected, the voltage at the input of the VCO is increased or decreased, restoring the ratio between the input frequency and the output frequency to the desired value.

Modern PLLs normally use digital frequency dividers in the control loop, which limits their maximum frequency to one that can be counted with digital circuits. Nevertheless, the first PLLs have been implemented many years before the appearance of the first digital counters. Such early PLLs were used for frequency division, not for frequency multiplication, like the modern PLLs. They used inside their control loop a circuit that distorted the sinusoidal output of their controlled oscillator, generating high-order harmonics. A high-order harmonic was selected with a filter and it was compared with the input frequency, detecting any deviation of the PLL from the intended frequency ratio.

The optical frequency combs can be considered as an evolution of the early PLLs that were used for frequency division, and they are necessary for the same reason as the early PLLs. By the time of the first PLLs, pulses could be counted only with mechanical counters, which could not work at the frequencies of quartz crystal oscillators. So a frequency-dividing PLL was used to bridge the gap between what mechanical counters could count and the frequency of the sinusoidal signal produced by a quartz oscillator, exactly like now optical frequency combs bridge the gap between what electronic digital counters can count and the frequencies of optical oscillators.

The main difference between an optical frequency comb and the early PLLs with harmonic generators is that the control loop of a frequency comb is much more complex, because it must control simultaneously 2 distinct output variables in order to keep the frequency ratio at the intended value, not a single output variable, like the control loop of a PLL or most other control loops that are frequently encountered and studied.

The loop control of a PLL needs to control a single variable, because a sinusoidal oscillator has a single degree of freedom, corresponding to its output frequency. The loop control of an optical frequency comb must control 2 variables, because a pulsed sinusoidal oscillator has 2 degrees of freedom, corresponding to the pulse repetition frequency and to the sinusoidal signal frequency.

In PLLs that are used for frequency multiplication of for frequency division, the frequency ratio is provided by an element inserted in the control loop, e.g. a digital frequency divider or a harmonic generator, which has an intrinsic frequency ratio, which does not have to be controlled by the control loop.

The word "difficult" may be interpreted subjectively, i.e. what is difficult for one may be easy for another and what is easy for the first may be difficult for the second, but in any case I have not compared the difficulty of the control loop of a frequency comb with the difficulty of another component of a frequency comb, but only with the difficulty of the control loop of a PLL, which is the device replaced by a frequency comb.

There is no doubt that the control loop of a frequency comb is much more difficult to design than the control loop of a PLL or of any other simple regulator with a single degree of freedom.

Perhaps you have designed yourself the control loop for a frequency comb and it is indeed "very simple", but I have seen tons of books and of research papers about optical comb frequencies, which describe a lot of details about other parts of the optical frequency combs, but none of them ventures to present the details of how the control loop actually works.

While I have designed PLLs, I did not have the opportunity to design a frequency comb, so perhaps the additional difficulty is not great, as you claim, but I suspect that this is not true, because if it were easy to describe that in a few words such a description would have existed in one of the many publications about frequency combs.

In any case, when you claim that a text is "confidently incorrect", you should better point to the exact affirmation that is incorrect.

When you just do not agree with some subjective assessment, like whether something is easy or difficult, using the word "incorrect" is itself incorrect.

In this particular case you cannot even disagree with my use of the word "difficult", because if you claim that designing the double control loop of a frequency comb is not more difficult than the single control loop of a PLL, that claim is certainly incorrect.

Admittedly I'm not well-informed on this topic at all, but I haven't run across that exact requirement. You need to know the pulse rep rate, which in practice may just be a matter of triggering the laser from a sufficiently-stable source rather than having to measure it separately -- and you need some way to get a carrier beatnote from a pair of lines, where the F-2F technique is a common approach -- but do you really need a priori knowledge of the PRF:carrier frequency ratio in order to make the whole thing work?

It is simple to make a pulsed oscillator, but making one where the pulse frequency and the sinusoidal frequency maintain a fixed ratio is not at all simple, especially when the frequency ratio is very large, like what is needed when the pulse frequency must be low enough to drive a digital counter and the sinusoidal frequency must be in the optical range, up to ultraviolet light.

If you have such an oscillator, by tuning the low frequency you can obtain light with an accurately known frequency. Alternatively, by tuning the high frequency to match light with a known frequency, e.g. produced by an optical atomic clock, you can obtain a pulse train with a known frequency, which may be used as a reference frequency, e.g. for a digital clock.

Has Sir never seen a rainbow?

May I kindly refer Sir, to Isaac Newton's prism experiment, as lovingly depicted on the cover of Pink Floyd's 'Dark Side of the Moon' album.