A frequency comb is a pulsed sinusoidal oscillator that satisfies the requirement that the ratio between the repetition frequency of the pulses and the frequency of the sinusoidal signal must be a fixed known value.
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.
This text is so confidently incorrect, that I have to wonder if it is LLM-generated. The control loop for a frequency comb is actually very simple. Generating the carrier-envelope offset frequency signal is the hard (Nobel prize worthy) part.
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.
They may have objected to your assertion in the first paragraph ("....the ratio between the repetition frequency of the pulses and the frequency of the sinusoidal signal must be a fixed known value.")
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?
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.