3 ms·

How 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 do

How 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 ago
Regarding 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 ago
The 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 ago
  OK. 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?
  - CamperBob2 2y ago
    Right. The risetime of the pulses determines how far out the useful comb lines extend (at least that's how it works in the RF world). 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 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
adrian_b 2y ago
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.

cycomanic 2y ago

Regarding 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 ago

The 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 ago
OK. 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?
- CamperBob2 2y ago
  Right. The risetime of the pulses determines how far out the useful comb lines extend (at least that's how it works in the RF world). 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 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

adrian_b 2y ago

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.