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My core question is about how to generate multi-frequencies for mode-locked laser. The key mechanism of mode-locking is the generation of multi-frequencies in the cavity.

In the passive mode locking the saturable absorber is driven by a very short pulse. But how mode-locking can be done in this way? How can I know the generation of multi-frequencies in this method?

In the passive Q-switched laser, there is also a saturable absorber in the cavity. What are the differences between these two methods?

Kerr lens mode locking is also a passive mode locking. When I googled this issue I only know it is implemented by passing a pulse through a Kerr medium and an aperture is put on the back of the Kerr medium. According to $n=n_0+n_2I$, the output pulse looks like chopped by the aperture. How multi-frequencies can be seen/generated in this method?

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  • $\begingroup$ Does my answer to this question answer your doubts: physics.stackexchange.com/questions/606234/… $\endgroup$ Mar 10, 2023 at 16:41
  • $\begingroup$ @JoséAndrade Thank you for your reply. I got some inspiration from your words. I still have a small question. When we feed the modulated light, like you say a wavelet (phase modulation or amplitude modulation), how is the phase locked between different modes in Kerr-lens method? $\endgroup$
    – Hsu Bill
    Mar 12, 2023 at 0:13
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    $\begingroup$ The phase-locking happens in an extremely passive way, or let's say, it's intrinsic. Its simply the fact that for the wavelet to exist the modes need to be locked and vice-versa-like the answer below. As the wavelet gains energy, depletes the gain medium and forces low-energy wings to disappear, the wavelet becomes the only thing oscillating in the resonator after a few 100s of roundtrips. There is no more pulse-breaking (de-coherence of the modes) because of the self-balancing effect of the linear and nonlinear phases together with the gain/loss mechanics of the (passive) saturable absorber. $\endgroup$ Mar 12, 2023 at 13:54
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    $\begingroup$ In other words, at first, there is a chaotic amount of modes oscillating, however there are a few that are stronger than the others and form the wavelet. As the mode-locking mechanism that I described in the other post happens, other modes are forced to "align" with those of the strongest wavelet, as they get depleted/phase-shifted. $\endgroup$ Mar 12, 2023 at 13:57
  • $\begingroup$ @JoséAndrade Thank you so much for your reply! I got it. $\endgroup$
    – Hsu Bill
    Mar 15, 2023 at 1:38

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At the beginning you say:

The key mechanism of mode-locking is the generation of multi-frequencies in the cavity.

If I got your thought correctly, then it is not true. The mode-locking is used to assure phase coherence between different modes that can exist within your laser cavity. That will cause your laser to be pulsed. The reason for that can be easily understood when you look at a Fourier transform of a pulse train - it consists of many coherent sine waves.

You can also inverse that logic. If you assure that your laser is pulsed in a controlled and stable manner, then you will get output that consists of different and coherent frequencies. Passive mode locking usually depends on an additional element within your cavity that periodically will change present losses affecting the dynamics of your laser.

Q-switching is a name for all methods that will change the cavity's Q-factor (parameter describing losses of your cavity). The first method you mentioned - the one employing a saturable absorber depends on the fact, that when certain intensity is reached within a cavity, the losses are getting significantly reduced and thus energy from your gain medium can be released as an impulse. As the result, the intensity drops, and the build-up must happen again. The Kerr cell and an aperture are producing a similar effect. When the intensity reaches a certain value, the light is getting focussed more tightly, and thus is not getting chopped by the aperture - your losses are reduced.

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  • $\begingroup$ Thank you so much for your reply and correction. I understand the principle of Q-switching. However, your statement about passive mode locking looks quite similar to Q-switching. I knew and googled the statement about passive mode locking but I found the similar statement as you typed. My residual confusion is how an introduction of saturable absorber in the cavity produces phase coherence between different modes in passive mode locking method? $\endgroup$
    – Hsu Bill
    Mar 6, 2023 at 14:28

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