I am confused about the way mode-locking is done in practice. If i understand the problem well, normally, in a laser cavity with a large enough bandwidth, we have many modes that would interact in an incoherent way and give a low power (this would be a continuous wave laser). If we are able to create some phase relation of the modes (for example all of them to have the maximum of one of the peaks at the same point) than we create a mode-lock laser. So the problem we need to solve is to somehow shift the phases of the modes in the cavity to go from some random noise to a nice tall peak. However, I read about an active way of achieving this, using an acustic-optic resonator. If I understand it well, this allows frequency modulation which can shift the present modes by c/2L and in the end you remain only with the central mode, while the others get lost as they are not able to reproduce themselves. So basically (part of) all modes are converted to some frequency and the rest is discarded. But I am really confused now. All this would shift the frequencies of the modes, not the phases. So you end up with "bunches" of light of the same frequencies, but out of phase. How is this any better i.e. different than random noise? I imagine that, given that you have just one frequency now, the noise shape will stay the same (before the shape was also changing in time, due to having different frequencies), but I am not sure I see how do you get such a nice, narrow peak from lots of out of phases "bunches" of light and not just noise. Any explanation would be greatly appreciated! Thank you!

• If this is related to your earlier laser question, you might want to look at Q-switching, which also produces higher powered pulse output, but is simpler to explain. Nov 30, 2019 at 16:25
• @ThePhoton it is not necessarily related, but I am reading laser stuff, so you can say it is. I understand how Q-switching works, that pretty clear. I am just confused about mode-locking. How does playing with frequencies solves the problem of phase difference. As far as I can tell, adjusting the frequency shouldn't influence the phase. Nov 30, 2019 at 17:28

In practice, there is usually a passive element relying on Kerr lensing that stabilizes the coherent modelocked beam over the CW one. The mode locked beam has a much higher peak intensity, and so if there is a material whose index of refraction is dependent on the intensity of the field (which is really all materials, the effect is just weak) then the modelocked beam will become spatially convergent, like it had passed through a lens. This allows the modelocked beam to be spatially filtered from the CW beam, effectively blocking it. Does that help?

• I am actually confused about the active mode-locking, not the passive one. Nov 30, 2019 at 17:26

Ok, let me see if I can answer this question. Active mode-locking via acousto-optical modulator can be achieved via amplitude modulation: basically you create losses at the same frequency of your cavity. In this sense a pulse that exists at the minimum loss point every roundtrip is the only surviving circulating E-field in the cavity. This is of course easier to understand in a time setting, not phase or frequency. Just imagine a time gate that only opens exactly at the same frequency as the time it takes the pulse to go through the cavity.

In the end it stabilizes as a short pulse also because the gain then is also modulated: as the mode-locked pulse passes through the medium it depletes its energy quite efficiently and so other modes also have a hard time getting gain.

Now, frequency modulation, or phase modulation, that you were probably referring to, and I dont really know what an acoustic-optic resonator is, and will not google it. So, if you modulate the phase seen inside the cavity, for example with a medium whose refractive index is modulated in time, to have the same frequency as the cavity, then from a single frequency, passing through such thing, creates sidebands at a frequency away equal to the modulation frequency. These sidebands now generate sidebands, which generate sidebands, which generate sidebands, you get the picture. Now all of them are phase locked, as they originate from one single frequency, and they are all spaced equally, the spacing the same as the modulation frequency. Now all of this will only be supported in a cavity where all this frequencies can coexist, so the spacing needs to be the same frequency as the cavity. Then the same thing with the gain above happens, as they are all now constructive interfering in a nice pulse, they deplete the gain more efficiently. Just imagine that at a certain point there was one mode, arbitrary phase, that had more power than others, and this mode and its sidebands were able to pull through and rise above all others, effectively stabilizing the mode-locking mechanism.

This whole process can also be thought as for example the end mirror oscillating with the same frequency as the cavity length, if you imagine such a scenario, this is the case of a phase modulation: total phase is proportional to length of the cavity (and creates the sidebands). Now the pulses prefer when the mirror is at either side of the oscillating movement, or zero velocity, because at every roundtrip this is reproducible. During a ramping up or ramping down, the cavity modes are effectively shifting like an accordeon, and this just generates a bunch of light modes negatively interfering. While at the turn around point the modes are fairly static.

No one likes active mode-locking either way :p (this is not true, though, just a small joke)