# Laser mode locking

I don't understand why we need to do mode locking in laser to generate short impulse ? Indeed, If I see this picture from wikipedia :

By using multiple frequencies and the limit conditions of my cavity, the laser will by itself generate pulse. I don't need something else (it is clear on the figure that I will have a large impulse).

Do we use absorbant to be sure to ONLY send the huge maximum and not the smaller other one ?

Thank you.

• At some level, yes. You want to mode lock to make sure that every pulse you ask for is the same pulse as all the other ones. You probably have never had the 'joy' of trying to use a free-running cavity - what a mess! – Jon Custer Apr 11 '16 at 22:14
• In short, your statement that "by using multiple frequencies and the limit conditions of my cavity, the laser will by itself generate pulse" is incorrect. You can verify this yourself by reproducing the animation from Wikipedia and then randomizing the phases between the modes; the pulse will then disappear. – Emilio Pisanty Apr 12 '16 at 19:33

Having read Madan Ivan's (nice) answer and the comments that follow it seems that your confusion stems from your assumption that the many standing modes are already in phase with one another. You said in a comment above that "only by boundary conditions there will have a place where sin are in phase", but the boundary conditions only dictate which modes can exist in the cavity, and do not have any implications on the relative phase of each of the cavity modes. Your statement is therefore technically wrong, and I think that this is what is causing the confusion. Each of the modes can exist in the cavity with a phase which is independent of all of the other modes, and thus a laser which is free-running with N modes of equal amplitude will produce noise, and not a highly ordered pulse train.

When modelocking a cavity, some nonlinearity (either 'passively' or 'actively' introduced) is required in order to establish a well defined phase relationship between each of the modes which is then reproduced each roundtrip, as is demonstrated by your nice graphic (i.e., the modes of the cavity are phase locked, hence "modelocking"). This then allows for the pulsed output.

You also asked why one mode will become dominant over another when modelocking is not used. This is simply because the net roundtrip loss for one particular mode is less, allowing it to build up and reach steady-state before the others. Once this occurs this mode will dominate the cavity and take the lion's share of stored energy, thus keeping all other modes suppressed. (Edit in light of a more recent comment: This can occur in such a way that a few modes can co-exist in the cavity if the gain and cavity loss profiles allow them to. However, the argument above still holds when considering the number of modes present in a modelocked pulse - $\sim 10^{6}$ - in comparison with a free-running cavity which allows for a few modes at any given time).

In order to stop this from happening and to cause a cavity to modelock, you need to set the cavity up in such a way that loss is reduced for high intensities, which are provided when the standing modes of the cavity are in phase. If this is done correctly, then the most stable operating point for the cavity will be the modelocked state, and not the single-longitudinal-mode state which would otherwise dominate.

• Ah i think i get it now. The problem for me was the fact that nodes for a given frequency would be at the same position with or without mode locking. But indeed I have forgotten that we also need to pay attention to how the sinus are alterning relative to each other (there is not only the nodes that are important). But just a last question : the mode locking only keep great intensity, so we only would see pulses. But it physically need in fact to "reset" phase of some modes. But how can it do it ? – StarBucK Apr 12 '16 at 10:59
• Because for me if there is wrong phase at the beginning with an absorber of intensity to realise mode locking, i would expect to see 0 signal everytime. – StarBucK Apr 12 '16 at 11:03
• Your second point is correct only if you ignore any perturbations to the cavity (causing phase noise), which will create an initial modulation on the signal and set the modelocking process off. This can be introduced to the cavity actively using an AOM to time-gate the pulses, or it can happen naturally in some cavities which have a strong tendency to self-Q-switch when left to run freely if a passive intensity filter is included. Perturbations with a higher intensity will be favoured by a modelocked cavity. This is how the phase is gradually 'reset' to favour pulsing with each roundtrip. – user113857 Apr 12 '16 at 11:12

First, there is more ways to mode-lock the laser than just the Q-switch.

Second -your second paragraph is not correct. If you would just have laser without mode-locking parts, one mode would suck in all the energy from the active media. This is described in pretty much every book on how lasers work. In one sentence this is because amplification in active media is proportional to the number of photons in the mode (because it is stimulated emission). And this is why we need the absorbant - to prevent laser from going in single mode regime.

Third, your second paragraph is not correct because without mode locking, for many modes your time average intensity would be pretty much constant with time.

Now clearly what mode-locking is, by definition, is a procedure to ensure that at a given moment of time/space peak of all your sine waves coincide, i.e. enhance each other, i.e. produce short pulse. I guess what you miss here mode-locking cares about phase of the modes relative to each other, this is important thing.

Basically short pulse generation and mode-locking are synonyms. You can't have one without having another.

• I am sorry but i dont really understand. If i look at my picture it represents the E field without anything else than the boundary conditions. But if I understand you, in fact without mode locking one mode would be really greater than the others so i wouldnt have what is on the picture where all sin are equal in amplitude. But only by boundary conditions there will have a place where sin are in phase. So the mode locking is only here to be sure that all sin amplitude are not too différent ?? – StarBucK Apr 12 '16 at 9:06
• Because again on my picture the author just draw 5 stationnary sinus with different fréquences. So the only hypothesis is "we have 5 frequencies emitting in the cavity". So if the mode locking is here to be sure to not have a standing wave with an amplitude really larger than the others i dont understand why we would have this. (Why one mode would be really larger than the others) – StarBucK Apr 12 '16 at 9:12
• @Madan Ivan, the second part of your answer only applies to homogeneously broadened media! Multiple modes should have no problem surviving in the cavity simultaneously if the gain medium was inhomogeneously broadened. And even with homogeneously broadened media the laser should have no problem jumping between different modes very quickly due to spatial hole burning. – Arturs C. Apr 12 '16 at 10:56