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Passive Mode Locking with Slow Saturable Absorbers: Surprisingly Stable!

Posted on 2017-08-31 as a part of the Photonics Spotlight (available as e-mail newsletter!)

Permanent link: https://www.rp-photonics.com/spotlight_2017_08_31.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Abstract: Some relatively simple reasoning would suggest that passively mode-locked lasers with a slow absorbers can hardly be stable - although they usually are. This article tells the history of how various explanations - partly wrong ones - have been found.

Ref.: R. Paschotta and U. Keller, “Passive mode locking with slow saturable absorbers”, Appl. Phys. B 73 (7), 653 (2001)

Dr. Rüdiger Paschotta

Today, I cover a relatively specialized subject in the area of ultrafast laser physics, which however is important for many such lasers and also gives interesting insight into the curious ways in which science often progresses.

The basic principle of passive mode locking is not overly difficult to understand. Essentially, a saturable absorber in the laser resonator leads to lower power losses for the intense peak of a circulating ultrashort pulse, compared with losses for light with low optical power hitting the absorber at other times. That mechanism favors the pulse peak and can therefore be imagined to form and stabilize a rather short pulse.

How Can Such Lasers be Stable?

Looking into the details, one will quickly come across difficult aspects, however. One of them is related to the fact that many absorbers used for mode locking of common ultrafast lasers are so-called slow absorbers, which means that they have a recovery time which is substantially longer than the pulse duration. That is often the case for lasers which are mode-locked with semiconductor saturable absorber mirrors (SESAMs), for example, particularly in the femtosecond pulse duration regime. Here, the SESAM's recovery time is often about an order of magnitude longer than the pulse duration. Already in the 1990s (if not earlier), some researchers realized a potentially serious technical problem with slow absorbers:

In conclusion, it should not be possible to obtain stable passive mode locking with a slow saturable absorber!

Well, that finding was actually not consistent with common experimental experience – such lasers are often found to be absolutely stable, producing nice pulses without any noise issue on the trailing part. Therefore, researchers have searched for explanations for that apparent discrepancy.

Soliton Mode Locking

An early root of reasoning was that some additional physical mechanisms could have a stabilizing effect. One such mechanism could indeed be identified for the case of soliton mode locked lasers (F. X. Kärtner et al., “Stabilization of solitonlike pulses with a slow saturable absorber”, Opt. Lett. 20 (1), 16 (1995)); I briefly describe it in the following:

Well, that's plausible, but works of course only for lasers with soliton effects.

Gain Saturation

Others have considered lasers where not only the absorption, but also the laser gain itself exhibits substantial saturation. In that case, positive net gain behind the pulse may actually be avoided. Such a mechanism, however, does not work in solid-state lasers, where the pulse energy is typically orders of magnitude below the gain saturation energy.

Something Was Missing!

Curiously, people seemed to ignore at that time the actually well known fact that even very simple picosecond solid-state lasers, not having substantial effects of chromatic dispersion and nonlinearity on the pulses, nor any significant gain saturation during a pulse, are also stable. So obviously there must be some still unidentified stabilizing effect even in such lasers. However, nothing seemed to happen for quite a few years. Maybe some people realized the problem but simply couldn't find an explanation.

The Solution

I came across this issue during my time as a group leader in the ETH Zurich. In my group, we had various lasers to which the soliton-based explanation could clearly not be applied. Furthermore, I had developed numerical models for mode-locked lasers which also confirmed the stability despite clearly positive net gain behind the pulse. When you find something like that in a simple model, it becomes much easier to find the reason, because such a physical model is, as I like to say, transparent: you can inspect any relevant quantity, while it is often very difficult to measure such things in experiments.

First I checked whether the stability might be a numerical artifact. You can imagine, for example, that if you had exactly zero intensity after the pulse in a numerical model, application of an arbitrarily high gain would still leave it at zero. However, that concern could quickly be ruled out; that is not exactly zero intensity after the pulse, and even adding some substantial numerical noise in every resonator round trip does not remove the stability.

A solution of the problem required some physical reasoning, which finally led to the following explanation:

Based on that idea, I could then do some simple analytical calculations, particularly for estimating the limits of stability. I found that stability is indeed lost when the recovery time of the absorber gets too long; that stability limit actually depends on how strongly the absorber is saturated. Such stability limits could be verified with numerical experiments. Such investigations led to the confidence that the finally discovered mechanism is really what stabilizes such simple lasers. The results have been published in Appl. Phys. B 73 (7), 653 (2001).

Of course, the described mechanism also works in soliton mode-locked lasers; this means that the previous implicit assumption that the other mentioned mechanism is solely responsible for stability in such lasers, is wrong. Indeed, some soliton mode locked lasers would be stable even entirely without that other mechanism.

Wrong Assumptions Lead to Wrong Results

By the way, there have been some theoretical papers which are entirely wrong. They started with the wrong postulation that stable mode locking is possible only when there is no positive net gain behind the pulse, and derived various consequences from that wrong assumption. That's now for the garbage bin.

There are actually researchers in the field – even well established ones – who still have not recognized the simple stabilizing mechanism and therefore claim in scientific talks e.g. that soliton mode locking is necessary to obtain stability in passively mode-locked femtosecond lasers.

Conclusions

Some conclusions should be drawn:

This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the Encyclopedia of Laser Physics and Technology.

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