Explanation For the Mode Instability In High-power Fiber Amplifiers With Few-mode Fibers
Ref.: C. Jauregui et al., "Impact of modal interference on the beam quality of high-power fiber amplifiers", Opt. Express 19 (4), 3258 (2011); A. V. Smith and J. J. Smith, "Mode instability in high power fiber amplifiers", Opt. Express 19 (11), 10180 (2011); encyclopedia articles on high-power fiber lasers and amplifiers and mode coupling
Several researchers recently made the troubling experience that high-power fiber amplifiers, when being operated at power levels of hundreds of watts or even above 1 kW, sometimes exhibit a kind of mode instability: when the pump power exceeds a certain threshold value, the beam quality of the output suddenly becomes quite poor. Obviously, this is related to the fact that the fiber core for the amplified signal is usually not single-mode, but rather supports a small number of guided modes. (One often uses such few-mode fibers because strictly single-mode fibers are more limited in effective mode area.) Some physical mechanism, which was initially not understood at all, appears to lead to mode coupling: a strong transfer of power from the wanted fundamental mode to unwanted higher-order modes. Substantial progress has now been made in identifying the physical origin of that mode coupling.
A first paper by Jauregui et al. (see above) pointed out that once we have some power in the fundamental mode (LP01) and a high-order mode (such as LP11), this can in different ways generate a kind of periodic grating in the fiber:
- A refractive index grating results from a Kramers–Kronig effect: modal interference generates a spatially varying intensity pattern, which leads to a variation of the upper-state population in the ytterbium dopant, and this finally to refractive index changes.
- Similarly, the local intensity variations lead to temperature variations, and these also influence the refractive index.
- In addition, there is a gain grating.
Jauregui et al. correctly pointed out that the period of such gratings – whatever their exact origin is – is perfectly in line what is needed to coherently couple light from the fundamental mode to a higher-order mode. However, they did not recognize another condition: the phase of such a grating also has to be suitable for that coupling. Indeed, one can see that a stationary index grating can not do the coupling for just that reason. More precisely speaking, the complex amplitude which it couples into the higher-order mode at any location is just 90° out of phase with the amplitude being there already. Therefore, that coupling effect cannot increase the magnitude of that amplitude. It is not clear at this point why their numerical simulations nevertheless appear to have demonstrated such a coupling, but it appears more interesting to look at later results presented by Smith and Smith (see above for the full reference).
Smith and Smith were aware of the above-mentioned phase problem, but recognized that this could be fixed with an additional assumption: that the light in the higher-order mode has a slightly different optical frequency. The effect of that frequency difference is that the modal interference pattern is moving. As the resulting refractive index pattern follows with some time delay, we get a phase lag which makes the coupling possible. It remains the question how some light at a different frequency gets into the fiber input, but there are several ways how this can happen. For example, the input signal may easily have a sufficiently large optical bandwidth – a few kilohertz are already sufficient for the thermal coupling, and a few hundred kilohertz for the Kramers–Kronig effect. The problem may even start simply as a kind of amplified spontaneous emission (ASE), as the mode coupling can easily generate a substantial effective gain of higher-order modes.
Although we have no proof yet that the described effects are exactly what caused the trouble in various previous experiments on high-power fiber amplifiers, the mechanism described by Smith and Smith is entirely plausible, concerning the basic physics and also quantitatively. It is only possible that even more physical mechanisms – yet to be identified – exist which can cause such mode coupling.
I assume that the authors are already examining in detail the impact of various design parameters of an amplifier which can influence the strength of that mode coupling. Having made a comprehensive numerical model, it is relatively simple for them now to check a number of such dependencies. This should also help to optimize designs for obtaining higher powers with still excellent beam quality. The ultimate remedy, of course, would be to realize fiber designs with very large mode area which are strictly single-mode. Alternatively, one can try to arrange somehow a strong loss for all high-order modes, but at it seems, this would have to be rather strong indeed.
I wished I could implement such mode coupling effects into my RP Fiber Power software, but this would be very time-consuming – for myself to develop it and for anyone executing such simulations. Note, however, that as long as effective gain resulting from such mode coupling is low enough, the effect is minimal. Only for these very high-power devices, one can encounter these effects.
Finally, I would like to express my high respect for Arlee V. Smith. The discussed paper is just another example of very high-quality and useful work. It is not only entirely correct, as far as I can see, but also reveals interesting and relevant new physics and explains this very well. Several other very high-quality papers of this author are cited in my encyclopedia, and often they have been very useful for my own research. That quality of papers – not their number! – characterizes an excellent researcher.
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 RP Photonics Encyclopedia.
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