As I was thinking about a nice analogy of solitons in microresonators that would explain it to the layman, somehow the “Mexican wave” crossed my mind. Curiously, it did this while perfectly maintaining its shape.
The Mexican wave (or The wave or “La Ola wave”) is the pattern that one can obtain in particular at sport events in stadiums when the audience is getting really excited. The spectators then stand up in a synchronized manner which moves around the stadium. Examples can be seen on Youtube for example here and here. As it goes around in the stadium the wave usually retains its shape. This is somewhat surprising because nobody actually tells the crowd when to stand up and when to sit down. Looking at these properties (the fact that it originates from an “excited” state, that it goes around in a circle and that it retains its shape while propagating) it seems a lot like the familiar dissipative soliton state in microresonators. Thinking about it, one can even come up with two more analogies which underpin to some extent the argument that the Mexican wave is similar to a soliton.
First, the nonlinearity that is required for a soliton: The Mexican wave is made by individual persons who stand up. Obviously, standing up is psychologically much easier if people around you are already standing. Just imagine standing up in a concert where everyone is sitting. Therefore this effect is clearly a nonlinear one: the more people are standing, the more people stand up (even if it is only to be able to see something). Second, the dispersion: as I said, there is nobody giving directions when to stand up. Therefore there is some general effect of dispersion when some people stand up earlier and some sit down later.
Given that there seems to be something like a nonlinearity and some dispersion in the system, I guess we have a good candidate for a soliton-like structure. After this “discovery” I looked into literature. And, although there is not too much prior work on this, it is not the first time that this idea was proposed. Two relevant papers that I found on this topic were I. Farkas, et al., Nature. 419, 131 (2002) and J. Cartwright, Europhys. News. 37, 22 (2006). As you can see, there is some controversy whether Mexican waves are solitons or some effect in an “excitable medium” but this discussion I will leave to the theorists (comments below are welcome!). I guess that by doing the right transformations, simplifications and approximations it can be shown that the two systems are equivalent anyways. Just like the Lugiato-Levefer equation and the coupled mode equations are somewhat the same.
Just one more comment: As the Mexican wave is probably more effective in motivating the sportsmen on the field than just random fluctuations of standing people, dissipative solitons in microresonators and the resulting coherent Kerr frequency combs are certainly more effective than the random unstable MI state. With this, enjoy riding The wave!
P.S. For readers who are now interested in dissipative solitons in optical (micro)resonators and their effects, have a look at these references: F. Leo et al., Nature Photonics. 4, 471 (2010) and T. Herr et al., Nat. Photonics. 8, 145 (2014).
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