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The thing I've been pondering is that as compared to other "sympathetic
vibration" / "resonance" / ... type examples I can think of, in this
case (or the comparable spring question) the system responds at its own
frequency which is a harmonic of the frequency at which you pump it....
So it *appears* to be multiplication of a frequency. (i.e. if an
optical analog existed it would amount to something such as putting 800
nm in and getting 400 nm out.)