Modulational Instability in a Layered Kerr Medium: Theory and Experiment

My second PRL was just published a couple days ago.

My coauthors are experimentalists Martin Centurion, Ye Pu, and Demetri Psaltis from Caltech and theorists Panos Kevrekidis from University of Massachusetts at Amherst (one of my primary collaborators), and Dimitri Frantzeskakis of the University of Athens. (I was the main theorist on the paper and the second author overall.)

Here is the abstract:

We present the first experimental investigation of modulational instability in a layered Kerr medium. The particularly interesting and appealing feature of our configuration, consisting of alternating glass-air layers, is the piecewise-constant nature of the material properties, which allows a theoretical linear stability analysis leading to a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between theoretical, numerical, and experimental diagnostics of the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, there are multiple instability regions rather than just one as in a uniform medium.


On November 13th, we submitted an archival follow-up to this paper to an applied math journal. I don't expect we'll hear from them for a while, but I have 4 other papers currently in press, and a couple should actually show up in their final form soon. (I've done the proofs for three of these. One of them is available online but hasn't been assigned to an official print issue and probably won't be for a little while. The 4th of these, for which we don't yet have the page proofs, will have an interesting blog entry when it finally comes out.) There's a 5th paper that just got virtually accepted ("more or less"): the referees just asked for a very small number of cosmetic changes and wrote lots of various positive statements about the science. However, this isn't an official acceptance, so I can't count it as in press.

We are currently looking at following up the above research with studies of multi-bump solitons in layered Kerr media. (We also may put the glass slides at an angle because then one gets a linear-profile spatial inhomogeneity in the nonlinearity coefficient, which can lead to some cool dynamic effects.) The experiments are just starting, and we'll see if we find something interesting. (The experiments in which we hoped to look at dislocation dynamics didn't work.)

I have a newer project that is joint with an experimentalist. I'm still trying to get the code to work to simulate the system. This is the one where you have a chain of beads that one then strikes to examine wave propagation. (This is very much like the Newton's cradle classroom demonstration and, in fact, there is even one direct analog of it that definitely works but still needs a theoretical explanation for the mechanism.) This one is currently at the level of trying to get the code to work by comparing the output with that from previous code that was used in other papers.