Modulational instability in nonlinearity-managed optical media

I've been so productive thus far today, so I might as well continue in this direction and blog about a paper of mine that just came out in Physical Review A today. This paper, which you can find here, is the archival sequel to a paper my collaborators and I published in Physical Review Letters late last year.

Anyway, here is the info:


Title: Modulational instability in nonlinearity-managed optical media

Authors: Martin Centurion, Mason A. Porter, Ye Pu, P. G. Kevrekidis, D. J. Frantzeskakis, and Demetri Psaltis

Abstract: We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear Schrödinger (NLS) equation with a piecewise constant nonlinearity coefficient and conduct a theoretical analysis of its linear stability, obtaining a Kronig-Penney equation whose forbidden bands correspond to the modulationally unstable regimes. We find very good quantitative agreement between the theoretical analysis of the Kronig-Penney equation, numerical simulations of the NLS equation, and the experimental results for the modulational instability. Because of the periodicity in the evolution variable arising from the layered medium, we find multiple instability regions rather than just the one that would occur in uniform media.


We are currently trying to do a little more of a follow-up with our layered optical media setup and then I think that this series of projects will be over. (Martin, the main experimentalist has left Caltech. Demetri Psaltis, whose lab he was in, is probably leaving Caltech, which is preventing new people from joining the project on the experimental side and this sort of thing puts things in limbo anyway. Ye is spread very thin, as he is working not just on this stuff but also on biomechanics stuff and on trying to find a tenure-track job. Anyway, the hope is to submit a final short paper with experiments and some numerics (on which Ye will be the first author) and then put this down. Panos, his students, and I are working on something theoretical that is related to our series of optics projects and the long-term hope is to find another lab (maybe at Oxford or elsewhere in England?) with which we can work on future experiments.

I'll try to write about this later when I blog more about my conference, but I was apparently extremely useful in hooking up a couple of people (by seeing something and realizing exactly who Person A should talk to) for a collaboration. I really like being useful. I wish I could do that more often. (I received a thank-you e-mail about this today.)