Kink stability, propagation, and length-scale competition in the periodically modulated sine-gordon equation

We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program that are not compatible with the existence of a radiative threshold predicted by earlier calculations. Second, we carry out a perturbative calculation that helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it reproduces accurately the observed kink dynamics. Fourth, we report on the occurrence of length-scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.

Thermally induced all-optical inverter and dynamic hysteresis loops in graphene oxide dispersions

We experimentally study the temporal dynamics of amplitude-modulated laser beams propagating through a water dispersion of graphene oxide sheets in a fiber-to-fiber U-bench. Nonlinear refraction induced in the sample by thermal effects leads to both phase reversing of the transmitted signals and dynamic hysteresis in the input- output power curves. A theoretical model including beam propagation and thermal lensing dynamics reproduces the experimental findings. © 2015 Optical Society of America.