Dispersion management is the technique of concatenating two or more optical fibers with different dispersion parameters to form a system with periodically varying dispersion. This technique makes it is possible to have both high local and low average dispersion in the system. The high local dispersion reduces four-wave mixing (an effect that distorts signals and produces intersymbol interference in transmissions), while the low average dispersion reduces the net cumulative effects of dispersion over long optical fiber spans. Overall, therefore, dispersion management reduces effects which are detrimental to the performance of optical-fiber based communication systems, thus allowing transmission capacity to be increased. In mathematical terms, what must be studied are nonlinear wave equations with rapidly varying coefficients. The theory of these equations is currently not well understood and will be advanced with support from this award.
The theme of this research is the development of new mathematical techniques with which to model the propagation of optical pulses in nonlinear optical fibers. It is important to properly understand the dynamics of such pulses in optical communication and information processing systems so that new techniques can be devised to increase their overall capacity. In particular, new mathematical methods for dealing with dispersion management will be investigated, in order to predict and improve the performance of such systems.
