Abstract： The mathematical modeling of various lightwave systems is complicated by the many deterministic and stochastic physical effects that contribute to determine these systems' behavior.  In addition, because of the extremely small error rates required of some of these systems, quantifying their performance presents an analytical and computational challenge.  In this talk I will discuss various mathematical models for studying optical fiber communication systems and Ti:sapphire femtosecond lasers. 

After reviewing the basic mathematical framework for describing optical fiber communication systems, I will describe recent work aimed at quantifying the effects of amplifier noise and dispersion management in these systems.  Amplifier noise is added to pulses as they propagate. Large noise-induced distortions are rare, but they are one of the main sources of errors.  The use of dispersion management has been shown to dramatically improve system performance.  It does so, however, by altering the pulse propagation, which makes it much more difficult to study these systems.  For both of these effects I will show how a combination of exact methods, asymptotic and numerical techniques can be used effectively to extract useful information about the system's behavior.

Finally, in the last part of the talk I will show how similar methods to those used for dispersion management in optical fiber transmission systems can also be used to study the behavior of Ti:sapphire femtosecond lasers.