Nonlinear and Stochastic Effects in Optical Fiber Communications

Abstract

Optical fiber communications have experienced a period of tremendous growth; in the last decade alone, system capacities have increased by four orders of magnitude. The complexity of these systems has also increased, however, making their mathematical modeling much more complicated. Also, because transmission errors are handled by electronic components at lower speeds, these systems are required to have extremely small bit error ratios, which predict actual error rates, a difficult mathematical and computational challenge. In this talk, I will describe recent work that has been aimed at overcoming these challenges. In particular, I will discuss two kinds of phenomena: dispersion management and the impact of stochastic effects such as amplifier noise.>/p>

Dispersion management is a recently adopted technique that is known to significantly improve system performance. At the same time, however, I will show how it dramatically alters the underlying properties of the system and results in a remarkably different set of dynamical equations.

Amplifier noise is another important physical effect: large noise-induced pulse distortions are rare, but those events are precisely one of the most likely causes of transmission errors. In this case, I will show how the careful application of importance sampling allows one to improve the efficiency of Monte-Carlo simulations by several orders of magnitude, thus making it straightforward to study events that would be almost impossible to observe with a brute force approach.