Analytical studies of modulation instability and nonlinear compression dynamics in optical fiber propagation

This paper summarizes analytic results describing the spectral broadening associated with fiber modulation instability as described by analytic breather solutions of the nonlinear Schrodinger equation. These solutions allow the prediction of spectral properties of both noise-driven and induced modulation instability processes. In the latter case, the ability to describe MI with an analytic formalism allows the design of optimized experiments to generate ultrashort pulse trains from weakly-modulated initial fields. These results are examples of only a very small number of analytic descriptions of optical field propagation in highly nonlinear fiber.