| With the demand for high speed data transmission increasing at a tremendous pace, the development of high-performance optical transmission systems is critical to meeting the ever increasing demands of world-wide telecommunications. To further increase available bandwidth, one must either decrease pulse width in single channel systems or decrease the distance between channels in wavelength division multiplexing (WDM) systems. In both cases, certain physical effects which are negligible for systems operating in previously standard regimes now play a significant role in determining the dynamics of pulse propagation. Higher order dispersion and randomness in dispersion, the subjects of this thesis, are two such effects which can severely limit stable pulse propagation in a conventional DM link. Part I of the thesis explores the extension of dispersion compensation to third order linear dispersion, and Part II focuses on a compensating technique for randomness in the dispersion. The parts are self-contained and may be read in either order. For both problems, the new models that arise are NLS-type equations with rapidly varying coefficients. We use averaging procedures to simplify these equations, and in the context of third order dispersion, prove a rigorous result on the validity of the asymptotic approximation. In general, the averaging approximations lead to complicated integro-partial differential equations, and special solutions for these equations, localized standing waves, are candidates for bit-carriers. By exploiting the underlying Hamiltonian structure of the models, we demonstrate the existence of such solutions by constrained minimization, and also verify their stability. Finally, for each problem, numerical simulations are necessary to complement theoretical results and explore system performance in real fiber units, and we develop and implement efficient numerical algorithms to solve both the evolution equations and nonlinear eigenvalue problems that arise. This work provides theoretical justification for the extension of the dispersion management technique to other contexts. |
