Mathematical Sciences: Study of Pulse Propagation in Birefringent Nonlinear Optical Fibers

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9622802 Yang The objective of this project is to study the propagation and interaction of optical pulses in birefringent nonlinear optical fibers. In such fibers, nonlinearity, dispersion and birefringence all play an important role, and the pulse evolution can be modelled mathematically by two coupled nonlinear Schroedinger equations. In this project, we will study the propagation of such pulses by examining the solution properties of these coupled equations. In particular, we will thoroughly investigate the internal oscillations, radiation and interaction of these pulses. A combination of analytical and numerical methods will be used. The analytical methods include Hirota's method and the perturbation methods. Hirota's method will be used to study the interaction behaviors of the optical pulses. The perturbation methods will be used to study their internal oscillations and radiation. The numerical methods will be used to check the analytical results as well as to deal with cases where analytical methods are not appropriate. The proposed research will provide theoretical guidance to the design of the fast-speed fiber-optic telecommunication systems. In addition, it will develop new analytical methods for studying non-integrable wave systems. %%% This project will study the propagation and interaction of optical pulses in birefringent nonlinear optical fibers. It is motivated by the ongoing experiments on high-speed fiber-optic telecommunication systems using solitonian pulses as information bits. It will address some basic theoretical questions arising in the design of such telecommunication systems. For instance, it will study the stability and degradation of pulse signals travelling along the optical fibers. Its results will contribute to the realization of the underlying new communication systems which could revolutionize the whole field of long-distance information transmission. ***