Pulse Dynamics in Optical Communications

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Over the past decade, tremendous strides have been made in increasing the transmission capacity of fiber optic communications systems. One technique that has enabled this increase involves transmitting multiple streams of data simultaneously down a single fiber line in a process known at wavelength division multiplexing (WDM). In order for this technique to work, interaction between the different data streams must be minimized. Another important development has been the appearance of all optical devices, system components that exploit parametric processes in optical fiber to perform data manipulation at faster rates than more tradition opto-electronic components. In contrast to WDM systems, these devices depend on strong interaction between different frequency components in order to function. Proposed is a consideration of the problem of interchannel interaction (the interaction of data streams centered at different frequencies) in the two limits suggested by WDM systems (weak interaction) and all optical devices (strong interaction). To meet this goal, asymptotics, multiple scale and soliton perturbation theory, variational methods, and symmetry reduction techniques will be used to obtain reduced equations for the dynamics of optical pulses in the relevant limit. These equations will be studied analytically and numerically in order to identify the parameter regimes that support stable and efficient system operation. Numerical simulations will be used at each stage of the analysis to compare results with experimental data. This University-Industry Cooperative Research (U-ICR)Program project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).