Variational Calculation of Optimum Dispersion Compensation for Nonlinear Dispersive Fibers

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Virginia Tech

In fiber optic communication systems, the main linear phenomenon that causes optical pulse broadening is called dispersion, which limits the transmission data rate and distance. The principle nonlinear effect, called self-phase modulation, can also limit the system performance by causing spectral broadening. Hence, to achieve the optimal system performance, high data rate and low bandwidth occupancy, those effects must be overcome or compensated. In a nonlinear dispersive fiber, properties of a transmitting pulse: width, chirp, and spectra, are changed along the way and are complicated to predict. Although there is a well-known differential equation, called the Nonlinear Schrodinger Equation, which describes the complex envelope of the optical pulse subject to the nonlinear and dispersion effects, the equation cannot generally be solved in closed form. Although, the split-step Fourier method can be used to numerically determine pulse properties from this nonlinear equation, numerical results are time consuming to obtain and provide limited insight into functional relationships and how to design input pulses.

One technique, called the Variational Method, is an approximate but accurate way to solve the nonlinear Schrodinger equation in closed form. This method is exploited throughout this thesis to study the pulse properties in a nonlinear dispersive fiber, and to explore ways to compensate dispersion for both single link and concatenated link systems. In a single link system, dispersion compensation can be achieved by appropriately pre-chirping the input pulse. In this thesis, the variational method is then used to calculate the optimal values of pre-chirping, in which: (i) the initial pulse and spectral width are restored at the output, (ii) output pulse width is minimized, (iii) the output pulse is transform limited, and (iv) the output time-bandwidth product is minimized.

For a concatenated link system, the variational calculation is used to (i) show the symmetry of pulse width around the chirp-free point in the plot of pulse width versus distance, (ii) find the optimal dispersion constant of the dispersion compensation fiber in the nonlinear dispersive regime, and (iii) suggest the dispersion maps for two and four link systems in which initial conditions (or parameters) are restored at the output end.

The accuracy of the variational approximation is confirmed by split-step Fourier simulation throughout this thesis. In addition, the comparisons show that the accuracy of the variational method improves as the nonlinear effects become small.

Nonlinear Schrodinger Equation, Dispersion Map, Pre-Chirping