Applications of the moment method to optical communications systems: Amplifier noise and timing jitter

Optical pulse propagation through a fiber is governed by the nonlinear Schrodinger equation. In most cases when the system is not dissipative, using the variational method can help reduce this partial differential equation that governs the pulse propagation into many ordinary differential equations. This reduction makes it easier to study the changes in pulse parameters and hence easier to study the pulse propagation through the fiber. However for dissipative system this method cannot be used. In a communication systems with high bit rates (>40 Gb/s) when ultrashort solitons are used as optical bits of information, the communication system becomes dissipative due to intra pulse Raman scattering in the fiber. In such a case, the system becomes non Hamiltonian and variational method cannot be used for such systems. We show that the moment method remains valid for both dissipative and non-dissipative systems and hence can be used to study the pulse propagation in both high and low bit rate systems. In particular we apply this method to study the effect of amplifier noise on the pulse parameters and analytically calculate the timing jitter due to the amplifiers that are used periodically to compensate the fiber losses.; Amplifiers used in soliton communications systems restore the soliton energy, but also add amplified spontaneous emission noise. This noise affects the soliton evolution along the fiber link limiting the total transmission distance by reducing the signal to noise ratio of the system. The amplifier induced noise also fluctuate the amplitude, frequency and position of the pulse thus causing timing jitter in the system that lead to increased bit error. We use the moment method to calculate the timing jitter at the end of the system and show using this method that several different techniques can help reduce the timing jitter at the end of the system.; For systems using bit rates <40 Gb/s the timing jitter is mainly due to Gordon-Haus effect which has its origin in amplified spontaneous emission-induced frequency fluctuations. By applying the moment method to such systems we show that dispersion compensation techniques can reduce timing jitter. However, at higher bit rates for which the pulse width becomes shorter than 5 ps, the Raman jitter induced by intra pulse Raman scattering in the fiber is likely to become the most limiting factor. For such a system we show that using parametric amplifiers instead of fiber amplifiers can reduce timing jitter. We apply the moment method not only to soliton systems but also to non-soliton systems and show that these techniques work for both the systems.