Collision induced timing shifts in wavelength-division-multiplexed optical fiber communications systems

Long distance repeaterless optical fiber communications systems are currently used to transmit most internet and telephone information worldwide. The growth of photonic telecommunications technology has produced systems with very high bit-rate per fiber, but this still falls short of its potential capacity. Currently systems that are able to transmit even higher bit-rates are being developed utilizing dense wavelength-division-multiplexing (WDM) to maximally utilize the bandwidth potential of optical fibers. One of the most important factors that limits the bit-rate achievable in a such a WDM optical communications system is the cross-talk between channels caused by pulse collisions. In this thesis a consistent mathematical theory is used to analyze the frequency and timing shifts caused collisions between two WDM channels. This theory is applied to the systems currently most promising for next-generation photonic telecommunications; the dispersion managed (DM) soliton and 'quasi-linear' systems. Self-contained formulae are obtained which accurately predict the timing shifts suffered in these systems with a wide range of parameters. These formulae require an order of magnitude less computational time that direct numerical simulations. Several mathematical techniques are introduced to obtain computationally efficient formulae for complete and incomplete collisions in both systems. For complete collisions we use the Poisson sum transform to change the calculation to a sum in the Fourier domain. For incomplete collisions we use asymptotic integration to obtain approximate formulae. For quasi-linear systems we simplify the Laplace method even further to obtain elementary formulae. We show that using a combination of these methods the timing shift for incomplete and complete collisions in a wide range of system configurations can be obtained in comparatively small computational times. We find that for systems with small DM map strength the timing shift from widely separated channels is significant. For quasi-linear systems with large DM map strength this is negligable and the timing shift decreases with the square of the channel frequency separation. We also find the timing shift from closely spaced channels is higher for quasi-linear systems than for DM soliton systems operating at the same average dispersion