Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
Modern high-speed fiber optics communications systems extensively use multiple frequency channels for transmission of information. One of the major limitations on the performance of these systems is caused by the nonlinear interaction of optical pulses from different frequency channels (interchannel collisions). With the increasing demand for faster transmission of information one can expect a corresponding increase in the number of frequency channels used. As a result, the importance of interchannel collisions between optical pulses is expected to increase, and an accurate description of the effects of these collisions is needed.
In this paper we study interchannel collisions between optical pulses using optical solitons as an example. We focus our attention on the effect of third order dispersion, which is the slope of the dispersion as a function of frequency. We develop a perturbation theory with two small parameters: the third order dispersion coefficient and the reciprocal of the frequency difference between the two channels. We find that the amplitude of the emitted radiation is proportional to the third order dispersion coefficient divided by the square of the frequency difference between the channels. Moreover, the radiation emitted in the collision can be described as resulting from a fast change in the dispersion coefficient. Therefore, soliton propagation in a given frequency channel influenced by many collisions with a random sequence of solitons from all other channels is equivalent to soliton propagation in fibers with weak disorder in the second order dispersion coefficient. As a result, one can expect the emergence of long-range intra-channel interaction, which leads to a severe random walk of the solitons and to loss of information.
