Analytic Studies On Certain Optical Pulse Interaction Problems With Symbolic Computation

In optical communication systems, the information transmitted are usually some optical pulse trains. Minimizing the distance between two adjacent pulses has been used to improve the capacity of the communication systems. When the soliton technique is applied to the optical communication systems, the problems of the interactions between two solitons have arisen, which cause soliton distortion and transmission deterioration in the optical communication systems, accordingly bring rising bit error rate and shorter transmission distance, and finally negatively affect the quality and capacity of the optical communication systems. With increasing data transfer rate, the interactions between two solitons should be studied in order to obtain the greatest possible transmission distance under the same bit rate.The common mathematical model describing the optical soliton transmission in the optical fibers is the nonlinear Schrodinger (NLS)-type model. In optical communication systems, numerical methods have been used to study the model, and the input data and output results all are numerical values. Obtaining the analytic solutions for the model is helpful for the understanding of the nature of the nonlinear phenomena described by the model. Typically, to obtain the analytic solutions for the model, ignoring some physical effects and reducing the computational accuracy would be required, so would be the complicated calculation process. With the development of science and technology, symbolic computation has been used to obtain the analytic solutions for the model. With the symbolic computation and the algebraic algorithm, the complex mathematical calculations and deductions can be conducted with computer to ensure the acquisition of the analytic solutions with absolute accuracy for the model.Integrating the current development of the optical soliton field, this dissertation an-alytically study the soliton solutions and interactions for the NLS-type models by means of symbolic computation and the bilinear methods. Main problems to be solved include: How the distance between optical solitons be minimized with the optical soliton inter-action diminished? Can optical solitons be compressed while maintaining its original space, thereby reduces the optical soliton interaction? Can spontaneous soliton amplifi-cation be achieved without requiring the periodical focus amplifier? Can optical solitons be controlled with the properties of optical transmission medium? What are under in-vestigation include the following four aspects:the generation of the bright and dark solitons and their interactions in the normal group velocity dispersion (GVD) regime of optical fibers; soli ton-effect pulse compression and their interactions; optical soliton amplification and their interactions; soliton control and their interactions. Specifically, the work is outlined as follows:(1) Generation of the bright and dark solitons and their interactions in the normal GVD regime of optical fibers:By analytic studies on the NLS model, higher-order NLS (HNLS) model, variable-coefficient NLS (vcNLS) model and vcNLS model with the losses, their one- and two- soliton solutions are obtained with symbolic computation. It concludes that the bright and dark solitons can be obtained in the normal GVD regime of optical fibers and the corresponding conditions for their generation are also given. Making the asymptotic analysis of the interactions between two solitons qualitatively, results indicate that the interactions between bright and dark solitons are inelastic in the HNLS model, while the interactions in the other three types of NLS models are elastic, with the energy conserved before and after the interactions. Changes in the physical parameters of the two-soliton solutions in the HNLS model can alter the optical soliton transmission mode. In the nonuniform fiber transmission medium, the dispersion decreasing fibers with different dispersion profiles can be selected to conduct soliton control, which exerts no effect on the optical soliton interactions. In addition, stability analysis of the soliton solutions for the vcNLS model is conducted to verify their stability.(2) Soliton-effect pulse compression and soliton interaction:The HNLS model is used to describe the soliton-effect pulse compression. The one-, two- and three-soliton solutions for the model are derived with symbolic computation, and the soliton-effect pulse compression mechanism is studied analytically. When the spacing between two optical solitons is comparatively small, the interaction will occur, which results in the phenomena of the soliton-effect pulse compression with optical solitons exhibiting pe-riodic changes. When the spacing between two optical solitons is comparatively large, optical solitons propagate without interactions. The above conclusions are verified by the three-soliton solution. Third-order soliton-effect pulse compression is confirmed to manifest higher compression factor being influenced by the combined effects of third- order dispersion (TOD), self-steepening (SS) and stimulated Raman scattering (SRS). However, due to the TOD effect, the third-order optical soliton is attached with an os-cillating structure, which leads to the lower-quality compressed optical solitons with the optical soliton width broadening.(3) Optical soliton amplification and their interactions in the anomalous GVD regime of optical fibers:Analytic studies on the three models(the vcHNLS model, HNLS model and vcNLS model with losses) are performed to acquire the one- and two- soliton solutions with symbolic computation. The dispersion-shifted fiber (DSF) and dispersion-decreasing fiber (DDF) are verified to realize the optical soliton amplification. For the vcHNLS model, the DDF with different dispersion profiles can be used to achieve the optical soliton amplification, with different dispersion profiles corresponding to different optical soliton amplification gain. While the HNLS model is mainly utilized in the DSF to investigate the optical soliton amplification, which can be realized via the energy exchange after the optical soliton interaction. In the vcNLS model with losses, the in-vestigation on the DDF with a new kind of dispersion profile suggests that the optical soliton can be amplified within a comparatively short distance with the amplification speed being controlled.(4) Soliton control and interaction:The vcNLS model and vcHNLS model are ana-lytically studied and their one-, two- and three-soliton analytical solutions are obtained via symbolic computation. With the DDF of different dispersion profiles conducting the change of the optical soliton amplitude or speed, soliton control can be realized and have no impact on optical soliton interaction. According to the dispersion profiles of the DDF, the optical soliton amplitude varies with the GVD parameter. Research on the dark soliton indicates that dark solitons can be controlled when the TOD coefficient function is proportional to the dispersion profiles of the DDF, even if there is higher-order effect. When the optical solitons propagate in the Gaussian DDF, provided that the optical soliton spacing is comparatively small, the optical solitons will not interact, and the capacity of the optical communication system will be improved. In addition, it is found via asymptotic analysis that the optical soliton interactions are elastic in the systems with the energy conserved.