Mathematics of Soliton Transmission in Optical Fiber

Abstract

Ring resonators are suitable for many applications in micro and nano optical communication. Optical soliton is a self-reinforcing solitary wave that maintains its shape while it travels at constant speed. Optical solitons are seen by a cancellation of nonlinear and dispersive effects in the medium which can be a fiber optic. In a Kerr effect medium such as fiber optics, high intensity of light causes a phase delay having similar temporal shape as the intensity. This nonlinear phenomenon occurs for a beam called self-phase modulation (SPM), which is generated by its intensity. Optical Chaos occurs in many nonlinear optical systems. One of the most common examples is a ring resonator. Chaotic behavior has been considered as a nonlinear property in physics, electronics, and communication. When a high-intensity short pulse is coupled to optical fiber, the instantaneous phase of optical pulse rapidly changes through the optical Kerr effect. The SPM and cross-phase modulation (CPM) effects change the phase of the pulse as a function of its intensity. Here, we derive the soliton equations based on solving the nonlinear Schrodinger and Maxwell equations. The main performance characteristics of ring resonators are transmittance, free spectral range, finesse, Q-factor, and group delay, which have been demonstrated.