The analytical derivation and applications of the NLS equation for nonlinear optical propagation in dielectric optical fiber devices

In this thesis, we shall model several optical fiber devices. The first is a redesign of the telecommunications fiber. The second is a redesigned close core optical fiber coupler. During our analysis and subsequent design of the nonlinear ultrafast telecommunication fiber, we first solved the linear problem for a circular dielectric-step fiber. We then solved the linear problem for a circular gradient dielectric cross-sectional fiber and compared the results. The gradient cross-section models the manufacturers ability to control a step fibers core radius ρ₀, and any subsequent diffusion of core-cladding material across the step interface. We concluded that, as long as the gradient region is small compared to the size of the core, any effects attributable to the gradient region could be modeled as a Taylor expansion of the step fiber solutions. We then analyzed the effects of dispersion and group velocity dispersion for the core-cladding step fiber configuration. We concluded that, for particular frequencies and core radii, the group velocity and group velocity dispersion could vanish, thus solving the timing jitter problem. We finally applied a multiscale expansion and small amplitude approximation to the linear step fiber problem. We took into account the Kerr nonlinearity, dispersion, and damping characteristics of the step fiber configuration. We concluded that Manakov vector-type equations with vector-train solutions can be found for particular guiding radii, susceptibility ratios, and frequency; thus allowing ultra high bit rate digital transmission of optical data.; During our analysis and subsequent design of the nonlinear mismatch fiber coupler, we first applied a multiscale expansion to Maxwells' equations for a mismatched coupler configuration, and subsequently derived the nonlinear envelope evolution equations. We concluded that fast pico-second directional coupling was possible with this configuration. We then studied the switching dynamics of this configuration, checking our ability to predict the switching criteria. We then studied the stability of this coupler configuration and concluded that fast pico-second switching was well within the stable regime. We finally concluded that although a great improvement over earlier coherent couplers, the switching lengths were still far too long for coupler application in optical computer processing.