In-Core Fiber Gratings: Coupling Analysis and Synthesis

Diffraction gratings formed in the core of optical fibers present unique means of coupling the light in and out of the fiber. These gratings can be used in a wide range of applications in fiber communications and sensors. In this dissertation, fiber-optic in-core gratings are analyzed using both rigorous and approximate methods. Local-normal -mode and scattering theories are used to develop a set of general coupled linear differential equations that describe the coupling process caused by planar gratings. Gratings that are formed at arbitrary angles with respect to the axis of the fiber are considered. Gratings with sinusoidal index variations are analyzed and shown to have a very narrow spectral widths (in the order of few Angstroms) with high diffraction efficiencies. Spectral widths and diffraction efficiencies can be controlled by changing the grating parameter; e.g. period, length, amplitude, and orientation of index modulation. Nonlinearities in index modulation, such as dc-bias, tapering, and chirp are analyzed. Approximate methods such as the First Born approximation, dielectric inhomogeneous thin film layers, and the optical-path methods are used in the analysis and have shown excellent agreement with the exact solutions especially for weak gratings. Synthesis techniques are also introduced for designing such gratings.