Analysis and synthesis of optical scattering filters using digital signal processing techniques

Abstract

This thesis describes analysis methods using lattice filter model of optical fiber gratings (that is classified as short period fiber gratings and long period fiber gratings), synthesis methods of optical fiber gratings using optimization algorithms, and design methods of optical lattice filters (such as Fabry-Perot $\acute{e}$talons, multilayer thin films, and directional couplers) using Schur algorithm. These propose the methods for analysis and synthesis of optical scattering filters (such as optical fiber gratings and optical lattice filters). Analysis of the optical scattering filters finds scattering data (such as spectrum, transfer function, and impulse response) from filter parameters (such as index, period, coupling coefficient, and reflection coefficient). In this thesis, we propose a new modeling structure for the long period fiber gratings. The proposed model has the multiport orthogonal FIR (finite impulse response) lattice filter configuration. Our multiport lattice filter model can be used to analyze (or to synthesize) phase-shifted long period fiber gratings, cascaded long period fiber gratings, and piecewise-uniform long period fiber gratings. We also propose a new method for analyzing the short period fiber gratings (fiber Bragg gratings (FBG) is the same meaning) with an arbitrary index profile and an arbitrary individual grating length. The proposed method is based on the lattice filter model which is widely used in the applications ranging from the digital filtering to speech synthesis and explosive seismic signal processing. Lattice filter interpretation provides us with an accurate and simple tool for analyzing an arbitrary index profile and arbitrary aperiodic fiber grating structures, and gives us further insight to the understanding of the short period fiber gratings. Synthesis methods are computing filter parameters to identify optical scattering filters from the scattering data. In this thesis, an algorithm of Schur to one dimen...