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 dimension inverse scattering problem on power series bounded in theunit circle is used for the determining the reflection coeffcients of multilayer medium (such as Fabry-Perot $\acute{e}$talons, multilayer thin films, and directional couplers) modeled by lattice filter. To synthesize the optical fiber gratings, we propose a powerful and simple synthesis technique using Broyden-Fletcher-Golffarb-Shanno algorithm for gain fitting of arbitrary spectrum. This proposal also propose and compare two new methods for synthesizing piecewise-uniform long period 6ber gratings. The proposed methods, which employ the Broyden-Fletcher-Golffarb-Shanno optimization algorithm based on the lattice fitter model, are used to design the equalizer which compensates for the non-flat gain characteristics of erbium-doped fiber amplifiers (EDFA). Multi-port lattice model for the long period fiber gratings is applied to synthesizethe long period fiber gratings for the erbium gain equalization using simulated annealing and steepest descent methods. We propose new methodology (using the simulated annealing technique followed by the steepest descent algorithm)for designing an ideal bandpass filter having linear phase as a cascade of two piecewise uniform FBGs (followed by a 100% fiber-optic reflector) for an ideal WDM filter bank. The proposed structure has two piecewise-uniform FBGs. The first piecewise-uniform FBGs are designed to get the desired (i.e., rectangular) bandpass amplitude spectrum. The second piecewise-uniform FBGs(together with a perfect reflector), which is an all-pass filter, are designed to flatten the group delay characteristics (not altering the amplitude spectrum)of the first FBGs.
이 논문에서는 광섬유 격자 (단주기 광섬유 격자와 장주기 광섬유 격자)의 lattice 필터 모델을 이용한 분석방법, optimization 알고리듬을 기초로 한 광섬유 격자의 합성방법, 그리고 Schur 알고리듬을 이용한 optical lattice 필터들 (Fabry-Perot $\acute{e}$talons, multilayer thin films, and directional couplers)의 설계방법들을 설명하였다. 이러한 내용들 중에서는 크게 광산란 필터 (광섬유 격자와 optical lattice 필터)의 분석방법과 합성방법으로 나누어진다.
광산란 필터의 분석방법은 인덱스와 주기, 결합상수, 반사계수등의 필터 파라메터로 부터 스펙트럼, 전달함수, 그리고 임펄스 응답과 같은 광산란 필터의 입출력 특성을 찾아내는 방법이다. 본 논문에서는 장주기 광섬유 격자를 위한 새로운 모델구조를 제안했고, 제안된 구조를 multiport lattice 필터 모델이라고 부른다. 이러한 multiport lattice 모델은 phase-shifted 장주기 광섬유 격자, cascaded 장주기 광섬유 격자, 그리고 piecewise-uniform 장주기 광섬유 격자의 분석을 위해 사용된다. 우리는 또한 정확하고 간단하게 단주기 광섬유 격자를 분석하기 위하여 신호처리분야등에서 널리 사용되는 lattice 필터 모델을 기초로 한 새로운 모델을 제안 하였다.
광산란 필터의 합성은 광산란 필터의 입출력 특성으로 부터 광산란 필터의 필터 파라메터를 계산하는 것이다. 본 논문에서는 lattice 필터로 모델링 되는 optical lattice 필터들을 설계하기 위하여 Schur 알고리듬을 사용 하였다. 우리는 Broyden-Fletcher-Golffarb-Shanno optimization 알고리듬을 이용하여 piecewise-uniform 광섬유 격자를 합성하는 방법을 제안하였다. 우리는 또한 multiport lattice 필터 모델을 이용하여 erbium-doped fiber amplifiers (EDFA)의 게인을 평탄화 시켜주기 위한 장주기 광섬유 격자를 설계하기 위한 방법을 제안하였다. 제안된 합성방법에는 simulated annealing과 steepest descent optimization 알고리듬을 사용하였다. 마지막으로 두개의 단주기 광섬유 격자를 사용하여 WDM 시스템에 사용되는 대역통과 필터를 설계하여 보았고, 제안된 합성방법은 선형적인 위상과 원하는 스펙트럼 특성을 가지는 대역통과 필터를 설계할 수 있다.
