本論文是以MATLAB為平台設計3個Kramers-Kronig relation積分轉換程式，來分析光譜的光學性質。主要是以與阻尼振盪模型相當的色散理論 (Dispersion Theory)為基礎,由光吸收或反射光譜去推算光吸收係數k(ω)及折射率n(ω)。亦即在頻率空間所呈現的複數折射率n ̃(ω)=n(ω)+ik(ω)或複數介電常數ε ̃(ω)=ε'(ω)+iε"(ω)的實部與虛部之間存在一相互關係，稱為做Kramers-Kronig relation，實部與虛部得以相互轉換。本論文在檢測或驗證程式轉換結果是否符合理論值，並比較色散理論模型下，不同阻尼係數 γ 對於Kramers-Kronig relation轉換結果的影響。之後再以矽晶體，利用3個Kramers-Kronig relation積分轉換程式做光學常數n和k的互相轉換，討論其誤差的來源，並以Singly Subtractive Kramers-Kronig relation修正原來轉換式所呈現的誤差。

This thesis investigates the robustness of three MATLAB computer programs in calculating the optical constants of materials based on given spectral data, using well-documented single crystalline silicon as a testing case. The real and imaginary parts of a complex function are correlated through the Kramers-Kronig integral transform between them. The foci of the current investigation are on the dispersive dielectric function  ̃ε ̃(ω)=ε'(ω)+iε"(ω), or refractive index function n ̃(ω)=n(ω)+ik(ω), where ε ̃(ω)=〖n ̃(ω)〗^2. The representation of material constants as a complex function of frequency is a manifestation of optical dispersion that emulates a damped mechanical oscillation system. The computer codes contain a factor that is characteristic of the scattering rate γ of the oscillator. The factor was found to be critical to obtaining reliable outcome. Such improvement in the consistency, i.e., the reduction in deviation of the recovered optical spectrum from the original one, is believe to originate from avoiding the singular point when evaluating the principal values of the conventional Kramers-Kronig integral transform. A modified calculation through the so-called singly-subtractive Kramers-Kronig relation was then implemented to demonstrate this strategy in minimizing the deviations.

目錄
論文審定書 i
誌謝 ii
摘要 iii
Abstract iv
目錄 v
圖目錄 vii
第一章、 緒論 1
1-1 背景知識 1
1-2 研究動機 3
1-3 論文大綱 4
第二章、 理論原理 5
2-1 光學常數 5
2-2 Kramers-Kronig relation原理 10
2-2-1 概述 10
2-2-2 Kramers-Kronig relation 推導 10
2-3 類比阻尼振盪之光學色散 14
2-4 MATLAB軟體介紹 20
第三章、 程式設計 22
第四章、 結果與分析 25
4-1 理論模型的轉換測試 25
4-2 單晶Silicon轉換結果 30
4-3 Singly subtractive K-K relation修正 33
第五章、 總結 35
5-1 結論 35
5-2 未來工作 35
參考文獻 36

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