非晶結構是一種晶格缺乏空間週期性排列的結構，在過去幾年受到許多研究人員的關注。非晶結構可以在不同材料中找到，例如金屬合金、矽、以及共聚物。另外在自然界的生物構造中都可以看到，像是鳥類的羽毛，或是昆蟲甲殼表面，這些結構讓生物體表面有光鮮亮麗的色彩。非晶結構的特性包括結構的無方向性以及非虹彩色彩，使非晶結構有完全光子能隙的特性。非晶結構有很多種形態，我們針對相分離非序性的非晶結構來討論。
在這份研究裡，我們利用時域有限差分法來分析非晶結構光學性質。第一部分討論非晶結構在可見光波長尺寸的特性。我們利用數值方法來模擬三維空間中混合物相分離的過程，藉由改變建構參數數值來建構不同特徵長度的非晶光子晶體，並分析它們的結構與幾何性質。我們利用數值分析來表示不同結構參數建構的非晶結構的模態密度，藉由模態密度討論結構的光學性質。我們也計算結構對應的空間傅立葉頻譜來檢測不同結構的特徵長度，並且利用特徵長度的變化來討論光子能隙的頻段變化。這些結果有助於以非晶介電質光子晶體為材料的光學顯示元件設計。
在第二部分，我們討論非晶結構在次波長尺度的光學性質。當多孔薄膜的孔洞尺寸遠小於可見光波長時，多孔薄膜的光學性質就可以用相同等效折射率的均質薄膜來表示。我們先檢測由不同建構參數數值建構的非晶結構對應的臨界特徵長度，當非晶結構的特徵長度小於臨界特徵長度，該非晶結構就可以視為有相同等效折射率的均質薄膜。我們也檢測次波長尺度非晶薄膜的光學性質，可以藉由改變薄膜特性來控制對應的光學性質。這些結果對於利用次波長尺度非晶結構製作光學薄膜元件有相當程度的幫助。

Amorphous structures have attracted increasing research attention due to their interesting characteristics, such as isotropic structures and noniridescent colors. In this work, studies are presented based on finite-difference time-domain (FDTD) method for analyzing the optical characteristics of amorphous structures. In the first part, we present photonic amorphous structures with different characteristic lengths and analyze their structural and topological properties. We present the numerical analysis to characterize the density of state (DOS) of amorphous structures based on different structural parameters. The corresponding spatial Fourier spectra of amorphous structures are calculated to examine the characteristic length, and the photonic band gap properties will be discussed in association with the characteristic length. These results are crucial for the design of new optical materials display devices base on dielectric amorphous photonic structures. In the second part, we investigate the effective optical properties of nanoporous materials with amorphous structures. If the pore sizes are much smaller than the wavelength of visible light, the nanoporous structure can be considered as a homogeneous medium with the same effective refractive index. By changing the properties of effective media, the optical properties of films can be controlled.

Abstract ........................................................................................ i
Contents ........................................................................................ ii
1 Introduction .................................................................................. 1
1.1 Introduction of Porous Structure ......................................................... 1
1.2 Amorphous Structure ...................................................................... 4
1.2.1 Structural Properties ............................................................... 7
1.2.2 Structural Analysis ................................................................. 8
1.3 Motivation ............................................................................... 9
2 Method ........................................................................................ 11
2.1 Construction of Structure ................................................................ 11
2.2 Effective Medium Model ................................................................... 13
2.3 Optical Simulation and Analysis of Amorphous structures .................................. 15
2.3.1 Finite-Difference Time Domain method ................................................ 15
2.3.1.1 Reflectance spectra ............................................................ 17
2.3.1.2 Density of States .............................................................. 17
2.3.2 Thin-Film interference .............................................................. 19
2.3.3 Pearson product-moment correlation coefficient ...................................... 21
2.3.4 CIE Color Map ....................................................................... 23
3 Amorphous Structure on the Wavelength Scale ................................................... 26
3.1 Effect of Construction Parameters on Structural and Optical Properties ................... 28
3.1.1 Time of Evolution ................................................................... 28
3.1.2 Mobility ............................................................................ 30
3.2 Effect of Structural and Material Parameters on Structural and Optical Properties ........ 32
3.2.1 Standard Deviation .................................................................. 32
3.2.2 Volume Fraction ..................................................................... 33
3.2.3 Refractive index .................................................................... 35
4 Amorphous Structure on the Sub-wavelength Scale ............................................... 38
4.1 Verification of Critical Characteristic Length ........................................... 38
4.1.1 Time of Evolution ................................................................... 41
4.1.2 Mobility ............................................................................ 42
4.1.3 Standard Deviation .................................................................. 42
4.1.4 Volume Fraction ..................................................................... 43
4.2 Effect of Different Parameters on Reflection ............................................. 44
4.2.1 Thickness ........................................................................... 44
4.2.2 Volume Fraction ..................................................................... 46
4.2.3 Incident Angle ...................................................................... 48
4.3 Effect of Spatial Arrangement ............................................................ 50
4.3.1 Verification of Critical Lattice Constant ........................................... 51
4.3.2 Thickness ........................................................................... 52
4.3.3 Volume Fraction ..................................................................... 54
4.3.4 Incident Angle ...................................................................... 55
5 Conclusion .................................................................................... 58
Bibliography .................................................................................... 58

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