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研究生: 林世宏
Lin, Shih-Hung
論文名稱: 彩色錐面發射雷射於染料摻雜液晶薄膜之研究與應用
Study of color cone lasing emission based on dye-doped cholesteric liquid crystal films and their Applications
指導教授: 李佳榮
Lee, ChIa-Rong
學位類別: 博士
Doctor
系所名稱: 理學院 - 光電科學與工程研究所
Institute of Electro-Optical Science and Engineering
論文出版年: 2011
畢業學年度: 99
語文別: 英文
論文頁數: 90
中文關鍵詞: 液晶光子晶體雷射器彩色錐面雷射
外文關鍵詞: liquid crystal, photonic crystal, laser, color cone laser
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  • 光子晶體是一種擁有週期性結構排列分布的介電物質,因為高度的折射率週期性分布可以造成布拉格反射而產生光子能隙結構。如果光波長位於光子能隙中的光子無法在光子晶體中傳遞,在能隙外的光子則直接穿透。膽固醇液晶可看作是一維的光子晶體,乃因為它也具有一維的折射率週期性結構以及布拉格反射特性。近年來使用染料摻雜膽固醇液晶之雷射受到廣泛研究,原因在於它有趣的雷射機制以及潛在的應用性。
    本論文題目為『彩色錐面發射雷射於染料摻雜液晶薄膜之研究與應用』,可分為下列四個主題做研究探討:
    (一) 第一個主題為『染料摻雜於單螺距膽固醇液晶之彩色錐面雷射研究』。研究 結果顯示雷射輸出特性為當出射斜角連續增加從0度到50度(相對於膽固醇液晶的螺旋軸)時,輸出雷射波長連續分佈從676.7到595.6 nm,且每個斜角發生的雷射輸出波長剛好皆發生於該角度膽固醇液晶反射波段之邊緣,此首次發現的彩色錐面發射雷射推翻了此種雷射器只能在正向(0度)產生雷射的傳統觀念。另外,以Berreman’s 4×4 matrix method 模擬不同入射角的光傳遞在膽固醇液晶之色散關係,模擬結果驗證在不同角度的極小光子群速與極大的光子狀態密度之波長正與對應相同角度之雷射波長相吻合,此結果證明了彩色錐面發射雷射現象符合一維分布回饋共振腔之光子能隙雷射理論。一些彩色錐面發射雷射之特點最後也做了詳細的探討。
    (二) 第二個主題為『染料摻雜於變化螺距與螺距梯度變化膽固醇液晶之可調控波段之彩色錐面發射雷射研究』。本研究中利用六個不同螺距以及一個具螺距連續的梯度變化之膽固醇液晶產生在不同色彩光波段下的彩色錐面發射雷射現象。實驗結果顯示彩色錐面發射雷射之雷射波段可在不同顏色區間做調控,且發射角度範圍亦可隨之調控。此可調控的彩色錐面發射雷射的一些重要特性亦作詳細探討,最後,此研究製作一個空間波段可調控之彩色錐面發射雷射器作為一實際應用。
    (三) 第三個主題為『染料摻雜於不同雙折射性之膽固醇液晶所產生的彩色錐面發射雷射輸出與其雷射特性與性能研究』。本研究發現了一個可與正向雷射具有的低能閥值相比擬且在某斜角(ring)發生的特殊圓對稱雷射輸出環。研究證明此雷射環輸出是基於所謂的邊緣重疊效應引致螢光光子狀態密度的增強所產生的,其中邊緣效應乃說明此雷射螢光波長(ring)剛好落於正向的反射波段短波長邊緣與該斜角的反射波段長波長邊緣相重疊處。此雷射環與正向雷射輸出特性可隨著液晶雙折射性的不同而做調變。本研究另以Berreman’s 4×4 matrix method 模擬在不同膽固醇液晶雙折射性下,不同入射角的光在膽固醇液晶內傳遞之色散關係,模擬結果驗證在不同反射頻帶寬度下,在某斜角之反射波段長波長邊緣與正向反射波段短波長邊緣重疊時,此斜角與實驗所測出不同雙折射性下所得到的雷射環角度互相吻合。此外,本實驗所量測到的雷射環與正向雷射訊號的雷射性能(例如:能量閥值與相對斜率效率)與液晶雙折射性間的相依性確認了此三個雷射訊號之間的正向交互作用與互相競爭的關係。
    (四) 第四個主題為『染料摻雜於折射率梯度變化膽固醇液晶之可空間調控彩色錐面雷射研究』。本研究中將不同雙折射性之膽固醇液晶依次注入空樣品盒,讓不同雙折射性的膽固醇液晶在盒內緩慢擴散分布與自我排列成連續雙折射性梯度變化的膽固醇液晶。實驗證實在液晶盒33毫米距離內隨著激發液晶盒位置的改變,所激發出來的彩色圓對稱錐面發射雷射環的波長與出射斜角可以在568.1–605.8 nm 與29°–50°之間作調控。

    Photonic crystals (PCs) are spatially-periodic dielectric structures with a high modulation of refractive index and thus with photonic bandgaps (PBGs). Planar cholesteric liquid crystal (CLC) can be regarded as a one-dimensional (1D) PC because of its particular selectivity of reflection band due to its spatially-periodic distribution of refractive index. In recent years, dye-doped CLCs (DDCLCs) have been widely investigated because of their interesting fundamentals of the edge lasing mechanism and associated potential applications.
    This dissertation is entitled “Study of color cone lasing emission (CCLE) based on DDCLC films and their applications” and includes four topics. They are described in brief as follows:
    (1) The first topic is “Color cone lasing emission in a DDCLC with a single pitch”. This work investigates a novel CCLE based on a 1D photonic crystal-like DDCLC film with a single pitch. The lasing wavelength in the CCLE is distributed continuously at 676.7–595.6 nm, as measured at a continuously increasing oblique angle relative to the helical axis of 0–50°. This work demonstrates that lasing wavelength coincides exactly with the wavelength at the long wavelength edge of the CLC reflection band (CLCRB) at oblique angles of 0–50°. This color cone laser is observed in a DDCLC cell that contradicts the conventional cases that normally only single or dual wavelengths of the edge lasing peak emitted at 0° can be observed in the DDCLC lasers reported previously. Simulation results of dispersion relations at different oblique angles using Berreman’s 4×4 matrix method agrees closely with experimental results, which result verifies that these CCLEs are based on photonic bandedge lasing theory. Some unique and important features of the CCLE are identified and discussed.
    (2) The second topic is “Band-tunable color cone lasing emission based on DDCLCs with various pitches and a pitch gradient”. This study elucidates a novel band-tunable CCLE based on DDCLC films with various pitches. For several CLC cells with different pitches it was shown experimentally that the lasing band on the CCLE can be tuned among various color regions measured within different angular ranges. Some important features of the tunable CCLE are also identified and discussed. A spatially band-tunable color cone laser, based on a single DDCLC with a gradient pitch, is developed as a real application.
    (3) The third topic is “Novel DDCLC cone lasers with various birefringence and associated tunabilities of lasing feature and performance”. This study investigates novel cone lasers based on DDCLC films with various LC-birefringences (n) and the tunabilities of their lasing feature and performance. A peculiar conically-symmetric lasing ring with a low energy threshold, comparable to those for the common lasing signals occurred simultaneously at the SWE and LWE of the CLCRB for 0°, is identified to occur at a certain nonzero oblique angle (ring). This lasing ring is induced by the enhancement of the density of photonic state for the fluorescence with a wavelength of ring based on an edge-overlapping effect, in which the ring just locates at an edge-overlapping spectral position of the SWE of the CLCRB for 0° and the LWE of the CLCRB for that ring. The lasing feature (i.e. the lasing wavelengths of the three lasing signals and the emitted angle of the lasing ring) are found to be tunable by varying the n of LCs. Simulated relation of an oblique angle, in which the SWE of that corresponding CLCRB just overlap to the LWE of the CLCRB for 0°, with the n can be obtained by the calculation of the dispersion relation of the planar CLC structure based on Berreman’s 4×4 matrix approach, and its result is highly consistent to the experimental one for the dependence of the ring on the n. Furthermore, the dependences of the lasing performance (energy threshold and relative slope efficiency) on the n for the three lasing signals are also measured, which results can thus identify qualitatively a positive interaction or competition among these lasing signals.
    (4) The fourth topic is “Spatially-tunable cone laser based on a DDCLC with a birefringence gradient”. This study develops and investigates a spatially-tunable cone laser based on a DDCLC film with a Δn gradient. A continuous Δn variation can be generated in the cell by the diffusion and self-organization of the CLCs after four DDCLC mixtures with a discrete variation of Δn are successively injected into the empty cell. Thus, the bandwidth of the CLCRB, the lasing wavelength and cone angle of the obtained conically-symmetric emitted lasing ring can be tuned continuously by continuously changing the pumped position of the cell with a Δn gradient. The tunable ranges for the lasing wavelength and emitted cone angle of the lasing ring are 568.1–605.8 nm and 29°–50° within a spatial interval of about 33 mm at the cell.

    摘要.....................................................I Abstract................................................III Acknowledgements........................................VI Contents................................................VII List of Figures.........................................X List of Tables..........................................XVI CHAPTER 1 Introduction..................................1 CHAPTER 2 Introduction to Liquid Crystal................4 2.1 Origin of Liquid Crystal............................4 2.2 Classification of Liquid Crystal....................5 2.2.1 Lyotropic Liquid Crysta1..........................5 2.2.2 Thermotropic Liquid Crystal.......................6 (a) Nematic Liquid Crysta1..............................6 (b) Smectic Liquid Crysta1..............................7 (c) Cholesteric Liquid Crystal..........................7 2.2.3 Polymeric Liquid Crystal..........................9 2.3 Physics of Liquid Crystal...........................10 2.3.1 Order Parameter...................................10 2.3.2 Optical Anisotropy................................10 2.3.3 Dielectric Anisotropy.............................12 2.3.4 Elastic Continuum Theory..........................13 CHAPTER 3 Optical Properties of Cholesteric Liquid Crystals and Dye-Doped Cholesteric Liquid Crystal Lasers.........15 3.1 Optics Propagate in Cholesteric Liquid Crystals.....15 3.1.1 Derivation of Matrix Wave Equations...............15 3.1.2 Dispersion Relation...............................20 3.1.3 Bragg Reflection..................................21 3.2 Basic Principles of Laser...........................22 3.2.1 Interaction of Single-Mode Light with the Atom....22 (a) Spontaneous Emission................................23 (b) Absorption..........................................24 (c) Stimulated Emission.................................24 3.2.2 Population Inversion..............................25 3.2.3 Optical Feedback and the Round-Trip Power Gain....26 3.3 Photonic Bandedge Lasing Theory.....................27 3.4 Preliminary Discovery of a Color Cone Lasing Emisisoin Based on a Dye-doped Cholesteric Liquid Crystal with a Single Pitch............................................31 CHAPTER 4 Materials used, Sample Preparation, and Experimental Setups.....................................32 4.1 Materials used......................................32 4.2 Sample Preparation..................................35 4.3 Experimental Setup..................................36 CHAPTER 5 Color Cone Lasing Emission in a Dye-doped Cholesteric Liquid Crystal with a Single Pitch..........39 5.1 Introduction........................................39 5.2 Experiments.........................................42 5.2.1 Sample Preparation................................42 5.2.2 Experimental Setups...............................42 5.3 Results and Discussion..............................43 CHAPTER 6 Band-tunable Color Cone Lasing Emission Based on Dye-doped Cholesteric Liquid Crystals with Various Pitches and a Pitch Gradient....................................52 6.1 Introduction........................................52 6.2 Experiments.........................................53 6.2.1 Sample Preparation................................53 6.2.2 Experimental Setups...............................54 6.3 Results and Discussion..............................55 CHAPTER 7 Novel Dye-doped Cholesteric Liquid Crystal Cone Lasers with Various Birefringence and Associated Tunabilities of Lasing Feature and Performance..........62 7.1 Introduction........................................63 7.2 Experiments.........................................64 7.2.1 Sample Preparation................................64 7.2.2 Experimental Setups...............................65 7.3 Results and Discussion..............................66 CHAPTER 8 Spatially-tunable Cone Laser Based on a Dye-doped Cholesteric Liquid Crystal with a Birefringence Gradient................................................75 8.1 Introduction........................................75 8.2 Experiments.........................................76 8.2.1 Sample Preparation................................76 8.2.2 Experimental Setups...............................77 8.3 Results and Discussion..............................77 CHAPTER 9 Conclusion and Future Works...................82 9.1 Conclusion..........................................82 9.2 Future Works........................................84 References..............................................85

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