摻鉻釔鋁石榴石晶體光纖擁有近紅外光的螢光頻譜，波長範圍涵蓋從1.2到1.6 微米，適合於發展可調波長固態雷射與光纖通訊的自發輻射光源及光放大器。本論文研究摻鈣或鈣/鎂的摻鉻釔鋁石榴石晶體光纖，經由加熱基座成長法與1500℃的退火處理下，分析鉻的離子價態，在經氧與氮環境退火後，鉻的三價與四價在八面體與四面體的濃度分佈首次被探討。
八面體的四價鉻離子能遷移至四面體約有4%，發現的遷移溫度發生於700℃以上，它們的相對穩定能經氧退火與氮退火處理後，在摻鈣/鉻的釔鋁石榴石晶體分別為0.25和0.3電子伏特；在摻鎂/鈣/鉻的釔鋁石榴石晶體則為0.47和0.49電子伏特。在摻鈣/鉻的釔鋁石榴石晶體光纖(Ca/Cr=113.1%)於氧環境下退火，約有35%與2.5%的鈣離子能電荷補償成位於八面體與四面體的四價鉻離子。而鈣離子的摻雜也產生了氧空缺。經由實驗計算得出，在氧環境與氮環境退火下，未反應的氧空缺與全部氧空缺的比值分別為63%與88%。因此可說明釔鋁石榴石晶體中未能大幅提升四面體的四價鉻離子的主因為未反應的氧空缺之存在。
而且，在加熱基座成長法抽拉釔鋁石榴石晶體光纖過程中，可以發現在每次降低直徑時，鈣離子有向外擴散且造成四價鉻離子數量的明顯衰減。因此，在加熱基座成長法實施前，利用電子鎗將三氧化二鉻（Cr2O3）與氧化物（氧化鈣或氧化鎂）蒸鍍於晶體周邊來提升四價鉻子濃度。由實驗發現，摻雜鈣離子的效率較佳於摻雜鎂離子，因為鈣離子較易溶入釔鋁石榴石晶體且有較少的缺陷出現。氧化鈣蒸鍍於釔鋁石榴石晶體並於1350℃ 的氧環境下退火，四價鉻離子濃度有效地提升了110%。且四價鉻離子數達到每立方公分1.76 10^18個，四價鉻離子與全部鉻離子之比值為5.5。

Cr4+ doped Yttrium aluminum garnet (YAG) has a strong spontaneous emission that can generate near-infrared emission from 1.2 to 1.6 μm. This broadband emission have aroused great interest in developing tunable wavelength lasers and amplified spontaneous emitter (ASE).In this dissertation, The valence states of Cr ions in Ca or Ca/Mg co-doped Cr:YAG single-crystal fibers are studied. The fibers were grown using the laser-heated pedestal growth (LHPG) method, followed by annealing treatments up to 1500 oC. The concentrations of the Cr3+ and Cr4+ ions in octahedral and tetrahedral sites in oxygen or nitrogen environments were characterized for the first time to our knowledge.
Above 700 oC, migration of Cr4+ between octahedral and tetrahedral sites takes place, the ratio is about 4%; its relative stabilization energy was estimated. For Ca,Cr:YAG annealed in an oxygen or nitrogen environment, it was 0.25 and 0.3 eV, respectively. For Mg,Ca,Cr:YAG annealed in oxygen or nitrogen, it was 0.47 and 0.49 eV, respectively. For the Ca,Cr:YAG crystal fiber (Ca/Cr=113.1%) with oxygen annealing, about 35% and 2.5% of Ca ions took part in charge compensation for Cr4+ in the octahedral and tetrahedral sites, respectively. The density of oxygen vacancies depends on the concentration of Ca ions. The estimated ratios of the unreacted oxygen vacancies to total oxygen vacancies were about 63% and 88% for oxygen and nitrogen annealing, respectively. The main limitation on the concentration of Cr4+ in the tetrahedral site of YAG is the presence of unreacted oxygen vacancies.
Furthermore, chromium ions tend to diffuse outward during the LHPG of YAG crystal fiber, in which the average Cr4+ ion concentration decreases significantly after each diameter-reduction step. The Cr4+ ions are replenished using an electron gun to deposit Cr2O3 and divalent-ion oxide (CaO or MgO) on the source rod circumference before growth. It was observed that Ca2+ has better efficiency to diffuse into the source rod more efficiently than Mg2+generating fewer defects and stacking faults. By CaO deposition and post growth annealing at 1350 oC under an oxygen environment, a 110% increase in Cr4+ concentration was obtained. The achieved Cr4+ concentration and the ratio of Cr4+ to total Cr were 1.76 10^18 cm^-3 and 5.5, respectively.

中文摘要i
Abstractii
Table of Contents iii
List of Tables v
List of Figures vi

Chapter 1 Introduction 1

Chapter 2 Cr ion oxidation states in Cr:YAG crystal fiber 6
2.1 Structure of YAG 6
2.2 The valence states of Cr in divalent ions co-doped Cr:YAG 9
2.2.1 Oxidation state of Cr3+ ions in octahedral sites 9
2.2.2 Oxidation state of Cr4+ ions in tetrahedral sites 13
2.2.3 Oxidation state of Cr4+ ions in octahedral sites 21
2.2.4 Oxidation state of Cr6+ ions in tetrahedral sites 23

Chapter 3 Fabrication and measurement of Cr:YAG crystal fiber 26
3.1 LHPG system and fabrication processes 26
3.1.1 LHPG apparatus 26
3.1.2 Fabrication processes of the Cr4+ single crystal fiber 28
3.2 Laser scanning confocal microscopy and fluorescence mapping 34
3.2.1 Measurement of concentrations of octahedral Cr3+ ions 34
3.2.2 Measurement of concentrations of tetrahedral Cr4+ ions 37

Chapter 4 Evolution of Cr ion oxidation states in Ca or Ca/Mg co-doped
Cr:YAG crystal fibers with annealing treatment 44
4.1 Composition and fluorescence measurements 45
4.2 Cr3+ and Cr4+ fluorescence spectra 47
4.3 The influence of nitrogen and oxygen annealing treatments 49
4.4 Discussion and analysis 52
4.4.1 Analysis of Cr ion oxidation states and the relative stabilizing energy 52
4.4.2 Reduced charge compensation efficiency due to oxygen vacancies 57

Chapter 5 Cr4+ enhancement by perimeter deposition and annealing treatment 58
5.1 Sample preparation 61
5.2 CaO, MgO, and Cr2O3 concentration profiles in the crystal fibers after perimeter deposition 64
5.3 Effects of annealing treatment, Cr contents and divalent co-dopant on the Cr4+ fluorescence intensity 64
5.4 The defect analysis of crystal fiber after perimeter deposition 70
5.5 Simulated ASE power and required Cr4+:YAG crystal fiber length 74

Chapter 6 Conclusions 76

References 79
Biography 88
Publication List 89

Chapter 1
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Chapter 2
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Chapter 3
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Chapter 4
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Chapter 5
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