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摻鉻釔鋁石榴石晶體光纖之生長系統改良與特性研究

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(1)國立中山大學光電工程研究所 博士論文. 摻鉻釔鋁石榴石晶體光纖之生長系統改良與特性研究 Growth System Improvement and Characterization of Chromium-doped YAG Crystal Fiber. 研究生:黃光瑤 撰 指導教授:黃升龍 博士 共同指導教授:鄭木海 博士. Kuang-Yao Huang Dr. Sheng-Lung Huang Dr. Wood-Hi Cheng. 中華民國 九十七 年 七 月.

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(5) 致謝 歷經在中山光電所超快雷射實驗室碩博士班七年的光陰,終於要畢業了!若 加上大學的四年,這是我在中山大學的第十一個寒暑,中山就像是我第二個家, 對中山和高雄多了那麼一點親切感。進入光電所超快實驗室,隨著黃老師轉任教 於台大,見證了中山超快的壯大繁榮期、自我要求期和現在的雙邊合作關係,期 間老師為中山學生兩頭跑很辛苦;學生也因老師繁忙必須學習自我成長與約束, 若說不幸也實屬大幸。回首這七年,雖有迷茫與挫折,卻也讓自己心智更有所成 長。 本論文的完成,首先我必須由衷地感謝我的家人,他們的關懷和支持,讓我 可以心無旁鶩的專心於學業。再來我要感謝我的指導教授黃升龍教授,老師細心 的教導,讓我在研究方面有所成長;令人驚豔的創意和浩瀚的學識,也一直是我 學習和追求的目標;對學生課業外的生活也能適時的關心,讓人更覺親近。我要 感謝中山歷屆的學長學弟們在實驗上的討論與協助,在生活上的互相扶持與關 心。感謝光裕學長和東佑學弟在論文和研究上的砥礪和協助,讓我在博班最後一 年,可以在研究上澄清困惑許久的問題,並順利完成投稿;感謝蔡政男老師在材 料濃度和結構分析上的幫助,和精神上的互相激勵,我倆同時入學亦同時畢業, 讓我你有份革命情感和親切感;感謝林彥勝教授在材料結構分析上的幫忙與建 議,令我受益良多;感謝平夷學長在生長熔區討論上的幫助,亦祝你順利畢業; 感謝小卓在實驗上的努力,使放大器的特性更為清楚,在娛樂上的提供,讓實驗 室的宅宅們可以在苦悶的實驗後得以紓解壓力;感謝小賴和志威的努力,讓 Cr4+:YAG 在經過五年漫長的焠鍊,得以產生雷射輸出;感謝阿東在鍍膜上的幫 忙,相信我,你已是實驗室鍍膜第一把交椅,亦祝你早日交到女朋友;感謝小 no、承廷、Sron、屁昌、蔡漢鐘老師在生活上的相互關懷和協助;感謝蘇小妹在 長晶上的幫助,使實驗進度得以加快,妳也算是我的徒弟,去海大要加油;感謝 台大譽達學弟將 ASE 光源運用於量測上,讓 Cr4+:YAG 得以發揮它的寬頻特性; 感謝晏聖在側鍍上的幫忙;感謝貴儀的江宏達先生在 EPMA 上的幫助。最後我 要感謝我的摯愛,可愛的筠茹,妳這六年多來的付出我點滴在心裡,希望未來的 人生我倆可以攜手共度。 最後再次感謝幫助過我的人,並謹以此文獻予你們。真摯的感謝大家!. 黃光瑤 僅誌于 中山西灣 2008.8.20.

(6) 中文摘要 摻鉻釔鋁石榴石晶體(Cr4+:YAG)為一引人注目的增益介質,主要是因其自發 輻射頻譜半高寬,為從 1253 奈米至 1530 奈米,涵蓋了大部份的光通訊低損耗波 段。如此寬頻的光譜特性,使其適合發展為光通訊用之自發輻射放大光源、光放 大器、和可調波長雷射。而將晶體生長成光纖的形態具有比塊材更佳的光波導效 果,同時產生更高的光增益。對於雷射的應用,因晶體光纖可承受較大之光強度 且散熱較佳,可發展低損耗閥值和高效率之雷射輸出。. 雷射加熱基座生長法因無坩鍋汙染,可生長高純度晶體光纖。本實驗室為解 決晶體光纖直徑縮小的問題,開發一種全新的包覆晶體光纖的技術,即共同提拉 雷射加熱基座生長法,以此技術可生長出雙纖衣晶體光纖結構。雖然此方法可以 生長出纖心尺寸小至 10 微米之雙纖衣晶體光纖,但生長之雷射功率的變化很容 易造成纖心直徑起伏的問題,因而影響其光輸出的效率。我們進一步研發一種可 穩定雷射功率擾動之熱電容機制,即管狀藍寶石輔助共同提拉雷射加熱基座之生 長法,同時結合雷射功率回授程式,以增加其穩定雷射功率的效果。利用此創新 的生長法,可生長出纖心小至 10 微米之雙纖衣晶體光纖,且纖心均勻度符合無 模態能量損耗之傳輸準則。. 利用自發輻射放大和光增益等量測之結果,配合數值模擬可穫得激發光吸收 截面積、自發輻射截面積、和激發光與訊號光之激發態吸收截面積。根據模擬, 激發光之激發態吸收損耗對光增益影響很大,若欲解決此損耗,必需採用激發光 在內纖衣傳輸之幫浦架構。而雷射的部份,我們在室溫下已成功做出一突破世界 記錄之低損耗閥值的摻鉻釔鋁石榴石晶體光纖雷射。此雷射具有雙斜率的特性, 在輸出穿透率為 3.8%之下,其雷射閥值為 2.5 毫瓦;在第二雷射閥值後,其斜率 效率為 6.9%。利用模擬可以預估,以一 7 公分的雙纖衣晶體光纖,在輸出穿透率 為 80%之下,可獲得 56%的斜率效率。我們也首次將自發輻射放大光源當做生 醫檢測系統裡之偵測光源,成功地達成一 3.5 微米之縱向解析度。. i.

(7) Abstract Cr4+:YAG is an attractive gain medium due to its broad 3-dB emission spectra all the way from 1253 nm to 1530 nm that just cover the low loss window of silica fiber. Such a broadband characteristic offers a potential to develop a broadband amplified spontaneous emission (ASE) light source, optical amplifier, and tunable laser. Growing the Cr4+:YAG bulk crystal into fiber form is necessary for generating larger gain by the better optical confinement of the waveguide structure. For the application of laser, it is superior to bulk crystal for reduced lasing threshold and better slope efficiency due to also the optical confinement effect and better heat dissipation. Laser heated pedestal growth (LHPG) method has been used to grow high purity crystal fibers due to its crucible free nature. A novel cladding technique, co-drawing LHPG (CDLHPG), was developed to solve core-reduction problem and obtained a double-clad fiber (DCF) structure. But the power fluctuation of heating laser caused large core variation of Cr4+:YAG DCF, and further impaired the optical performance. An innovating method for suppressing the fluctuation of heating power, sapphire tube assisted CDLHPG technique, was developed and combined with power feedback control program. By this technique, 10-μm-core Cr4+:YAG DCFs which meet the adiabatic propagation criterion were fabricated. By comparing with ASE and optical amplifier experimental data, cross sections of pump absorption, emission, and excited-state absorptions (ESAs) of pump and signal were determined. Pump ESA loss limited the optical performance that could be solve by using cladding pump scheme. A record-low threshold Cr4+:YAG DCF laser with two slopes with respect to absorbed pump power was achieved at room temperature. The threshold pump powers were 2.5 mW and 96 mW in the low and high absorbed pump powers with the same output coupler transmittance of 3.8%, respectively. The slope efficiencies of the fiber laser were 0.4% and 6.9%, respectively. By numerical simulation, 56% slope efficiency can be achieved with a length of 7 cm and an output reflectance of 80%. Our group also firstly used the ASE as the light source of optical coherence tomography, an axial resolution of 3.5 μm was achieved.. ii.

(8) Table of Contents 中文摘要…………………………………………………………………………… i Abstract …………………………………………………………………………… ii Table of Contents …………………………………………………………….…… iii List of Tables…………………………………….………………………………… v List of Figures……………………………………………………………...……… vi. Chapter 1 Introduction ………………...………………………………………… 1 Chapter 2 Numerical model of Cr4+:YAG crystal fiber devices………………... 4 2.1 Properties of Cr4+:YAG crystal…………………………………………. 4. 2.2 Energy levels of Cr4+:YAG………………………………………….... 10. 2.3 Distributed model of ASE and amplifier……………………………... 12. 2.4 Lumped model of laser……………………………………………….. 14. Chapter 3 Cr4+:YAG crystal fiber growth……………………………………….. 17. 3.1 Laser heated pedestal growth (LHPG) system…………………………. 17 3.2 Single crystal fiber growth…………………………………………….... 19. 3.3 Double-clad crystal fiber (DCF) growth………………………………... 22. 3.4 Sapphire tube assisted co-drawing LHPG growth…………………….... 23. 3.4.1 Sapphire tube assisted growth system……………………………. 24 3.4.2 Growth system improvement……………………………………... 26. 3.4.3 Fabrication of 10-μm-core DCF………………………………….. 30. Chapter 4 Characterization of Cr4+:YAG crystal fibers………………………... 34. 4.1 Structure analysis……………………………………………………….. 34. 4.1.1 X-ray diffraction analysis of crystallinity……………………….... 34. 4.1.2 High-resolution transmission electron microscopy of DCF…….... 36. 4.2 Composition analysis………………………………………………….... 41. 4.2.1 Single crystal fiber………………………………………………... 41. 4.2.2 Double-clad crystal fiber…………………………………………. 44 4.3 Fluorescence mapping and analysis…………………………………….. 46. 4.3.1 Fluorescence and doping profiles of Cr:YAG single crystal fiber... 46. iii.

(9) 4.3.2 Fluorescence and doping profiles of Cr:YAG DCFs…………….. 4.3.3 Emission and absorption spectra of Cr:YAG DCF in the inner cladding region………………………………………………….... 47 48. 4.4 Propagation loss analysis……………………………………………….. 53. Chapter 5 Optical performance and discussion…………………………………. 56. 5.1 ASE light source………………………………………………………... 56. 5.2 Optical amplifier………………………………………………………... 58. 5.2.1 Insertion loss…………………………………………………….... 58. 5.2.2 Gain measurement………………………………………………... 61. 5.3 Analysis and discussion……………………………………………….... 65. 5.3.1 Cross sections of absorption, emission, and ESAs of pump and signal……………………………………………………………... 65. 5.3.2 Cladding pump scheme………………………………………….... 67. 5.3.3 Pump ESA spectrum…………………………………………….... 70. 5.3.4 Comparison between CDF and EDF……………………………... 73 5.4 Double-clad fiber laser…………………………………………………. 76 5.4.1 Laser performance………………………………………... 76. 5.4.2 Optimization of DCF laser………………………………………... 80. 5.4.3 Estimation of tuning range………………………………………... 82. 5.5 Application: light source of optical coherence tomography……………. 83. Chapter 6 Conclusions and future work…………………………………………. 86. References…………………………………………………………………………... 89. Biography. 98. Publication list. 99. iv.

(10) List of Tables Table 1.1. Table 2.1.. Table 2.2. Table 2.3. Table 2.4. Table 4.1. Table 4.2. Table 4.3. Table 4.4. Table 4.5. Table 5.1.. Table 5.2.. Table 5.3. Table 5.4.. Table 5.5. Table 5.6.. Techniques of broadband emission light sources…………………... List of the Cr4+-ion doped hosts with the 3-dB emission bandwidth ∆λ, peak wavelength, emission cross section σe, fluorescence lifetime τf, and ∆λσeτf product at room temperature.......................... Physical and optical properties of Cr4+:YAG crystal……………….. Comparison of ionic radius mismatch between dopants and YAG host cations…………………………………………………………. Parameters extracted from Gaussian fitting of the Cr4+:YAG absorption and emission spectra……………………………………. Summary of the diffraction line widths and angular distances in Fig. 4.1……………………………………………………………… Average doping concentration of Cr4+:YAG raw materials………… Average doping concentrations of Cr4+:YAG crystal fibers………... Multi-peak Gaussian fittings of emission spectrum at DCF inner cladding…………………………………………………………….. Multi-peak Gaussian fittings of absorption spectrum at DCF inner cladding [4.19-4.22]………………………………………………... Summary of the absorption, emission, pump ESA, and emission ESA cross sections in the previous literatures. The cross-section values must be multiplied by 10-19 cm2…………………………….. List of the power budget of fibers with several core diameters and with one watt pump power. The second column is the power-budget estimation of the ASE experiment with 25-μm core fiber. The third and forth columns are the simulation results of 10and 5-μm core fiber………………………………………………… Parameters used for ASE and amplifier simulations in cladding pump scheme……………………………………………………….. Parameters of the CDF and a typical Erbium doped fiber, where the σ as is the absorption cross section for emission wavelength. The νs is assumed to be the 1400 nm center emission wavelength for calculating I ssat …………………………………………………….. List of coatings for Cr4+:YAG DCF laser…………………………... Summary of the parameters fitting with laser performance……….... v. 2. 5 6 8 11 36 41 43 50 51. 65. 66 68. 73 76 81.

(11) List of Figures Fig. 2.1. Fig. 2.2. Fig. 2.3. Fig. 2.4.. Fig. 2.5. Fig. 2.6. Fig. 2.7. Fig. 3.1. Fig. 3.2. Fig. 3.3. Fig. 3.4. Fig. 3.5.. Fig. 3.6. Fig. 3.7. Fig. 3.8. Fig. 3.9.. Fig. 3.10.. Fig. 3.11. Fig. 3.12.. Fig. 3.13. Fig. 3.14. Fig. 3.15.. The cubic structure of garnet crystal……………………………….. Relation between Cr4+ and Ca2+ concentrations in literature [2.8]…. The relation between normalized Cr4+ and Ca2+ concentrations [2.9]………………………………………………………………… The dependence between normalized 4+ and Ca2+ concentration Crt several samples with or without oxygen annealing treatment [2.10]. 4+ 4+ Crt mean the Cr ions in tetrahedral sites………………………... Cr4+:YAG absorption spectrum and Gauss fitting of absorption wavelength peaks…………………………………………………... Cr4+:YAG emission spectrum and Gauss fitting of emission wavelength peaks…………………………………………………... The Cr4+:YAG energy level diagram……………………………….. The LHPG system………………………………………………….. Growth chamber……………………………………………………. Illustration of single crystal fiber growth by the LHPG method…… Laser power as a function of source rod diameter. The inset shows a photograph of YAG molten zone…………………………………. (a) Photograph of a Cr4+:YAG single-crystal fiber with a 70-μm diameter grown by the LHPG method. (b) The end face SEM image of the 70-μm Cr4+:YAG crystal fiber………………………... Drawing of the YAG atomic structure viewed from <111> direction…………………………………………………………….. (a) Scheme of CDLHPG method. (b) Molten zone drawing during growth process. (c) Photograph of side view of the Cr4+:YAG DCF. (a) The polished end of a single-clad Cr4+:YAG-silica fiber. (b) The polished end of Cr4+:YAG DCF……………………………………. (a) The schematic of sapphire tube assisted CDLHPG system. (b) The end view and side view of the sapphire tube with fused-silica capillary…………………………………………………………….. (a) The two-dimensional simulation of temperature distribution in the sapphire tube heating zone. (b) Temperature distribution at the heating zone center in transversal position. (c) Temperature distribution in the longitudinal position……………………………. Flow chart of power feedback control system……………………... (a) Laser power variation as a time function without power feedback control. (b) In a power feedback control, 0.1% power stability can be reached…………………………………………….. (a) Side-view photograph of the DCF during growth process. (b) Result of core boundary identification……………………………... Core diameter of DCF as a function of CO2 laser power and the fitting curve………………………………………………………… The control panel of CDLHPG growth system……………………... vi. 6 9 9. 9 10 11 12 18 18 19 20. 21 21 22 23. 24. 25 27. 27 28 29 30.

(12) Fig. 3.16. Fig. 3.17.. Fig. 3.18. Fig. 3.19. Fig. 4.1. Fig. 4.2. Fig. 4.3. Fig. 4.4. Fig. 4.5. Fig. 4.6. Fig. 4.7. Fig. 4.8. Fig. 4.9. Fig. 4.10. Fig. 4.11. Fig. 4.12.. Fig. 4.13. Fig. 4.14.. Fig. 4.15.. Fig. 4.16.. Fig. 4.17. Fig. 4.18. Fig. 4.19.. The heating zone of the sapphire tube assisted in CDLHPG method……………………………………………………………… Core diameter variation for fibers fabricated with and without using sapphire tube. The insets are the side view and end view of a 10-μm-core Cr4+:YAG DCF………………………………………... Cr4+:YAG DCF cores of (a) 17-μm, (b) 15-μm, and (c) 10-μm diameters without the use of sapphire tube………………………… Cr4+:YAG DCF cores of (a) 11-μm, (b) 8.5-μm, and (c) 4-μm diameters with the use of sapphire tube……………………………. X-ray diffraction patterns of raw material and 400-μm Cr4+:YAG crystal fiber…………………………………………………………. Atomic image of the core. The inset shows an atomic drawing of YAG structure viewed from <111>-direction………………………. The SAED pattern of the core……………………………………… A cross-sectional image of Cr4+:YAG DCF………………………... (a) The HRTEM image of region A in Fig. 4.4, and (b) is an enlargement of the rectangular area in (a)………………………….. HRTEM image of region B in Fig. 4.4……………………………... Electron diffraction patterns in (a) outer cladding and (b) inner cladding…………………………………………………………….. The SAED pattern showing hkl diffractions, as indexed…………... Doping profile of (a) Cr2O3 and (b) CaO with multiple regrowth…. Doping profiles of fiber cross section with various growth speed…. Average Cr2O3 concentration of fibers with different multiple regrowths and the curve of empirical equation……………..……… (a) and (b) are the major composition of the Cr4+:YAG-silica SCF and Cr4+:YAG DCF by EPMA measurement. The inset images are the polished end face……………………………………………….. LSCM-measurement profiles of (a) Cr3+ fluorescence and (b) Cr4+ fluorescence to EPMA line-scan measurements…………………… Measurements the Cr4+:YAG DCF, (a) doping concentration profiles of Cr2O3 and CaO by using EPMA method, and (b) fluorescence profiles of Cr3+ and Cr4+ by using the LSCM technique…………………………………………………………… (a) The Cr3+ fluorescence spectra of Cr:YAG DCF core and inner cladding. (b) Gaussian peaks fits to fluorescence spectrum at inner cladding…………………………………………………………….. (a) The Cr4+ fluorescence spectra of Cr4+ in core and inner cladding of Cr:YAG DCF. (b) Fit Gaussian peaks to fluorescence spectrum at inner cladding……………………………………………………. Absorption spectrum of Cr-doped glass……………………………. Emission spectra of Cr-doped-glass SCF under pump wavelength from 750 to 1000 nm……………………………………………….. Pump wavelength dependence of emission peaks and bandwidths in the Cr-doped SCF………………………………………………... vii. 30. 31 33 33 34 37 38 39 39 40 40 41 43 43 44. 45 47. 48. 49. 49 51 52 52.

(13) Fig. 4.20.. Fig. 4.21.. Fig. 4.22. Fig. 5.1.. Fig. 5.2. Fig. 5.3. Fig. 5.4. Fig. 5.5. Fig. 5.6. Fig. 5.7.. Fig. 5.8. Fig. 5.9.. Fig. 5.10. Fig. 5.11.. Fig. 5.12.. Fig. 5.13. Fig. 5.14. Fig. 5.15. Fig. 5.16.. The ASE output power of Cr-doped glass SCF with 900-nm pump. The inset is the fluorescence spectrum by 900-nm pump wavelength…………………………………………………………. (a) Core diameter profile in the propagation axis. (b) Tapering angle of the 10-μm-core fiber fabricated with sapphire tube during LHPG growth. It meets the 1.35-degree adiabatic criterion. (c) Autocorrelation curve of the core diameter for a 10-μm-core DCF... Propagation losses of the Cr4+:YAG DCFs with various core diameters…………………………………………………………… ASE powers versus pump powers for the samples with core diameters of 920, 100, and 25 μm. The dots and the lines represent the measured and simulated data…………………………………… The comparison of spectra between Cr4+:YAG fluorescence and ASE output…………………………………………………………. The refractive index profile of a 320-μm-diameter Cr4+:YAG DCF.. The simulation results of mode coupling efficiencies between the SMF28 and the Cr4+:YAG DCF using different signal wavelengths. The measured and simulated insertion losses. The inset shows the measurement scheme……………………………………………….. Measurement configuration of optical amplifier…………………… (a) The spectrum of signal power density in various pump power in bi-direction pump scheme. (b) The curve of gross gain as function of pump power……………………………………………………... Gain measurement scheme with double signal pass and bi-direction pump………………………………………………………………... (a) The spectrum of signal power density in various pump power in bi-direction pump and double pass scheme. (b) The curve of gross gain as function of pump power……………………………………. End and side views of cladding pump Cr4+:YAG DCF scheme……. Core fibers of 5, 8, and 10 μm in various cladding diameters with one watt incident pump power. (a) The ASE power. (b) The corresponding optimum fiber length to (a). (c) ASE efficient curves. (d) Ratios of pump ESA loss. (e) Signal gain……………… Gain simulation of 5, 8, and 10-μm-core fiber pumped in various cladding diameters with one watt incident pump power. (a) The gain spectra in 100-μm-cladding pump. (b) The gain saturation profile………………………………………………………………. Measurement scheme of pump ESA spectrum……………………... Cross-section spectra of pump GSA and ESA……………………... Solid and dash lines are the ratio of pump ESA to GSA cross sections of experiment and literature results, respectively…………. A schematic of the room-temperature CW Cr4+:YAG DCF laser experiment…………………………………………………………... viii. 52. 54 55. 57 58 59 60 60 61. 62 63. 64 67. 69. 70 71 72 72 77.

(14) Fig. 5.17.. Fig. 5.18.. Fig. 5.19.. Fig. 5.20. Fig. 5.21. Fig. 5.22. Fig. 5.23. Fig. 5.24. Fig. 5.25. Fig. 6.1.. Lasing characteristics of the room-temperature CW Cr4+:YAG DCF laser. (a) and (b) were the laser output powers of Cr4+:YAG DCF laser with low and high absorbed pump power, respectively………. Measured lasing spectra with peaks at ~ 1421 nm and ~ 1444 nm under the absorbed pump powers of 257 mW and 12 mW with the corresponding SMSRs of 55 dB and 36 dB, respectively………….. Polarization measurement of the room-temperature CW Cr4+:YAG DCF laser. (a) Each of the 360° plots present the normalized transmitted laser output vs. various polarizer orientations at different incident pump powers. (b) The measured polarization extinction ratio of the linear polarized output……………………… Simulations of (a) slope efficiency ηs and (b) threshold Pth in terms of the crystal fiber length Lg and output coupler reflectance R2……. The estimated tuning range of Cr4+:YAG DCF laser………………. The therapeutic window of tissue…………………………………... The OCT system……………………………………………………. The 238-nm broadband ASE light source of Cr4+:YAG DCF after long-wavelength pass filter………………………………………… (a) The simulation and (b) experiment of interference signal profiles of OCT system…………………………………………….. Refractive index profiles of Cr4+:YAG DCF with and without high refractive index material (TiO2) deposition in the inner cladding layer…………………………………………………………………. ix. 78. 79. 80 81 83 83 84 85 85. 88.

(15) Chapter 1 Introduction Due to the fast growing communication need, the required capacity of the optical fiber network has been more than doubled every year. And the technology break through in dry fiber fabrication opens the possibility for fiber bandwidth all the way from 1.3 to 1.6 μm. The fast increasing demand of communication capacity results in the emergence of wavelength division multiplexing (WDM) technology, enabling tens or even hundreds of channels with different wavelengths transmitted simultaneously on an optical fiber [1.1]. In consequence, it necessitates the requirement of broadband spectral characteristics of all the optical components used in the optical network systems. Broadband light source and optical amplifier are the key components in WDM networks. Table 1.1 summaries the various techniques for generating broadband emission light source and optical amplifier. Edge emitting light emission diode (EELED) and superluminescent diode (SLD) used the multiple quantum well to cover the broadband gain with designated pump current [1.2]. The current dependent gain spectra limit the application in optical communication system. A supercontinuum technique used an amplified pulse laser by an Erbium-doped fiber firstly. Then the pulse laser is broadened with a dispersive fiber due to the self phase modulation of Kerr effect [1.3]. High cost and complicated configuration are the disadvantages. Rare-earth-element doped silicate fibers are the most common optical fiber light sources. They are highly efficient and mature techniques already [1.4-1.11], but the gain bandwidth cannot fully cover the whole 1.3 to 1.6 μm bandwidth with a single fiber amplifier. Cr4+:YAG is an attractive gain medium for broadband light source and optical amplifier because of its ultra-broadband emission spectra from 1253 to 1530 nm. Besides, the 0.9~1.2 μm optical pumping absorption range for Cr4+:YAG covers available 910~1060-nm broad-stripe diode laser with generous wavelength tolerance. As shown in Table 1.1, the end pump scheme with laser diode (LD) leads to a compact, cost-effective package. The crystalline host offers higher thermal conductivity and hence a higher power handling capability than glass fibers.. 1.

(16) Table 1.1. Techniques of broadband emission light sources [1.2-1.11]. Technique. Generating scheme. Emission range (nm). EELED or SLD. P. N. 6nm In0.57Ga0.33As0.72P0.2. 1300~1580. 8.7nm In0.53Ga0.47A. Supercontinuum Pulse laser. Er3+ doped fiber. 1420~1700. EDFA Dispersive fiber. RE3+ ions doped. Pump Laser. Tm3+ doped fiber. 1480~1510 Pump/Signal Multiplexer. Pr3+ doped fiber Cr4+:YAG crystal fiber. 1530~1610. LD. Cr4+:YAG crystal fiber. 1280~1360 1253~1530. This dissertation contains four main chapters. In chapter 2, the properties of Cr4+:YAG are introduced. Based on the absorption and emission spectra of Cr4+:YAG, precise energy-level diagram was obtained. Furthermore, we established distributed numerical model for the amplified spontaneous emission (ASE) and optical amplifier, and lumped model for laser, respectively. In chapter 3, a well known growth technique for crystal fibers, the laser heated pedestal growth (LHPG) method [1.12] was introduced. The fiber diameter was difficult to be reduced to below 30 μm that was limited by the few-tens of microns focal spot size of the laser used in the LHPG system. To further reduce the core size, a co-drawing LHPG (CDLHPG) technique was developed [1.13]. A double-clad crystal fiber (DCF) structure is formed with an additional inner cladding layer made of fused silica and YAG mixture. The fiber core diameter is reduced during the formation of the inner cladding layer, and can be as small as 10 μm. However, the fiber core diameter is very non-uniform because the core size is very sensitive to the power stability of the heating laser (< 0.5% power fluctuation in our case) during the growth process, especially when the core diameter. 2.

(17) is small. As a result, the 10-μm-core fiber has about 60% peak-to-peak core variation typically. So a sapphire tube assisted CDLHPG technique cooperated with power feedback controller was developed to solve the difficulty [1.14]. A 10-μm-core Cr4+:YAG DCF was successfully fabricated, and fulfilled the adiabatic propagation criterion. In chapter 4, we used X-ray diffraction to measure and compare the crystal quality of the Cr4+:YAGs grown by Czochralski (CZ) and LHPG methods. The micro structures in core and inner cladding of Cr4+:YAG DCF were also characterized with high-resolution transmission electron microscopy (HRTEM). The core region still remained crystalline structure in <111> orientation and the inner cladding had γ-Al2O3 nano-crystals surrounded with mixture of YAG and silica. The major compositions and Cr doping concentrations were also measured by electron probe micro-analyzer (EPMA) to analyze the influence of growth parameters. The fluorescence of Cr3+ and Cr4+ doped in YAG and mixture of YAG and silica were mapped to analyze the relation between compositions. Propagation loss of the DCF was also measured and discussed in the subsection. The loss was improved from around 0.6 dB/cm for the single crystal fiber to 0.02 dB/cm for the uniform-core DCF. In chapter 5, the ASE and optical gain were measured and data were used to determine the cross sections of absorption, emission, and excited-state absorptions (ESAs) of pump and signal. A knotty difficulty for pump ESA loss perplexed the optical performance. Cladding pump scheme and shifting of the pump wavelength was discussed to suppress the pump ESA loss and improve the optical performance. In addition, an ultra-low threshold (2.5 mW) Cr4+:YAG DCF laser was demonstrated with 6.9% slope efficiency. The ASE of Cr4+:YAG DCF was used to be the light source of optical coherence tomography (OCT). A theoretical-limit axial resolution of 3.5 μm was demonstrated. Finally, in chapter 6 conclusions and future improvements are described.. 3.

(18) Chapter 2 Numerical model of Cr4+:YAG crystal fiber devices Host material for solid-state gain medium must possess excellent optical, mechanical, thermal properties, and easy fabrication for withstanding the serve operating conditions in practical applications. Solid-state host materials are classified into crystalline solids and glasses. Compared with glass hosts, crystals have better mechanical, thermal properties, and stable optical emission spectrum.. 2.1 Properties of Cr4+:YAG crystal Garnets are important gain hosts in the infrared emission bands. Some of the synthetic garnets are: yttrium aluminum garnet Y3Al5O12 (YAG), gadolinium gallium garnet Gd3Ga5O12 (GGG), and gadolinium scandium aluminum garnet Gd3Sc2Al3O12 (GSAG), and so on [2.1-2.3]. Transition metal doped garnet crystals are attractive gain media because of their ultra-broadband emission spectra. The active electrons of transition metal ions are not completely shelled by the electron cloud. The subtle interplay between the Coulomb fields of the host matrix ions and the electron-phonon coupling permit ultra-broad absorption and emission spectra. Among the transition-metal-doped crystals, Cr4+-ion doped garnet is an attractive gain medium due to its broad emission band from 1.1 μm to 1.7 μm that just covers the optical communication bands. Besides, the optical pumping absorption range for Cr4+-doped garnets cover the near-infrared region that broad-stripe diode laser with generous wavelength tolerance are available. The optical characteristics of Cr4+ ion doped in various hosts are listed in Table 2.1. The widest 3-dB emission bandwidth of is 277 nm for Cr4+:YAG covering the wavelength range from 1.2 to 1.6 μm. In addition, Cr4+:YAG has large ∆λσeτf product, the symbols in sequence mean the 3-dB emission bandwidth, emission cross section, and fluorescence lifetime. Therefore, Cr4+:YAG has a potential for a broadband light source in optical communication. Such broad band characteristics offer unprecedented one-for-all, convenience, flexibility, and simplicity to multi-band component manufactures in optical communication. The fiber configuration was fabricated to confine the pump and signal lights in a small-core area with a high intensity for enhancing gain. At present, the Cr4+:YAG 4.

(19) crystal has also been widely used as the gain medium for tunable solid-state lasers in the near infrared (NIR) region and as the saturable absorber medium for Nd:YAG lasers due to its large pump absorption cross-section [2.4-2.5]. In addition, some physical and optical properties of Cr4+:YAG crystal are listed in Table 2.2 [2.5-2.6]. YAG belongs to the garnet family with a cubic space group Ia3d. The stoichiometric formula is {A3}[B2](C3)O12, where A, B, and C denote different lattice sites with respect to their oxygen coordination that are dodecahedral, octahedral, and tetrahedral, respectively [2.3]. Figure 2.1 shows the YAG structure, the site symmetry is dodecahedral for the Y3+ ions, octahedral for 40% for the Al3+ ions, and tetrahedral for 60% of the Al3+ ions. Compound with the garnet structure have interesting properties. For example, YAG is a good laser host material for the rare-earth ions and Cr3+. The dodecahedron sites are ideal for the rare-earth ions and the octahedral sites are of appropriate size for Cr3+ ion. Table 2.1. List of the Cr4+-ion doped hosts with the 3-dB emission bandwidth ∆λ, peak wavelength, emission cross section σe, fluorescence lifetime τf, and ∆λσeτf product at room temperature [2.1-2.3]. Emission Host. Peak. Emission. σe. τf. (10-17. (μs). nm⋅μs⋅. spectra. wavelength. bandwidth. (nm). (nm). (nm). cm2). Y2SiO5. 1162-1416. 1260. 254. —. 0.7. —. Forsterite. 1167-1345. 1244. 178. 1.4. 3.9. 9.7. LAG. 1254-1486. 1370. 232. 3.4. 5.6. 44.2. YAG. 1253-1530. 1380. 277. 3.1. 4.5. 38.6. YSAG. 1289-1525. 1407. 236. 3.3. 3.3. 25.7. GGG. 1327-1557. 1442. 230. 4.5. 2.2. 22.8. YGG. 1337-1575. 1456. 238. 4.3. 1.9. 19.5. YSGG. 1421-1701. 1561. 280. 5.2. 1.3. 18.9. GSGG. 1432-1732. 1582. 300. 3.6. 2.0. 21.6. GSAG. 1461-1737. 1599. 276. 4.8. 1.7. 22.6. 5. (10. -19. ∆λσeτf. cm2).

(20) Table 2.2. Physical and optical properties of Cr4+:YAG crystal [2.5-2.6]. Crystal. YAG. Melting point. 1970 oC. Hardness (Mohr). 8.5. Density. 4.56 g/cm3. Refractive index. 1.82 @ 1 μm. Thermal conductivity. 11-13 W/m⋅K. Thermal change in refractive index. 7.3×10-6 K-1. Thermal expansion coefficient. 8.0×10-6 K-1. Lattice constant. 12.01 Å. 3-dB emission range. 1253-1530 nm. Absorption cross section. 22×10-19 cm-2. Emission cross section. 7×10-19 cm-2. Excited-state absorption cross section of pump. 4.18×10-19 cm-2. Excited-state absorption cross section of signal. 1.4×10-19 cm-2. Fluorescence lifetime at 25 oC. 4.5 μs. 3+. Al 3+ Al 3+ Y. Fig. 2.1. The cubic structure of garnet crystal. 6.

(21) The NIR emission spectrum from 1.2 μm to 1.6 μm is attributed to the transition between the 3A2 and 3T2 energy state of Cr4+ ions in the tetrahedral site of YAG. Because most Cr ions in the YAG structure have the smallest lattice mismatch of 11.9% in the Al3+ octahedral site, they tend to become octahedrally coordinated Cr3+. In order to incorporate the Cr in the quadrivalent, divalent ions need to be co-doped as the charge compensator to change the Cr3+ ions to Cr4+ ions. In 1997, Markgraf, et al. had examined several divalent ions, including Ca2+, Mg2+, Cu2+, Co2+, Fe2+, Mn2+, Zn2+, Ni2+, and Sr2+ [2.7]. Other divalent ions were excluded, such as Be2+, Pb2+, and Cd2+, due to safety concern. The results found the only successful co-dopants were Ca2+ and Mg2+ that radiated the NIR fluorescence from Cr4+ tetrahedral sites. Ca2+ ions are typically adopted as the co-dopants for good lattice match. Table 2.3 summaries the lattice mismatch between dopant ions and YAG ions. Ca2+ ions enters Y3+ dodecahedral site with a lattice mismatch of 8.7% which is better than Mg2+ ions’ replacing Y3+ dodecahedral site with a lattice mismatch of -11.1%. Crt4+ charge compensation depended on Ca2+ ions concentration was investigated in [2.8]. The relation between normalized Crt4+/total Cr and Ca2+/total Cr is shown in Fig. 2.2. There is no Crt4+ in the YAG host without charge compensator, and the ratio of Crt4+/total Cr is increased with increasing Ca2+/total Cr. In literature, the ratio of Crt4+/total Cr is below 6% that saturated in 5-fold atomic concentration of Cr to Ca. In our research, there are only less than 1% of the Ca2+ ions become active in charge compensation when Ca and total Cr ions are in the same quantity [2.9]. The low compensation efficiency may be explained by large lattice mismatch (i.e. +8.7%) with Ca2+ ions incorporated into the dodecahedrally coordinated Y3+ sites. The large lattice mismatch is also accompanied by the production of oxygen vacancies, which result in the de-activation of Ca2+ charge compensation. By annealing in oxygen atmosphere at 1350 oC for 4 hours, the ratio of Crt4+/total Cr can be improved to 5.5% [2.10]. It is the combined effects of oxygen vacancy re-fill under oxygen atmosphere and the Crt4+ ions migrated ion from the octahedral to tetrahedral sites.. 7.

(22) Table 2.3. Comparison of ionic radius mismatch between dopants and YAG host cations [2.7]. Host ion. Y3+ (D). Al3+ (O). Al3+ (T). Dopant. Ionic radius (Å). 1.159. 0.675. 0.53. Cr3+ (O). 0.755. +11.9%. Cr4+ (O). 0.69. +2.2%. Cr4+ (T). 0.55. +3.8%. Cr6+ (T). 0.44. -17.0%. Ca2+ (D). 1.26. Ca2+ (O). 1.14. Mg2+ (D). 1.03. Mg2+ (O). 0.86. Mg2+ (T). 0.71. Cu2+ (O). 0.87. Cu2+ (T). 0.71. Co2+ (O). 0.79. Co2+ (T). 0.72. Fe2+ (O). 0.75. Fe2+ (T). 0.77. Mn2+ (O). 0.81. Mn2+ (T). 0.80. Ni2+ (O). 0.83. Ni2+ (T). 0.69. Zn2+ (O). 0.88. Zn2+ (T). 0.74. Sr2+ (D). 1.40. Sr2+ (O). 1.32. +8.7% +68.9% -11.1% +27.4% +34.0% +28.9% +34.0% +17.0% +35.8% +11.1% +45.3% +20.0% +50.9% +23.0% +30.2% +30.4% +39.6% +20.8% +95.6%. D, O, and T denote ions in dodecahedral site, octahedral site, and tetrahedral site, respectively.. 8.

(23) Crt4+ / total Cr (%). 7. 7. 6. 6. 5. 5. 4. 4. 3. 3 After annealing. 2. 2. Before. 1. 1 0. 0 0. 10. 2+. 20. 30. 40. Ca / total Cr. Crt4+ / total Cr (%). Fig. 2.2. Relation between Cr4+ and Ca2+ concentrations in literature [2.8].. Fig. 2.3. The relation between normalized Cr4+ and Ca2+ concentrations [2.9].. 4+. Crt /total Cr ions (%). 9 8. A3 (w/o annealing). A4 (w/ annealing). A5 (w/ annealing). A5 (w/o annealing). w/ annealing. A3 (w/ annealing). 7 6 5 4 3 2. w/o annealing. 1 0 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 2+ 2+ Ca Ca /total /total Cr Crions ions. Fig. 2.4. The dependence between normalized Crt4+ and Ca2+ concentration several samples with or without oxygen annealing treatment [2.10]. Crt4+ mean the Cr4+ ions in tetrahedral sites.. 9.

(24) 2.2 Energy levels of Cr4+:YAG The absorption spectrum of Cr4+:YAG crystal was measured from 600 nm to 1400 nm. It exhibits two broad-band peaks centered at approximately 609 nm and 1034 nm. Figure 2.5 shows the absorption spectrum and the Gauss fitting of absorption wavelength peaks. The absorption spectrum is contributed from Cr4+ ions in the tetrahedral sites with 5 broad absorption bands. The strong absorption band at 665 nm belongs to the transition of 3B1→3E(3T1), the 609 nm is the phonon excitation band [2.11, 2.12]. The 1034 nm and 1124 nm bands are attributed to 3B1→3A2(3T1) and its phonon excitation band. The 893 nm is the 3B1→3E(3T2) transition. There is another strong absorption band at 480 nm that is attributed to the 3T1→3T2 translation in octahedral site. The 609 nm absorption band has overlapping with the Cr3+:YAG stronger absorption bands in 4A2→4T2 transition. Therefore, the suitable pump source is from 800 nm to 1200 nm. Figure 2.6 shows the fluorescence spectrum of the Cr4+:YAG in tetrahedral site. It has 5 emission sub-bands corresponding to transitions from 3B2(3T2) to 3B1(3A2) with spin energy levels. The broad band emission is from 1.1 μm to 1.7 μm with a 3-dB bandwidth of 277 nm. Table 2.4 summaries list the properties of the absorption and emission of the Cr4+ in tetrahedral sites of YAG.. Absorption spectrum (a.u.). 2.5 2.0 1.5. (1). 1.0. (2). (4). 0.5. (3) (5). 0.0 600. 800. 1000. 1200. 1400. Wavelength (nm) Fig. 2.5. Cr4+:YAG absorption spectrum and Gauss fitting of absorption wavelength peaks.. 10.

(25) 0.8 0.6. (5). 0.4. (2). (4). 4+. Cr fluorescence (a.u.). 1.0. (3). 0.2 (1). 0.0 1100. 1200. 1300. 1400. 1500. 1600. 1700. Wavelength (nm) Fig. 2.6. Cr4+:YAG emission spectrum and Gauss fitting of emission wavelength peaks.. Table 2.4. Parameters extracted from Gaussian fitting of the Cr4+:YAG absorption and emission spectra. Cr4+:YAG absorption spectrum ν0 (cm-1) ΔνFWHM (cm-1). No.. λ0 (nm). Δλ (nm). 1. 609. 61. 16420. 1647. 3. B1→3E(3T1)+[ Δν]. 2. 665. 41. 15038. 928. 3. B1→3E(3T1). 3. 893. 113. 11198. 1423. 3. B1→3E(3T2). 4. 1034. 136. 9671. 1278. 3. B1→3A2(3T1)+[ Δν]. 5. 1124. 24. 8897. 190. 3. B1→3A2(3T1). Assignment. Cr4+:YAG fluorescence spectrum. 1. 1162. 25. 8606. 185. 2. 1288. 116. 7764. 701. 3. 1356. 70. 7375. 381. 4. 1428. 107. 7003. 525. 5. 1436. 282. 6964. 1381. Δν is the phonon bandwidth.. 11. 3. B2(3T2)→3B1(3A2).

(26) Td. 3. -1. Energy (10 cm ). 18. D2d. 16. N3. 14. p. 12. T1. σesa 3. E. 3. T2. 3. N2. 8 6. σa. 4 0. E. s. σesa. 3. 10. 2. 3. (5). 3. A2. (1) (4). (3). (2) (1). N1. Ng. A2 B2. 3. (2). (3). (4). (5). σe,τf 3. B1. Fig. 2.7. The Cr4+:YAG energy level diagram.. 2.3 Distributed model of ASE and amplifier The energy level diagram of the Cr4+:YAG crystal is shown in Fig. 2.7. It is basically a four-level system. The numbers with brackets correspond to the absorption and emission peaks of Table 2.4. The various tiles indicate the 3-dB absorption bandwidth. The Cr4+ ions at ground state 3A2 are excited to the 3T1 or 3T2 state which depends on the wavelength of pumping light. The ions then relax non-radiatively to the meta-stable state 3B2(3T2). When the electrons transit from 3B2(3T2) to 3B1(3A2), photons are generates by stimulated and spontaneous emissions. The broadband spontaneous emission spectrum covers from 1.1 to 1.7 μm as shown in Fig. 2.4. The definitions of Ng, N1, N2, and N3, are the population densities of 3A2, 3B1(3A2), 3. B2(3T2), and 3E(3T1), respectively. The Cr4+ ions at 3B2(3T2) not only involve in the. spontaneous and stimulated emissions to the lower state 3B1(3A2), also the ESAs of the ASE and pump to a higher state 3E(3T1). N1 and N3 are assumed to be negligible due to the fast non-radiative relaxation rates [2.13, 2.14]. The electrons at 3B1(3A2) are relaxed to the ground state 3A2; the electrons at 3E(3T1) is relaxed to the meta-stable state 3B2(3T2). The rate equation for N2(z) is given by. 12.

(27) ⎤ ⎡ σ e (ν i )I ASE (z ,ν i ) 1 ⎥ dN 2 (z ) σ a I p (z ) , N g (z ) − N 2 ( z )× ⎢ = + ⎢ dt hν p hν i τf ⎥ ⎦ ⎣ i. ∑. N o = N g (z ) + N 2 ( z ) ,. (2.1). (2.2). where σa is the absorption cross section at pumping frequency νp, σe(νi) is the stimulated emission cross section at emission frequency νi, Ip(z) is the pumping intensity, IASE(z) is the total ASE intensity including both the forward and backward ASEs, τf is the fluorescence lifetime, and h is Planck’s constant [2.15, 2.16]. The total ion density No is equal to the sum of Ng(z) and N2(z) since the population densities in all other energy states are assumed to be negligible. To simplify Eq. (2.1), the following parameters are defined I sa =. hν p. σ aτ f. I se (ν i ) =. ,. hν e (ν i ). σ e (ν i )τ f. (2.3). (2.4). ,. where Isa and Ise(νi) are the absorption and emission saturation intensities, respectively. Then the Eq. (2.1) can be rewritten as ⎡ dN 2 (z ) I p (z ) N g (z ) − N 2 (z )× ⎢ = ⎢ dt I sa τ f ⎣ i. ∑. ⎤ I ASE (z ,ν i ) 1 ⎥ . + I se (ν i )τ f τf ⎥ ⎦. (2.5). From Eqs. (2.2) and (2.5), the steady-state solution of the population density N2(z) can be expressed as I p (z ) N 2 (z ) = N 0 ⋅. I p (z ). I sa. I (z ,ν i ) + 1 + Σ i ASE I sa I se (ν i ). .. (2.6). Therefore, the transport equations for the pumping and ASE intensities can be expressed as 13.

(28) dI p ( z ) dz. [. ]. p = − σ a ⋅ N g ( z ) + σ esa ⋅ N 2 ( z ) + α plp × I p ( z ),. ± (z ,ν i ) = ±σ (ν )N (z ) dI ASE e i 2 dz s ± (ν i ) σ e (ν i ) × I ASE (z,ν i ) + M × 2hν i Δν i × 1 − σ esa. {[. ± (z,ν i ), m α plASE × I ASE. ]. (2.7). } (2.8). p s where σ esa and σ esa are the ESA cross section of pump and ASE, respectively, α plp. and α plASE are the propagation loss constants of crystal fiber at pump and spontaneous-emission center wavelengths, respectively, νi is the emission frequency, M is the mode number of ASE [2.17], and ∆νi is the bandwidth of the emission. spectrum [2.16, 2.18, 2.19]. The positive and negative signs in Eq. (2.8) represent the forward and backward propagating ASEs, respectively. The Cr4+ ions within a differential fiber length dz contribute to the generation of the spontaneous emission and also the amplification of the forward and backward ASEs. The governing equation for the signal in the Cr4+:YAG fiber amplifier can also be expressed as s ⎡ σ esa (ν i )⎤ × I (z,ν ) − α s × I (z,ν ), dI s (z,ν i ) = σ e (ν i )N 2 ( z )× ⎢1 − i pl s i ⎥ s dz ⎣ σ e (ν i ) ⎦. (2.9). where Is is the signal intensity, α pls is the propagation loss constant of the signal.. 2.4 Lumped model of laser The Cr4+:YAG fiber laser is simulated in a lumped model with a four-level laser system. Based on the rate equations, the population density of N2(t) and cavity laser intensity IL(t) can be obtained. The energy level diagram for simulation model was already shown in Fig. 2.5. The rate equation of N2(t) is similar to the Eq. (2.1) and can be expressed as: ⎡ σ I (t ) dN 2 (t ) σ a I p 1 ⎤ = + N g (t )− N 2 (t )× ⎢ e L ⎥. dt hν p τ f ⎥⎦ ⎢⎣ h ν L. 14. (2.10).

(29) where σe is the emission cross section at laser frequency νL. The cavity laser intensity has dependence on population density N2(t) and photon lifetime tc. It can be expressed as [2.20]. (. ). ⎡ c dI L (t ) 1⎤ L = I L (t ) ⋅ ⎢ ⋅ σ e − σ esa ⋅ N 2 (t ) − ⎥ , dt t c ⎥⎦ ⎢⎣ n g. (2.11). where c and ng are the light velocity in vacuum and the refractive index of gain L medium, respectively, σ esa is the ESA cross section at laser wavelength, tc is the. photon lifetime. The absorbed pump power Pabs and pump intensity Ip can be expressed as follows:. {. [. Ip =. Pin ⋅ η in ⋅ e. (. p − α pl ⋅Lg. ]. p − σ a N g (t )+ σ esa N 2 (t )+ α plp L g. Pabs = Pin 1 − η in ⋅ η out ⋅ e. ) ⋅ ⎡1 − e − (α ⎢⎣. a ⋅Lg. }. ,. (2.12). )⎤ ⎥⎦. πr 2. ,. (2.13). where Pin is the incident pump power, ηin and ηout are the coupling efficiencies at the input and output faces, respectively, Lg is the gain medium length, r is the radius of the gain medium. The photon lifetime tc depends on the propagation loss of the signal in the fiber, and is shown as. tc =. 2 n g Lg. (. L ⎧⎪ ⎡ − 2⋅α pl ⋅ Lg c ⋅ ⎨1 − ⎢ R1R2 ⋅ e ⎪⎩ ⎣. ). ⎤ ⎫⎪ ⎥⎬ ⎦ ⎪⎭. ,. (2.14). where the R1 and R2 are the reflectance at the input and output faces, L. respectively, α pl is the propagation loss of cavity laser power. In addition, perfect mode matching between pump and cavity mode is assumed, i.e. rp = rL = r, where rp and rL are the pump and radiative light radii, respectively. The temperature dependency of the crystal fluorescence lifetime is included in the numerical analysis [2.21]. The empirical equation below is used to obtain the corresponding value of fluorescence lifetime [2.15] 15.

(30) τ f = τ f 0 − τ fT ⋅ T ,. (2.15). where τf0 is the fluorescence lifetime at reference 0 oC reference temperature. T is Celsius the temperature. The thermal lifetime coefficient τfT means the sensitivity of τf to the crystal temperature. Based on the simulation results of ASE and amplifier, the efficiencies of Cr4+:YAG crystal fiber can be increased by reducing core diameter, but it also raises the pump ESA loss. Cladding pump scheme should be adopted to suppress pump ESA then improve the ASE and gain performance, even though the fiber length should be lengthen to tens of meters. The detailed experimental demonstration and analysis will be discussed in chapter 5.. 16.

(31) Chapter 3 Cr4+:YAG crystal fiber growth For the applications of ASE light source and optical amplifier, the gain media in fiber form is necessary for generating a larger gain by the better optical confinement of the waveguide structure together with a longer propagation length of the gain region. For the applications of lasers, the fiber structure of the gain media can also be superior to bulk crystal for reduced lasing threshold and better slope efficiency due to also the optical confinement effect and better heat dissipation. A well-known growth technique for crystal fibers is the LHPG method. It is crucible-free and can, therefore, produce high-purity, low-defect-density single crystal fibers.. 3.1 Laser heated pedestal growth (LHPG) system There are many kinds of growth methods for fabricating single crystal fibers, such as solidification in capillary tubes [3.1], edge-defined film-fed growth [3.2], μ-CZ [3.3], μ-PD [3.4] and so on. The common disadvantages of these growth methods are crucible contamination, scanty flexible growth parameters. The LHPG method is a well-established technique for the growth of single crystal fibers. The LHPG method involves melting one end of a source material, then dipping a seed crystal into the free end of the molten zone. With a speed ratio between pulling seed and feeding source rod, various sizes of crystal fibers can be obtained. The contamination problems from crucibles and furnace components are virtually eliminated with this technique. Therefore it has the potential to produce purely single-crystal fibers. In addition, various materials in a wide melt-temperature range can be grown with the LHPG method. The scheme of our LHPG system is shown in Fig. 3.1. A 100-watt polarized CO2 laser at a wavelength of 10.6 μm is used as the heat source. After two reflective mirrors, the laser beam passes through a zinc selenide (ZnSe) power attenuator. The CO2 laser power is adjustable by rotating the angle of the power attenuator. Then, the 5-mm diameter laser beam is expanded to 30 mm with a ZnSe beam-expansion telescope.. 17.

(32) Mirror 1 100-W CO2 laser Power detector. Mirror 2. Power Beam splitter attenuator. Growth chamber ZnSe telescope PC. Fig. 3.1. The LHPG system.. Paraboloidal mirror. ZnSe window CO2 laser beam Planar mirror. Reflaxicone. inner cone outer cone. Fig. 3.2. Growth chamber.. The beam expansion can ease the difficulty of subsequent beam alignment steps. Then the expanded laser beam enters the growth chamber. The growth chamber was designed to bring the CO2 laser beam to be axially, azimuthally symmetric focused on the molten zone as shown in Fig. 3.2. Within the growth chamber, the CO2 laser beam passes through a set of reflexicon elements. The reflaxicon can convert the laser beam from Gaussian distribution to annulus of half-Gaussian cross-section. After a 45 degree planar mirror, a paraboloidal mirror with 25-mm focal length focus the laser beam on the top end of the source rod. The reflaxicons and paraboloidal mirror were made of oxygen-free copper, and by the diamond-turning technology. The use of a parabolic mirror rather than a spherical mirror eliminates spherical aberration. The 18.

(33) 25-μm focal spot size is important for stable growth of small diameter fibers. All mirrors of the LHPG growth chamber have gold coating on the copper surfaces with optical quality for reflectivity enhancement and copper substrate protection. The pulling and seeding mechanism are outside the chamber, and consist of computer-controlled linear stage driven by stepping motor with gearbox to reduce vibration. The maximum pulling length is 50 cm. The pulling speeds are in the range of 0.5 to 60 mm/min.. 3.2 Single crystal fiber growth Source material can be prepared in the forms of either round or square rods from a single crystal, polycrystalline, and sintered or pressured powder material. In this research, commercial CZ-grown single-crystal rods in round or square cross-section manufactured by CASIX were used as the source rods. The crystal fiber growth process is shown in Fig. 3.3. A seed rod with <111> orientation is used to determine the crystallographic orientation of the fiber to be grown. Firstly, the source rod is heated by the focused CO2 laser beam to melt the top end, and then the seed rod is dipped into the molten zone. Finally, a single-crystal fiber is grown by pulling the seed and feeding the source rod upward simultaneously at a constant speed ratio. Push. Oriented seed Grown crystal CO laser beam. Pull. 2. Molten zone. Source material Feed. Fig. 3.3. Illustration of single crystal fiber growth by the LHPG method.. The fiber-to-source rod diameter ratio can be controlled by setting the pull/feed speed ratio. At steady state, the volume of molten zone is constant due to conservation 19.

(34) of mass. The volume of crystal added to the fiber must equal the volume of the source rod melted per unit time. Therefore, the ratio of fiber diameter to source rod diameter is given by. Df Ds. vs , vf. =. (3.1). where Df and Ds are diameters of the fiber and source rod, respectively. vf and vs are speeds of pulling and feeding, respectively. Figure 3.4 shows the laser power necessary to form a stable molten zone in YAG. The growth power is proportional to the source rod diameter with a power of 1.88. The inset shows the molten zone of YAG. Typically, the axial temperature gradients are very steep at the growth interface (~ 103 °C/cm) and this permits faster growth rates (~ a few mm/min) compared with bulk crystal growth process (~ 0.5 mm/hour). Since YAG is a congruent material that maintains its composition right up to the melting point, YAG single crystal fiber is easy to grow by the LHPG method without adding a solvent.. CO2 laser power (W). 20 16 12. P∝Ds1.88. 8 4 0 0.2. 0.4. 0.6 0.8 Fiber diameter, Ds (mm). 1. Fig. 3.4. Laser power as a function of source rod diameter. The inset shows a photograph of YAG molten zone.. We have grown YAG single-crystal fibers along <111> orientation with diameters from 23 to 920 μm. Figure 3.5(a) shows the photograph of a 70-μm-diameter fiber of Cr4+:YAG grown at 10 mm/min, the diameter variation is about ±1.1% over a 1 cm. 20.

(35) length of the fiber. Figure 3.5(b) shows the end face SEM image of the 70-μm Cr4+:YAG crystal fiber, the shape of the facet is similar to a hexagon. This shape can be explained by the 6-fold symmetry of the fiber cross-section, as expected from a <111>-cut cubic crystal. Figure 3.6 is a drawing of the YAG atomic structure where hexagonal structure can be clearly seen.. 70 μm. 100× (a). (b) 4+. Fig. 3.5. (a) Photograph of a Cr :YAG single-crystal fiber with a 70-μm diameter grown by the LHPG method. (b) The end face SEM image of the 70-μm Cr4+:YAG crystal fiber.. Y - purple, Al - blue, O - red Fig. 3.6. Drawing of the YAG atomic structure viewed from <111> direction.. 21.

(36) 3.3 Double-clad crystal fiber (DCF) growth Based on the simulation results, it will have better optical performance when the fiber diameter can be reduced to below 10 μm. Due to the limitation of the 25-μm focal spot size, it will be hard to reduced the fiber diameter to 10 μm. An innovative CDLHPG technique was developed to solve the problem [1.13, 3.5]. Figure 3.7(a) shows the schematic of the CDLHPG method. Firstly, a 70-μm diameter Cr:YAG crystal fiber was obtained by a two-step growth from a 500-μm diameter source rod. Then it was inserted into a fused-silica capillary tube with 76 and 320-μm inner and o. outer diameters. The 1970 C melting temperature of the YAG is comparable to the o. 1600 C soften temperature of the fused silica. The molten zone drawing during growth process of the CDLHPG method is shown in Fig. 3.7(b), the heating of the CDLHPG method caused a strong inter-diffusion between the YAG core and fused-silica capillary, and an inner cladding layer made of the mixture was formed. With properly controlled growth parameters, Cr4+:YAG DCF were obtained. The core diameter of the DCF was controlled during the growth process by adjusting the CO2 laser power and the fiber growth speed. Figure 3.7(c) is the photograph of the side view of the DCF.. Cr4+:YAG crystal fiber Fused silica tube. CO2 laser. Molten zone. Core Inner cladding Outer cladding Cr4+:YAG crystal fiber Fused silica capillary. (a). (b). (c). Fig. 3.7. (a) Scheme of CDLHPG method. (b) Molten zone drawing during growth process. (c) Photograph of side view of the Cr4+:YAG DCF. 22.

(37) (a). (b). Fig. 3.8. (a) The polished end of a single-clad Cr4+:YAG-silica fiber. (b) The polished end of Cr4+:YAG DCF.. Figure 3.8(a) shows the polished end of the single-clad Cr4+:YAG-silica fiber that the silica all diffuses into the YAG. By controlling the heating laser power, the Cr4+:YAG DCF can be fabricated. The end face is shown in Fig. 3.8(b). In this way, the core diameter of Cr4+:YAG DCF can be reduced to around 10 μm. But the degree of difficulty in growth process rises with the reduction of core diameter. That is because the core-diameter uniformity of DCF becomes very sensitive to laser heating power. By growth experiments, the 10-μm core fiber has around 60% core variation even if the power fluctuation of the heating laser is within 0.5% typically.. 3.4 Sapphire tube assisted co-drawing LHPG growth Tong et al. successfully fabricated silica wires with diameters down to several tens of nanometers by using an indirect heating mechanism through the tip of a tapered sapphire tip in their fiber drawing system [3.6]. To improve the core uniformity of small-core crystal fiber, we propose, for the first time, to use the thermal capacitance effect in a similar way to suppress the power fluctuation of heating laser by incorporating a sapphire tube in the CDLHPG system.. 23.

(38) 3.4.1 Sapphire tube assisted growth system The schematic of the sapphire tube assisted CDLHPG growth system is shown in Fig. 3.9(a). As shown in Fig 3.9(b), the length of the sapphire tube was 1.5 mm, and the outer and inner diameters were 1200 μm and 480 μm, respectively. The capillary with a 70-μm Cr4+:YAG single-crystal fiber inside was inserted into the sapphire tube for DCF growth. A donut-shape CO2 laser beam was focused and shone around the outer wall of the sapphire tube to heat up and generate a strong thermal radiation for melting the filled silica capillary. A negative pressure of 200 torrs prevented the generation of bubbles inside the waveguide during the growth process.. Cr4+:YAG Negative pressure pump. Air gap Sapphire tube. Paraboloidal mirror Sapphire tube. 1500 μm Planar mirror. CO2 laser beam. 76 μm. Reflaxicon. Cr4+:YAG crystal fiber inserted capillary. inner cone. (a). 320 μm 480 μm 1200 μm. (b). Fig. 3.9. (a) The schematic of sapphire tube assisted CDLHPG system. (b) The end view and side view of the sapphire tube with fused-silica capillary.. The steady-state temperature distribution of the heating zone was simulated with a finite element method. Considering the effects of heat convection, heat conduction, and thermal radiation in a two-dimensional included, the simulation result is shown in Fig 3.10(a). The temperature of the sapphire tube is almost isothermal distribution in the cross-section of the longitudinal direction.. 24.

(39) Fused silica capillary with inserted Cr:YAG crystal fiber Air gap. Temperature (oC). Sapphire. Sapphire. 2050. 2025. 2000. 1975. 1950. (a). 1970. 2040 2030. 1968 Temperature ( C). 2010. o. o. Temperature ( C). 2020. 2000 1990 1980. 1966 1964 1962. 1970 1960. 0. 200. 400. 600. 800. 1000. 1200. Transversal position (μm). 1960. 0. 500. 1000. Longitudinal position (μm). (b). (c). Fig. 3.10. (a) The two-dimensional simulation of temperature distribution in the sapphire tube heating zone. (b) Temperature distribution at the heating zone center in transversal position. (c) Temperature distribution in the longitudinal position.. 25. 1500.

(40) A larger volume of the sapphire tube compared with fused silica capillary has the larger thermal capacitance to suppress power fluctuation of heating laser. The transversal and longitudinal positions of the heating zone center are extracted from Fig. 3.10(a) as shown as Fig. 3.10(b) and (c). The transversal temperature distribution has a large fall down in the air gap between the sapphire tube and fused silica capillary. The longitudinal temperature distribution in the fused silica capillary center has maintained at around 1970 oC in the heating range. It implies that the molten zone of the DCF growth with sapphire tube is longer than that without sapphire tube, i.e. the sapphire tube assisted DCF growth has a lower temperature gradient than that without sapphire tube assisted growth.. 3.4.2 Growth system improvement Besides the sapphire tube assisted CDLHPG technique to improve the core-reduction process, the power feedback control of the heating laser is also refined with an automatic LabVIEW program. The flow chart of power feedback control system is shown in Fig. 3.11. The laser power passing through a linear polarizer is detected by a power meter. An A/D card (National Instruments, NI-DAQPad 6020E) catches the electric signal to send to a computer. A calibrated LabVIEW program calculates the adjustment value then uses a stepping motor control card (Advantech PCI-1240) to control the rotation angle of the linear polarizer by employing a linear stage. Figure 3.12(a) is the power variation of detected laser without feedback control. The typically power variation is around 5%. Obviously, the power variation is ten times to the value of 0.5% power stability requirement with 60% core variation in 10-μm core fiber. With the feedback control system, 0.1% power stability can be obtained as shown Fig. 3.12(b). It is around a factor of 50 improvement with the power feedback control system.. 26.

(41) CO2 laser. Linear polarizer. Powermeter. Stepping motor driver. A/D card. LabVIEW program. Fig. 3. 11. Flow chart of power feedback control system.. Power variation ~ 5%. (a). Power variation ~ 0.1%. (b) Fig. 3.12. (a) Laser power variation as a time function without power feedback control. (b) In a power feedback control, 0.1% power stability can be reached.. Besides, the core boundary identification of the DCF during the growth process is another important issue. A CCD camera catching the real-time side view image of the 27.

(42) DCF is included into the growth system to identify the core boundary. The NI company had exploited the vision assistant auxiliary software to help user analyze about image problem in the LabVIEW program. A side-view photograph of DCF during the growth process is shown in Fig. 3.13(a). The image resolution is 640×480 pixels that depends on the frame card (NI-PCI-1405). To operate in coordination with an optical microscope (56 magnifications), the resolution of the image is around 1 μm. Based on the shade contrast of the photograph, the interfaces of the core, inner cladding, and outer cladding can be determined. The identified core boundary is shown in Fig. 3.13(b). By calculating the ratio of outer diameter and core diameter in pixels counts, the core-size of DCF can be obtained. The calculated core-size of DCF should multiply 0.6 to calibrate the distortion from the cylindrical refraction. With the core-size calculation, we can modify the heating laser power to obtain the expected core size of DCF.. (a). (b). Fig. 3.13. (a) Side-view photograph of the DCF during growth process. (b) Result of core boundary identification.. In order to simplify the growth procedures and be more precise to obtain the expected core-size of DCF, a friendly operation interface in the computer is necessary. With data from several growth processes, the core diameter of DCF as a function of heating laser power is shown in Fig. 3.14. By curve fitting, an empirical formula can be obtained as follow 28.

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