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研究生:劉子銘
研究生(外文):Tzu-Ming Liu
論文名稱:高重覆率鎖模固態雷射
論文名稱(外文):High Repetition-rate Mode-locked Solid-state Lasers
指導教授:孫啟光孫啟光引用關係
指導教授(外文):Chi-Kuang Sun
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:光電工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:142
中文關鍵詞:鎖模雷射飛秒光學固態雷射脈衝量測高重覆率
外文關鍵詞:phase retrivalHigh repetition-rateMode-locked laserfemtosecond optics
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高重覆率鎖模固態雷射在釵h實際應用上扮演越來越重要的角色。在光通訊的領域裡,它具有潛力成為「分波(WDM)-光分時(OTDM)混合多工」的光源。在頻率量測學的領域裡,高重覆率雷射可以增加頻率量測的解析度與訊雜比。在一些量測的應用上,高重覆率雷射可以降低每個脈衝的能量並同時維持高平均必v,這對於達到高訊雜比而言是個很重要的特性。雖然高重覆率鎖模固態雷射對這些應用來說是一種有利的工具,但它仍然存在一些障礙,使得它無法獲得更好的發展。例如:「分波-光分時混合多工」的通訊系統仍然缺乏高必v、高重覆率的多頻道光源,因而無法利用到頻率域(frequency domain)的資源。在頻率量測的領域裡,現有高重覆率鎖模固態雷射的工作波長仍然缺乏一些特定原子或分子躍遷的頻段。除此之外,一旦高重覆率鎖模固態雷射建好,它的脈衝重覆率就無法隨意的倍增,任何的倍增都需要更改到共振腔的設計。
在本論文中,我們克服了上述障礙,讓高重覆率鎖模固態雷射在釵h高重覆率雷射的相關應用中變得更有用、更靈活。針對頻段缺乏的問題,我們採用二倍頻的頻率轉換方式達成了紅色與藍色波段的高重覆率飛秒雷射。在110 百萬赫玆的重覆率之下,我們首次將腔內二倍頻的技術運用在鉻貴橄欖石(Cr:forsterite)雷射上。結果我們在620奈米附近的紅光波段產生了平均必v為24毫瓦的高重覆率170飛秒脈衝。對於長度較短的雷射共振腔而言,頻率轉換比較適合在共振腔外進行與提昇。所以,在二十億赫玆重覆率的鈦藍寶石雷射共振腔外,我們運用另一個共振腔來提昇轉換效率,建造了第一個重覆率為二十億赫玆的高必v飛秒藍色光源。在鈦藍寶石(Ti:sapphire)雷射以740毫瓦必v的激發之下,腔外共振腔可以有效的產生150毫瓦必v、波長為409奈米的藍光飛秒脈衝。

針對「分波-光分時混合多工」缺乏高必v光源的問題,我們利用高重覆率飛秒脈衝雷射的寬頻特性,完成了第一個高必v的高重覆率多頻道光源。當我們在高重覆率飛秒鉻貴橄欖石雷射內置入一個腔內標準具(Etalon)時,可以在1230奈米的波長附近產生十二個鎖相的頻道,每個頻道具有9-19皮秒的脈衝寬度。同時,我們可以直接從共振腔獲得280毫瓦的平均必v。藉由調整標準具的頻寬,我們還可以將特定頻道的脈衝寬度降至1.8皮秒。

針對重覆率的調整缺乏靈活度的問題,我們發明了一個運用腔內平面的技術來倍增脈衝的重覆率。首先,我們建造了一個自啟動且小巧的高重覆鉻貴橄欖石雷射,它的重覆率為100百萬赫玆,工作波長在1230奈米附近,是一個適用於可攜式醫療診斷用途的雷射光源。為了達到小巧的目的,雷射共振腔的色散是由雙啁啾(Double-chirped)鏡子來補償,以取代傳統占空間的稜鏡對(Prism pair)技術。透過半導體飽和吸收鏡(SESAM)的輔助,雷射的鎖模可以自動啟動。接著我們置入一個低反射率的腔內平面,將共振腔分為兩個次腔,透過次腔長度比例的控制,我們可以將飛秒脈衝的重覆率從100百萬赫玆倍增到500百萬赫玆,甚至到更高的十億赫玆以上。與傳統的耦合腔方式相比,這個新發展的技術提供了一個更具彈性且對於相位變化較不敏感的方式來增加飛秒脈衝固態雷射的重覆率。

為了能夠獲得高重覆率脈衝的光場完整資訊,我們研發了一項新的技術,將頻譜資訊加入三重自相關函數(triple-autocorrelation)的量測中。從三重自相關函數量測獲得的時域形狀以及對應的頻譜,確切的光場大小與相位可以透過Gerchberg-Saxton演算法精確的獲得,整個演算過程的複雜度只需O(n)。


High repetition rate (HRR) mode-locked solid-state lasers have increasing importance in many applications. In optical communications, it’s a potential source for the hybrid wavelength-division multiplexed (WDM) and optical time-division multiplexed (OTDM) systems. In frequency metrology, HRR lasers can increase the resolution and signal to noise ratio (SNR) of frequency measurement. In the domain of measuring applications, HRR lasers reduce the optical pulse energy while maintaining a high average power, which is important for achieving high SNR. Although HRR mode-locked lasers are advantageous to these applications, there are still some hindrances for better development. In WDM/OTDM hybrid communication system, it still lacks a high power HRR multi-channel source to exploit the spectral domain resources. In frequency metrology, there are still some spectral black holes corresponding to specific transition level of atoms or molecules. Besides, once a HRR mode-locked solid-state laser is built, the repetition rate can’t be easily multiplied without changing the cavity geometry.
In this thesis, we circumvented these hindrances and made HRR mode-locked lasers more promising and more flexible in many HRR applications. Complete information of HRR pulses can be characterized with developed auxiliary technique. For the problem of spectral black holes, we employed frequency conversion such as second harmonic generation (SHG) to achieve HRR femtosecond lasers at red and blue wavelengths. Based on an 110-MHz Cr:forsterite laser, we first used intracavity frequency doubling to obtain HRR femtosecond pulses around 620-nm. Red pulses with 170-fs pulse width were obtained with 24-mW average power. For the frequency conversion of short cavity length, it’s better to employ external resonant cavity to enhance the conversion efficiency. As a consequence, based on a 2-GHz Ti:sapphire laser, we demonstrated a 2-GHz-repetition-rate high-power femtosecond blue sources for the first time. Pumped by the 2-GHz Ti:sapphire laser with 740-mW output power, 150-mW femtosecond pulses at 409nm can be efficiently generated from the resonant cavity.

For the development of high power WDM/OTDM sources, we exploit the broadband nature of HRR femtosecond lasers and demonstrated first high power HRR multi-channel sources. By inserting an intracavity etalon into a HRR femtosecond Cr:forsterite laser, 12 phase-locked channels with 9–19-ps pulse width near 1230 nm could be generated. Average output power of 280-mW can be obtained from a single laser oscillator. By tuning the etalon bandwidth, we can shorten the pulse width in a specific channel to 1.8 ps.

For the improvement of repetition rate flexibility, we invented an intracavity flat surface technique to multiply the repetition rate. We first built a compact self-started HRR Cr:forsterite laser at 100-MHz for the application of portable clinical use operating around 1230 nm. Instead of prism pairs, double-chirped mirrors were employed to compensate the group delay dispersion of the laser cavity. The laser mode-locking was self-started with the help of a semiconductor saturabe absorber mirror. By adopting an intracaity flat surface with low reflectivity and controlling the ratio of subcavity lengths, the repetition rate of this compact femtosecond Cr:forsterite laser can be multiplied from 100 MHz to 500 MHz in femtosecond regime. Repetition rate higher than 1GHz can also be achieved. Compared with the conventional coupled cavity method, this newly developed technique provides a flexible and phase insensitive way to increase the repetition rate of femtosecond solid-state lasers.

For the diagnosis of ultrashort HRR pulses, we developed a new technique. By adding spectral information into triple-optical-autocorrelation measurements, we made the triple-autocorrelation method capable of providing complete knowledge of HRR laser pulses. With the measured temporal intensity of an optical pulse and its corresponding spectral intensity obtained with a spectrometer, exact intensity and phase variations in time can all be recovered with the Gerchberg-Saxton algorithm through an iterative calculation with an O(n) complexity.


CONTENTS
CHAPTER 1 INTRODUCTION 1
1.1 Ultrashort pulse duration and high pulse
repetition-rate 1
1.2 Development of HRR mode-locked solid-state
lasers 3
1.3 Advantages and hindrances of HRR mode-locked
solid-state lasers 3
1.4 Solutions 5

CHAPTER 2 PRINCIPLES OF KERR LENS MODE LOCKING
WITH SLOW SATURABLE-ABSORBERS 13
2.1 Basic concept of the mode locking 13
2.2 Development of mode-locking techniques 15
2.3 Principles of Kerr lens mode locking 17
2.3.1 Optical Kerr effect and self-focusing 18
2.3.1.1 Nonlinear susceptibility 18
2.3.1.2 Self-focusing 20
2.3.2 The master equation of soliton mode locking 20
2.3.2.1 Self-phase modulation 20
2.3.2.2 Group delay dispersion 23
2.3.2.3 Gain dispersion 26
2.3.2.4 Saturable absorption 27
2.3.2.5 Master equation of pulse shaping dynamics 29
2.4 Cavity design for Kerr lens mode locking 33
2.4.1 Astigmatism compensation 33
2.4.2 Dispersion compensation 35
2.4.3 Semiconductor saturable absorber
mirror (SESAM) 39

CHAPTER 3 EXTENDING THE OPERATION WAVELENGTH
OF HIGH REPETITION-RATE MODE-LOCKED
SOLID-STATE LASERS 46
3.1 Motivation 46
3.2 Femtosecond HRR Cr:forsterite laser 47
3.2.1 System setup 47
3.2.2 Performance 49
3.3 Femtosecond HRR red sources 51
3.3.1 Introduction 51
3.3.2 Experimental setup 53
3.3.3 Intracavity frequency doubling to red
wavelength 55
3.4 Femtosecond HRR blue sources 62
3.4.1 Introduction 62
3.4.2 Resonant cavity enhanced SHG 63
3.4.3 Experimental setup 68
3.4.4 Performance and discussions 71

CHAPTER 4 HIGH REPETITION-RATE MULTI-CHANNEL
SOURCE 79
4.1 Motivation 79
4.2 Experimental setup 82
4.3 Results and discussions 82
4.3.1 Multi-channel generation 82
4.3.2 Multi-channel management 86

CHAPTER 5 A FLEXIBLE TECHNIQUE TO MULTIPLY THE
REPETITION-RATE OF PASSIVE MODE-
LOCKED FEMTOSECOND LASERS 94
5.1 Motivation 94
5.2 Compact, self-started, and HRR femtosecond
Cr:forsterite laser 95
5.2.1 Introduction 95
5.2.2 Experimental setup and performance 96
5.2.3 Sub-micron resolution nonlinear optical
microscopy system 100
5.3 Repetition-rate multiplication by an
intracavityflat surface with low reflectivity 102
5.3.1 Principles 102
5.3.2 Experimental setup 103
5.3.3 Results and discussions 105



CHAPTER 6 CHARACTERIZATION OF HIGH REPETITION-
RATE PULSES WITH THIRD-HARMONIC-
GENERATION BASED TRIPLE
AUTOCORRELATION 114
6.1 Introduction 114
6.2 Triple autocorrelation for direct pulse shape
measurement : Principles 116
6.3 Obtaining pulse shape with THG based triple
autocorrelation 117
6.4 Phase retrieval 122
6.5 Characterizing the dispersion of pulses 124
6.6 Phase verification with FROG 128
6.7 Algorithm accuracy: TOAD with GS vs. PG-FROG 131

CHAPTER 7 SUMMARY 136


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[7.5]T.-M. Liu, H.-H. Chang, S.-W. Chu, and C.-K. Sun, “Locked multichannel generation and management by use of a Fabry–Perot etalon in a mode-locked Cr:forsterite laser cavity,” IEEE J. Quantum Electron. 38, 458-463 (2002).
[7.6]T.-M. Liu, S.-W. Chu, S.-P. Tai, C.-K. Sun, F. X. Kärtner, and J. G. Fujimoto, “Compact self-started femtosecond Cr:forsterite laser for non-linear optical microscopy,” Technical Digest of Conference on Laser and Electro-Optics, San Francisco, California, May 16-21, 2004 (Optical Society of America, Washington DC, 2004), CThFF4.
[7.7]M.-C. Chan, T.-M. Liu, and C.-K. Sun, “Compact self-started femtosecond Cr:forsterite laser used for nonlinear optical microscopy with fiber based endoscope system,” manuscript in preparation.
[7.8]T.-M. Liu, F. X. Kärtner, J. G. Fujimoto, and C.-K. Sun, “Multiplying the repetition rate of passive mode-locked femtosecond lasers by an intracavity flat surface with low reflectivity,” submitted to Optics Letters.
[7.9]T.-M. Liu, Y.-C. Huang, K.-H. Lin, G.-W. Chern, C.-J. Lee, Y.-C. Hung, and C.-K. Sun, “Triple-optical autocorrelation for direct optical pulse-shape measurement,” Appl. Phys. Lett. 81, 1402-1404 (2002).
[7.10]T.-M. Liu, Y.-C. Huang, G.-W. Chern, K.-H. Lin, Y.-C. Hung, C.-J. Lee, and C.-K. Sun, “Characterization of ultrashort optical pulses with third-harmonic- generation based triple autocorrelation,” IEEE J. Quantum Electron. 38, 1529-1535 (2002).
[7.11]C.-K. Sun, T.-M. Liu, Y.-C. Huang, and G.-W. Chern, “Method and system for measuring an ultrashort optical pulse,” United State Patent, Patent No. :US 6734976 B2.
[7.12]C.-K. Sun, S.-W. Chu, T.-M. Liu, and P. C. Cheng, "High intensity scanning microscopy with a femtosecond Cr:Forsterite laser," J. Scanning Microscopies 22, 95-96 (2000).
[7.13]P. C. Cheng, F. J. Kao, C.-K. Sun, B. L. Lin, T.-M. Liu, Y.-S. Wang, M.-K. Huang, Y.-M. Wang, J.-C. Chen, and I. Johnson, "Multi-photon excited fluorescence spectra of common bio-probes," J. Scanning Microscopies 22, 187-188 (2000).
[7.14]F.-J. Kao, P. C. Cheng, C.-K. Sun, B.-L. Lin, Y.-M. Wang, J.-C. Chen, Y.-S. Wang, T.-M. Liu, and M.-K. Huang, "Multi-photon spectroscopy of plant tissues," J. Scanning Microscopies 22, 193-194 (2000).
[7.15]T.-M. Liu, S.-W. Chu, C.-K. Sun, B.-L. Lin, P. C. Cheng, and I. Johnson, "Multi-photon confocal microscopy using a Femtosecond Cr:forsterite laser," J. Scanning Microscopies 23, 249-254 (2001).
[7.16]S.-W. Chu, I-H. Chen, T.-M. Liu, P.-C. Chen, C.-K. Sun, and B.-L. Lin, “Multimodal nonlinear spectral microscopy based on a femtosecond Cr:forsterite laser,” Opt. Lett. 26, 1909-1911 (2001).
[7.17]S.-W. Chu, I-S. Chen, T.-M. Liu, C.-K. Sun, S.-P. Lee, B.-L. Lin, P.-C. Cheng, M.-X. Kuo, D.-J. Lin, and H.-L. Liu, “Nonlinear bio-photonic crystal effects revealed with multi-modal nonlinear microscopy,”Journal of microscopy- OXFORD, 208, 190-200 (2002).
[7.18]S.-W. Chu, T.-M. Liu, and C.-K. Sun, “Real-time second-harmonic-generation microscopy based on a 2-GHz repetition rate Ti: sapphire laser,” Opt. Express, 11, 933-938 (2003).
[7.19]S.-W. Chu, S.-Y. Chen, T.-H. Tsai, T.-M. Liu, C.-Y. Lin, H.-J. Tsai, and C.-K. Sun, “In vivo developmental biology study using noninvasive multi-harmonic generation microscopy,” Opt. Express, 11, 3093-3099 (2003).
[7.20]J.-W. Shi, Y.-H. Chen, K.-G. Gan, Y.-J. Chiu, J. E. Bowers, M.-C. Tien, T.-M. Liu, and C.-K. Sun, “Nonlinear behaviors of low-temperature-grown GaAs-based photodetectors around 1.3 �慆 telecommunication wavelength,” IEEE Photon. Technol. Lett. 16, 242-244 (2004).
[7.21]C.-K. Sun, S.-W. Chu, S.-Y. Chen, T.-H. Tsai, T.-M. Liu, C.-Y. Lin, and H.-J. Tsai, “Higher harmonic generation microscopy for developmental biology,” J. Struct. Biol 147, 19-30 (2004).


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