利用光子晶體光纖製造長週期光纖光柵與超連續光譜

國

立

交

通

大

學

光電工程研究所

碩

士

論

文

利用光子晶體光纖製做長週期光纖光柵與超連續光

譜

Long-Period Grating and Supercontinuum

Generation Using Photonic Crystal Fiber

研 究 生：陳厚仁

指導教授：謝文峰 教授

林奎輝 教授

利用光子晶體光纖製造長週期光纖光柵與超連續光

譜

Long Period Grating and Supercontinuum

Generation Using Photonic Crystal Fiber

研 究 生：陳厚仁

Student：Hou-Ren Chen

指導教授：謝文峰 教授

Advisor：Wen-Feng Hsieh

林奎輝 教授 Kuei-Huei Lin

國 立 交 通 大 學

光電工程研究所

碩 士 論 文

A Thesis

Submitted to Institute of Electro-optical Engineering College of Electrical Engineering and Computer Science

National Chiao Tung University in Partial Fulfillment of the Requirements

for the Degree of Master

in

Electro-optical Engineering June 2007

Hsinchu, Taiwan, Republic of China

利用光子晶體光纖製作長週期光纖光柵與超連續光

譜

研究生：陳厚仁 指導教授：謝文峰 教授 林奎輝 教授 國立交通大學光電工程研究所

摘要

在此篇論文，我們研究兩個主題: 第一，我們使用兩種鋸齒狀元件在光子晶體光纖 上產生易變、可調的長週期光纖光柵。長週期光柵的中心波長、截止頻帶和穿透損失可 以被大範圍的調整。我們在啾頻的長周期光柵上觀察到不等間距的干涉條紋，干涉條紋 與交互作用的長度和長周期光柵兩端啾頻的程度有關，干涉條紋可以被消除，當我們減 小交互作用的長度和啾頻的量。藉著利用這可調的長週期光柵，我們也對摻鉺光纖放大 器作增益平坦化，並且也被證實。第二，我們也研究不同起始穿透率摻鉻釔鋁石榴石之 摻釹釩酸釓固態激發的 Q-開關 (Q-switched) 鎖模雷射。在輸出偶合鏡反射率 R = 60%， 飽和吸收體穿透率 T0= 40%，並且激發功率 15 瓦時，有最大的 Q-開關波包脈衝能量大 約 0.096 毫焦耳。最後，我們藉由高脈衝能量的 Q-開關鎖模雷射耦合至光子晶體光纖， 產生了 950 nm 至 1450 nm 寬的超連續光譜。 i

Long Period Grating and Supercontinuum Generation Using

Photonic Crystal Fiber

Student: Hou-Ren Chen Advisor: Prof. Wen-Feng Hsieh Prof. Kuei-Huei Lin

Institute of Electro-optical Engineering National Chaio Tung University

Abstract

In the thesis, we investigate two topics: First, we report a method for generating versatile tunable long-period gratings (LPGs) in photonic crystal fibers (PCFs) by using two kind of corrugated devices. The central wavelength and rejection bandwidth of LPGs can be tuned over a broad spectral range with adjustable transmission loss. Spectral fringes with uneven spacing wre observed in chirped LPGs, depending on the interaction length and the amount of chirping between the two ends of the LPG, and can be removed by reducing interaction length and chirping. By utilizing a stress-induced LPG, gain flattening of an erbium-doped fiber amplifier has also been demonstrated. Second, We investigated the Q-switched and mode-locked operation in a diode-pumped Nd:GdVO4 laser by the

permutation of initial transmittance T0 of Cr4+:YAG crystal. The highest pulse energy of

Q-switched envelope about 0.096 mJ with output coupler of R = 60% and initial

iii

transmission T0 = 40% of a Cr:YAG saturable absorber can be obtained at the 15 W pump

power. Finally, supercontinuum is generated by using a Q-switched mode-locked laser coupling into photonic crystal fiber.

 

致謝

還記得不久前才剛考完碩士班入學考試，進到小天王實驗室，兩年的時間， 轉眼間就過去了，即將從小天王實驗室畢業，但是隨即又再度進到小天王實驗室 @@＂，同時也是邁入另一個階段，首先，當然要感謝這兩年間謝老闆的悉心指導， 很有耐心的陪我們研讀論文，培養我們撰寫文章和口頭報告的技巧，也教導我們 很多做人處事的道理，並且總是以聊天的方式來緩和 meeting 緊張的情緒；以及 林奎輝老師總是會撥空來交大和我討論課業，實驗上問題，也會常常關心我生活 上的事情，尤其在日本報告的那段時間，承蒙老師的照顧，帶著我們四處遊玩， 真是謝謝林奎輝老師；家弘學長在討論上和實驗上幫助我很多，讓我獲益匪淺， 並且在韓國報告期間，途中還感冒發燒，在藥局買成藥越吃越嚴重 =.=，謝謝學 長的照顧，當然不能忘記好久不見的 “胖奶油＂ ，長期在實驗室中伴隨著大 iv  家。 這兩年期間，和碩二的夥伴從一開始的不太熟到最後培養了深厚的情誼。陳 IC 啊!!陳 IC，這兩年應該和你最熟了吧!!碩一的時候一起坐在裡面，雖然你常 常會＂肖肖＂，但還是常常幫我解決很多程式的 Bug…你是高手!!，碩二的時候 發現你不只肖肖，還很＂鹹濕＂ XD；B47 的另一個成員，小詹，妳做事的嚴謹 總是讓我印象深刻，但是迷糊也是讓我印象深刻 XD，碩二的時候能一起到日本 報告加旅遊，這是一個很好的回憶，妳也是我見過最純真的女生 >/////< ；賴 小新，(小賴，賴阿婆)，妳真是實驗室的開心果，實驗室如果少了妳，應該就不 會這麼熱鬧了吧，回想什麼時後開始和妳變熟的，我想是碩一和妳在圖書館看固 態物理到半夜那時候開始吧…哈，碩二的時候也常常討論到半夜，其實大部分時 間都在＂拉賽＂XD，也謝謝妳請我吃大餐，也祝妳到美國這八個月一切順利，如 果我有去參加研討會，在去讓妳包吃包住，還有，一年後我會變瘦的=.=+；香腸 (吸哥)，碩一的時候真的和你不熟，一度還覺得你是怪角 XD(不要恨我)，後來 才發現你是高手，真後悔沒在妳身上學個一招半式，真是虧大了；伍佰，碩一的  

  v    的大學八卦..哈；老徐，成 為上 色的棕儂學弟 XD， 你們 科會 NSC96-2628-M-009-001-MY3 計劃的支持， 讓我的研究得以順利完成。 2008.07.18 厚仁 於交大雷射診斷實驗室 時候和你不熟，但是你的染的金毛卻讓我印象深刻，到了碩二因為一個＂三國遊 戲＂讓我們變的還不錯熟.，也感謝你友情贊助陳 IC 市上櫃公司的老闆時，要記得我是你同學嘿。 另外雷射組的智章學長，在我的研究上和想法上提供我很多的意見，真的很 謝謝你；還有 Pochi，雷射組接下來剩下我們和智章學長了，以後我們要相依為 命了 XD，另外還有光子晶體組的志賢學長和材料料組的小豪，你們常常在實驗 室的打情罵俏，讓我看起來覺得好羞喔>///<，另一方面從被小豪誘拐進到 DLSR 的世界後，有機會就會一起去拍照，讓我學習到很多攝影的技巧，你是高手!!； 小郭，你對事情總是用 Discovery 式，博大精深的精闢解說，真是讓我忘塵莫及， 你也是高手。此外小天王實驗室的松哥、信民、黃董、維仁、老媽媽國峰學長、 水晶晶晴如學姐，碩班時間很少和你們互動，也常常缺席你們的聚餐活動，還蠻 遺憾的。另外還有一群可愛的學弟妹，嬌滴滴的阿肥儂儂，名字很像蔡健雅的智 雅學妹、博大精深程度快跟小郭同等級的建輝學弟、還有即將跳進 DSLR 無底洞 和 muscle 超大的冠智學弟(大隻佬)，可愛的小布丁學妹，超 幫忙搞笑和辛苦準備 meeting 的點心真是辛苦你們了 最後要感謝我的家人一路上全力的支持和鼓勵，得以讓我無後顧之憂的往前 衝，也要感謝 v 小姐，伴我度過碩士班一段不算短的時間，最後感謝國

Content

Abstract (in Chinese)………. i

Abstract (in English)……….. ii

Acknowledgement………. iii

Content……….. vi

List of figures……….... ix

List of tables……….... xii

Chapter 1 Introduction………...1

1.1 Significance of this thesis………. 1

1.2 Background………... 1

1.2.1 What are photonic crystal fibers……….1

1.2.2 Applications of photonic crystal fibers……….. 5

1.2.3 Supercontinuum generation using PCFs……… 5

1.2.4 Fiber gratings………. 7

1.2.4.1 Fiber Bragg grating………. 7

1.2.4.2 Long period grating………... 11

1.3 Why long period grating made of photonic crystal………. 13

1.4 Why Q-switched mode-locked solid state laser……….. 14

1.5 Organization of the thesis………15

References………. 16

Chapter 2 Theory………... 22

2.1 Dispersion relation of PCF -- beam propagation method………... 22

2.2 Coupled mode theory of long period grating……….. 25

2.3 Model for passively Q-switched laser with simultaneous mode-locking………... 29

References………. 35

Chapter 3 Experimental………... 36

3.1 Experimental setup of LPG……… 36

3.1.1 Corrugated device……… 36

3.1.2 Photonic crystal fiber………... 37

3.1.3 Un-polarized white light source………... 38

3.1.4 Measurement of transmission spectra of LPG………. 38

3.2 Experimental setup of Supercontinuum……….. 40

3.2.1 Q-switched mode-locked laser………. 40

3.2.2 Supercontinuum generation………. 43

Chapter 4 Stress-Induced Versatile Tunable Long-Period Grating

in Photonic Crystal Fibers……… 44

4.1 Transmission spectra of LPGs made by V-grooved……… 44

viii

4.1.1 Constant LPG………... 44

4.1.2 Chirped LPGs………... 46

4.1.3 Polarization dependent LPG……… 48

4.1.4 Generation and elimination of spectrum fringe………50

4.2 Transmission spectra of LPGs made by metallic post……… 52

4.2.1 Chirped LPGs………... 52

4.3 Simulation of constant LPGs……….. 54

4.4 Application……….. 59

4.4.1 Gain flattening of Erbium Doped Fiber Amplifier………... 59

4.5 Summary………. 60

References……… 62

Chapter 5 Supercontinuum generation using Q-switch mode-locking

Nd:GdVO4

and Nd:LuVO4 laser with Cr4+:YAG saturable absorber……..

63

5.1 Q-switch mode-locking Nd3+:GdVO4 with Cr4+:YAG saturable absorber………..63

5.2 Simulation of Q-switching mode-locking………... 69

5.3 Supercontinuum generation by QML laser using PCFs……….. 71

5.4 Summary………. 72

List of Figures

Fig. 1.1 Scanning electron microscope image of the end of photonic-crystal-fibers for

index-guiding PCF and photonic bandgap fiber……… 4

Fig. 1.2 Phase mask technique for writing fiber Bragg grating……… 10

Fig. 1.3 The reflection and transmission spectra of a uniform Bragg grating……….. 10

Fig. 1.4 A schematic diagram of a chirped fiber Bragg grating……… 11

Fig. 3-1 Novel corrugated devices: wrapping a long copper wire on a cylindrical metallic post, and V-grooved plate……….. 36

Fig. 3-2 Scanning electron microscope image of photonic crystal fiber region and core……. 37

Fig. 3-3 Structure of un-polarized white-light……….. 38

Fig. 3-4 Schematic of the experimental setup and generation of LPGs in PCFs by mechanical stress onto corrugated device……… 39

Fig. 3-5 Schematic diagram of diode-pumped Q-switched mode-locked Nd:GdVO4 laser. 41

Fig. 3-6 Schematic diagram of noncollinear autocorrelator……….. 42

Fig. 3-7 The experimental setup of supercontinuum generation………..43

Fig. 4-1 Schematic of the mechanism for tuning the grating periodicity………. 45

Fig. 4-2 Measured transmission spectra of constant-period gratings obtained by adjusting the anglebetween the straight PCF and the V-grooves………... 45

Fig. 4-3 Resonant wavelengths measured at different grating periods, as well as the calculated effective indices differences with respect to resonance wavelengths. ………. 45

Fig. 4-4. Transmission spectra for chirped single-LPG by the V-grooved metallic plate……. 48

Fig. 4-5 Transmission spectra for LPFG in PCF taken with polarized light and corresponding to maximum and minimum amplitudes of transmitted power……….. 49 Fig. 4-6. Transmission spectra for Spectral fringes can be obtained from chirped single-LPGs,

and the fringes can be eliminated with proper configuration……… 51

Fig. 4-7. Transmission spectra for Spectral fringes with different pressures……… 51

Fig. 4-8. Transmission spectra for spectral fringes can be obtained from chirped dual-LPGs, and the fringes can be eliminated with proper configuration……… 52

Fig. 4-9 Schematic of the chirped dual-LPG by period metallic post………... 53

Fig. 4-10. Transmission spectra for chirped single-LPG with different curvatures by wrapping a long copper wire on a cylindrical metallic post………. 54

Fig. 4-11. The cross section of PCF appear in the CAD windows………55

Fig. 4-12. Material dispersion of the high pure fused-silica fiber………. 56

Fig. 4-13. The effective index of core mode and high order cladding mode……… 58

Fig. 4-14. Transmission spectrum for simulation and experiment, and resonant wavelength is 1286 nm………. 58

Fig. 4-15. The gain flattened EDFA spectrum between 1528 nm and 1562 nm by using the chirped LPGs………. 60

Fig, 5-1. The average power versus pump power at CW state, and QML states with T0 = 80%, 55%, and 40%... 64

Fig, 5-2. Pulse train of QML with T0 = 40%, and 80%... 64

Fig, 5-3. Temporal expansion of Q-switching envelope of 80% Cr4+:YAG with fitting…….. 66

Fig, 5-4. Temporal expansion of Q-switching envelope of 55% Cr4+:YAG with fitting…….. 66

Fig, 5-5. Temporal expansion of Q-switching envelope of 40% Cr4+:YAG with fitting…….. 67

Fig, 5-6. Repetition rates versus the pump power at the QML states with T0=80%, 55%, and 40%... 68

Fig, 5-7. The estimated pulse energy versus the pump power at the QML states with T0=80%, 55%, and 40%... 69 Fig. 5-8. Calculated result for the temporal shape of a single Q-switch pulse for saturable

xi

absorbers of T=40% with R=60%... 70 Fig. 5-9. Calculated result for the temporal shape of a single Q-switch pulse for saturable absorbers of T=55% with R=60%... 70 Fig. 5-10. Calculated result for the temporal shape of a single Q-switch pulse for saturable absorbers of T=80% with R=60%... 71 Fig. 5-11. The evolutions of spectral broadening for the experimental observation as pumping power increases………. 72

 

List of Tables

Table 4-1. The coefficient of Sellmeier equation used in highly pure fused-silica fiber. 56

xii