臺灣博碩士論文加值系統

在本篇論文中，我們主要透過數值模擬的方式，來分析一雙色被動鎖模光纖雷射系統下之束縛態光孤子的交互作用。首先，我們藉由利用Complex Ginzburg-Landau equation (CGLE)的模型，透過數值模擬，來嘗試著找出CGLE的穩定解。我們可以透過數值解來找出單一脈衝的穩定解、雙脈衝的穩定解、甚至是多脈衝的穩定解。第二，利用我們先前所找出的穩定解，並於我們的數值模型裡面加入不同波長之光纖雷射脈衝；透過自相位調變(Cross-Phase Modulation)的影響，讓兩個不同波長之脈衝產生交互作用；並找出，在何種條件下，存在束縛態的穩定解。而在以下模擬過程中，為了分析方便，我們假令此多加入的副脈衝為一背景常數位能；換言之就是，它並不會受到主脈衝的交互影響而產生任何變化。

我們設置了不同型態背景位能的模擬模型：像是利用調變不同的位能振幅、位能寬度、穩態型的位能(主副脈衝等速度)、移動型的位能(主副脈衝距有速度差)、以及周期性型的位能。並透過相位圖，我們可以嘗試著解釋並分析在不同條件下之一雙色被動鎖模光纖雷射系統之主脈衝的行為模式。

我們在模擬中，發現初始的相位差在各個不同位能條件模型系統中扮演者非常重要的角色。並於論文最後對雙色被動鎖模光纖雷射系統之性質來討論。

關鍵字：光孤子、被動鎖模光纖雷射、束縛態

In this thesis, we analyze the behavior of the Interaction of bound-state solitons in a two-color passive mode-locked fiber laser system by using numerical method. At first, we try to find the bound-state solutions of Complex Ginzburg-Landau equation (CGLE) model, such as single pulse, double-humps, and multi-humps. Second, based on those solutions, we add the other color of fiber laser into our simulation model which is linked by cross-phase modulation. For the following works, we assume the other color of fiber laser as a constant background potential which means it would not be changed in our simulation model.

We set several types of background potential, such as using different amplitude or width of potential, stationary potential, moving potential, and periodical potential. Based on the result of phase-diagrams, we try to explain the behaviors of two-color passive mode-locked fiber laser system in different cases.

We find out that the initial phase-difference plays an important role in this simulation model. And we conclude some properties of two-color system based on our results.

Key Words: soliton, passive mode-locked fiber laser, bound-state

Chapter 0 Introduction

Chapter 1 Two colors fiber laser system
1.1 Complex Ginzburg-Landau equation (CGLE)
1.2 Two colors fiber laser system based on CGLE

Chapter 2 Numerical Method
2.1 Finite difference
2.2 Crank–Nicolson method
2.3 Newton’s iteration
2.4 Perfectly Matched Layer

Chapter 3 Simulation
3.1 Bound-state solitons in CGLE
3.2 Multi-pulses solution
3.3 Interaction of bound-state with another color pulse in double-pulses system
3.3.1 Stationary background pulse V
3.3.2 Moving background pulse V
3.4 Interaction of bound-state with another color pulse in triple-pulses system

Chapter 4 Summary

Reference

[1] Govind P. Agrawal , “Nonlinear Fiber Optics” , 4th , Elsevier Inc. (2007)

[2] N. N. Akhmediev ,A. Ankiewicz ,and J. M. Soto-Crespo “Multisoliton Solutions of the Complex Ginzburg-Landau Equation” , Phys. Rev. Lett. , 79 , 4047‐4051 (1997)

[3] C. Farrell, U. Leonhardt , “The Perfectly Matched Layer for nonlinear and matter waves”, arXiv : cond-mat (2004)

[4] N. Akhmediev , and A. Ankiewicz , “Dissipative Solitons” , Springer-Verlag Berlin Heidelberg (2005)

[5] William H. Press, Brian P. Flannery, Saul A. Teukolsky, William T. Vetterling , “Numerical Recipes in Fortran: The Art of Scientific Computing” , 2th , Cambridge University Press. (1992)

[6] Wei-Wei Hsiang , Chia-Hao Chang , Chien-Po Cheng , and Yinchieh Lai , “Passive synchronization between a self-similar pulse and a bound-soliton bunch in a two-color
mode-locked fiber laser” , Opt. Lett. , 34 , 1967‐1969 (2009)

[7] N. N. Akhmediev , V. V. Afanasjev , and J. M. Soto-Crespo, “Sigularities and special soliton solutions of cubic-quintic complex Ginzburg-Landau equation” , Phys. Rev. E Lett. , 53 , 1190‐1201 (1996)

[8] Wonkeun Chang , Nail Akhmediev , and Stenfan Wabnitz , “Effect of an external periodic potential on pairs of dissipative solitons” , Phys. Rev. A Lett. , 80 , 013815-1-5 (2009)

[9] J. M. Soto-Crespo , and N. N. Akhmediev , “Multisoliton regime of pulse generation by lasers passively mode locked with a slow saturable absorber” , O.S.A. , 16 , 674-677 (1999)