Vectorial Numerical Analyses and Applications of Soliton Fission Process in Highly Nonlinear Fibers

本篇論文主要探討超短脈衝雷射光在非線性光纖中傳播時會發生的現象。在非線性光纖光學中，此現象已被研究多年，近來隨著超短脈衝雷射的成熟以及光子晶體光纖的研發，利用此現象所產生的光源更邁入實用化的階段，不論在光通訊、頻率量測、或生醫影像上均可見到其應用。雖然在時域上觀察此現象只會看到高階光孤子的分裂，但是在頻域上它其實可以是超連續光譜或僅為光孤子的自頻率位移。 一直以來，描述此現象所用的數值模型主要是純量型非線性薛丁格方程式，它直接由馬克士威爾方程式推導而來且已被證實具有相當的正確性。然而基於某些原因，我們猜測也許利用向量型非線性薛丁格方程式來描述此現象可以得到更精確的結果。本篇論文介紹各種不同型式的非線性薛丁格方程式，最後推導出一組最具一般性的向量型方程式，利用此向量型方程式以及SSFM數值方法，我們開發出一隻可用於模擬此現象的Matlab程式。 利用此程式，我們模擬了兩個不同的光孤子分裂現象，它們在頻域上分別是超連續光譜以及光孤子自頻率位移。利用向量型方程式可同時算出兩垂直方向上的分量，進而進行一連串分析：例如各個光孤子的極化狀態及它們的變化趨勢。我們也發現這兩種光孤子分裂現象對入射光脈衝的極化敏感度大不相同，對此我們也提出合理的解釋。 由於該程式可以預測實驗的結果，因此我們利用此程式針對光子晶體光纖產生的光源作應用面的分析。此類光源經常被用在生醫影像方面，由於這方面應用經常要求光源具有可變波長的能力，因此我們針對調整波長提出兩種可行的辦法並比較兩者優缺點。最後，我們也探討如何去產生某一個特定波長的光源，以及改進並加大該光源功率的方法。This thesis investigates the phenomena of short-pulse propagation in highly nonlinear fibers. In nonlinear fiber optics, such kinds of phenomena have been studied extensively. With the development of short-pulsed laser and highly nonlinear photonic crystal fibers (PCF), more and more applications utilizing these kinds of light sources such as optical communication, frequency metrology, and biomedical images have been proposed. In time domain, the pulse evolution results may be dispersive waves or Raman solitons depending on their dispersion regime (normal dispersion or anomalous dispersion). In frequency domain, they may be supercontinuum (SC) or soliton self-frequency shift (SSFS). Since continuously, numerical model such as nonlinear Schrödinger equation (NLSE) of scalar form has been developed to describe these phenomena. However, due to some reasons, we suspected that it would be more appropriate to use the NLSE of vector form in describing such phenomena. We introduce some NLSE in different forms and finally derive the generalized NLSE of vector form. Base on the vector NLSEs and symmetrized SSFM, we developed a simulation program to describe the short pulse evolution inside highly nonlinear fibers. Using this program, we simulate two different cases of soliton fission processes, which are SC and SSFS in frequency domain, respectively. We then analyze the SOP of each soliton and their trend of changes. We also find that the polarization sensitivities are quite different for these two cases. Some possible reasons for such difference are proposed. Since the simulation results can fit the experimental data, we try to use the program to analyze the PCF-based light sources. Such light sources are usually used on the applications of biomedical images. Thus the wavelength tuning capability is required. We propose two methods to tune the wavelengths and compare their advantages and disadvantages. Finally, we try to generate a light source with a pre-specified wavelength. We also show possible ways to improve the performance of such light sources.Chapter 1 Introduction 1 1.1 Motivation 1 1.2 Thesis Overview 2 References of Chapter 1 3 Chapter 2 Theory and Numerical Models 5 2.1 Fiber Nonlinearity 5 2.2 Scalar Nonlinear Schrödinger Equation 6 2.2.1 Simplified Scalar NLSE 7 2.2.2 Generalized Scalar NLSE 8 2.3 Vector Nonlinear Schrödinger Equations 11 2.3.1 Simplified Vector NLSEs 12 2.3.2 Generalized Vector NLSEs 14 2.4 Occasions to Use the Vector NLSEs 17 2.5 Split-Step Fourier Method 19 References of Chapter 2 24 Chapter 3 Experiment and Simulation 25 3.1 Vector Soliton Fission in a Tapered Fiber 25 3.1.1 Tapered Fiber 25 3.1.2 Simulation Results 26 3.1.3 Experimental Results 34 3.2 Soliton Fission in an Isotropic PCF 36 3.2.1 Photonic Crystal Fiber NL-3.5-975 36 3.2.2 Experiment Results 37 3.2.3 Simulation Results 40 3.3 Discussion on Polarization Sensitivity 51 References of Chapter 3 54 Chapter 4 Analysis of PCF-based Light Source 55 4.1 Applications 55 4.2 Wavelength Tuning 58 4.2.1 Wavelength Tuning by Adjusting Power 58 4.2.2 Wavelength Tuning by Adjusting Fiber Length 61 4.2.3 Discussion and Comparison 65 4.3 Generation of Some Specific Wavelength 66 References of Chapter 4 73 Chapter 5 Conclusion 75 Appendix A Datasheet of Nonlinear PCF NL-3.5-975 77 Appendix B Simulation Parameters 79 Appendix C Acronyms 8