1Fundamental Mathematics of Nonlinear Emission Photonic Glass Fiber and Waveguide Devices1
1.1Introduction1
1.2Newton Iteration Algorithm for Nonlinear Rate Equation Solution1
1.2.1SingleVariable1
1.2.2MultiVariable3
1.3RungeKutta Algorithm for PowerPropagation Equation Solution4
1.3.1SingleFunction4
1.3.2MultiFunctions6
1.4TwoPoint Boundary Problem for PowerPropagation Equations in a Laser Cavity7
1.4.1Principle7
1.4.2Shooting Method and Relaxation Method7
References92Fundamental Spectral Theory of Photonic Glasses10
2.1Introduction10
2.2JuddOfelt Theory10
2.3Transition Probability and Quantum Efficiency12
2.4Fluorescence Branch Ratio13
2.5Homogeneous and Inhomogeneous Broadening of Spectra14
References153Spectral Properties of YtterbiumDoped Glasses16
3.1Introduction16
3.2Formation Region of Yb2O3Containing Glasses16
3.3Laser Performance Parameters of YtterbiumDoped Glasses17
3.3.1Minimum Fraction of Excited State Ions17
3.3.2Saturation Pump Intensity18
3.3.3Minimum Pump Intensity18
3.3.4StorageEnergy and Gain Parameters18
3.4Spectral Properties of Yb3＋Doped Borate Glasses19
3.4.1Compositional Dependence of Spectral Properties19
3.4.2Dependence of Spectral Properties on Active Ion Concentration22
3.5Spectral Properties of Yb3＋Doped Phosphate Glasses23
3.5.1Compositional Dependence of Spectral Properties23
3.5.2Dependence of Spectral Properties on Active Ion Concentration26
3.6Spectral Properties of Yb3＋Doped Silicate Glasses28
3.6.1Compositional Dependence of Spectral Properties28
3.6.2Dependence of Spectral Properties on Active Ion Concentration32
3.7Spectral Properties of Yb3＋Doped Germanate Glasses34
3.8Spectral Properties of Yb3＋Doped Telluride Glasses36
3.8.1Compositional Dependence of Spectral Properties36
3.8.2Dependence of Spectral Properties on Active Ion Concentration39
3.9Dependence of Spectral Property and Laser Performance Parameters on Glass System43
3.9.1Dependence of Spectral Property on Glass Systems43
3.9.2Dependence of Laser Performance Parameters on Glass Systems46
3.10Dependence of EnergyLevel Structure of Yb3＋ on Glass Systems51
3.11Cooperative Upconversion of Yb3＋ Ion Pairs53
3.11.1Cooperative Upconversion Luminescence53
3.11.2ConcentrationQuenching Mechanics57
3.11.3Concentration Dependence of Luminescence Intensity59
3.12Fluorescence Trap Effect of Yb3＋ Ions in Glasses60
References634Compact Fiber Amplifiers65
4.1Introduction65
4.2Level Structure and Numerical Model66
4.3Dependence of Gain and Noise Figure on Concentrations67
4.4Doping Concentrations with ShortLength High Gain71
References725Photonic Glass Fiber Lasers74
5.1Introduction74
5.2Fundamental Physics of Fiber Laser74
5.2.1Lasing Conditions of Laser74
5.2.2Threshold Gain75
5.2.3Phase Condition and Laser Modes76
5.2.4Population Inversion Calculation76
5.3Numerical Models of RareEarthDoped Fiber Lasers80
5.3.1Configuration and PowerPropagation Equations of Fiber Laser80
5.3.2Output Power of a TwoLevel Fiber Laser81
5.3.3Output Power of a ThreeLevel Fiber Laser83
5.3.4Output Power of a FourLevel Fiber Laser84
5.3.5Output Power of Yb3＋Doped Fiber Laser85
References906Broadband Fiber Amplifiers and Sources91
6.1Introduction91
6.2Pr3＋Tm3＋Er3＋CoDoped Fiber System92
6.2.1General Rate and PowerPropagation Equations with Two Wavelength Pumps92
6.2.2Gain Characteristics with 980nm Pump96
6.2.3Gain Characteristics with 793nm Pump99
6.2.4Gain Characteristics with Double Pumps105
6.3Gain Characteristics of Pr3＋Er3＋CoDoped Fiber System131
6.3.1Rate and PowerPropagation Equations131
6.3.2Dependence of Gain on Fiber Parameters134
6.4WDM Transmission System Cascaded with Tm3＋Er3＋CoDoped Fiber Amplifiers139
6.4.1WDM System with Single Pump140
6.4.2WDM System with Dual Pumps141
References1437Photonic Glass Waveguide for Spectral Conversion145
7.1Introduction145
7.2Theoretical Model and Spectral Characterization 146
7.2.1Theoretical Model 146
7.2.2Spectral Characterization 148
ContentsixxContents7.3DoublyDoped System 148
7.3.1Energy Transfer Model 149
7.3.2Quantum Efficiency of Photonic Glass Waveguide 152
7.4TriplyDoped System 159
7.4.1Energy Transfer Model 159
7.4.2Quantum Efficiency of Photonic Glass Waveguide 163
7.5Performance Evaluation of scSiSolar Cell with Photonic Glass Waveguides 171
References1748Photonic Glass Waveguide for WhiteLight Generation177
8.1Introduction 177
8.2WhiteLight Glasses 178
8.2.1Tm3 Tb3 Eu3 CoDoped System 178
8.2.2Yb3 Er3 Tm3 CoDoped System 185
8.3EmissionTunable Glasses194
8.3.1Tb3 Sm3 Dy3 CoDoped System 194
8.3.2Tm3 Yb3 Ho3 CoDoped System 205
References214Appendix 1Matlab Code for Solving Nonlinear Rate and Power Propagation Equation
Groups in Co Doped Fiber Amplifiers or Fiber Sources219
A1.1Nonlinear Rate Equation Group and Coupled PowerPropagation
Equation Group of a ThreeActive IonsCoDoped System219
A1.2Code for Solving Linear Rate Equation Group220
A1.3Code for Solving Nonlinear Rate Equation Group220
A1.4Code for Variation of Gain with Fiber Length222
A1.5Code for Variation of Gain with Active Ion Concentration223Appendix 2Matlab Code for Solving PowerPropagation Equations of a Laser
Cavity with FourLevel System225Index228
內容試閱：
Luminescence of transition metal ions and rare earth ions has important applications in optoelectronic devices and systems including fiber amplifiers, fiber lasers, and fiber sources. With advances in integrated photonic devices and broadband and compact fiber optic devices, it is necessary to make active fiber devices that have short interaction length and have broadband gain and emission spectra by using high concentration active ion doping and multi active ion doping techniques. For low concentration doped fiber devices, the dependence of emission intensity on excitation power generally is a linear relationship. However, in highly doped and multiply doped fiber devices, the relation is not linear and but nonlinear, due to the interaction between rare earth ions such as upconversion, cross relaxation, energy transfer, and so on. In this book, thus, the active fiber and waveguide devices including high concentration doping and multi rare earth doping are defined as nonlinear emission photonic fiber and waveguide devices.
This book consists of eight parts as follows：
Chapter 1 introduces the fundamental mathematics of nonlinear emission photonic glass fiber and waveguide devices. In the design and analysis of the photonic glass fiber and waveguide devices, one of most important tasks is to solve a multi variable rate equation group and power propagation equation group. The methods introduced in this chapter are Newton iteration, Runge Kutta algorithms and their combination as well as solution of two point boundary problem, which are effective numerical techniques for highly doped or codoped fiber amplifiers, fiber sources, and fiber laser systems.
Chapter 2 introduces the fundamental of spectral theory of photonic glasses. In this chapter, spectral properties of rare earth doped glasses, including absorption and emission cross sections, spontaneous emission transition probability, fluorescence branch ratio and quantum efficiency, and homogeneous and inhomogeneous broadening of fluorescence spectra and their calculating methods, are summarized.
Chapter 3 systematically reports the spectral properties and laser performance parameters of ytterbium doped glass systems. Ytterbium ions can be used as sensitizers to other active ions due to simple level structure and strong absorption coefficient, ytterbium ion doped fiber can be used as a high power fiber laser system for industrial processing, and ytterbium ion doped glass waveguides can be used as a spectral converter because its emission wavelength matches well with the spectral responsivity of single crystal silicon solar cell.
Chapter 4 presents the modeling and numerical results of compact ytterbium erbium co doped fiber amplifiers, which are supposed to obtain higher internal gain and higher gain per unit length in fiber amplifiers using numerical solutions of rate and evolution equations of signal, pump power, and amplified spontaneous emission.
Chapter 5 introduces the fundamentals of lasers and a numerical model of ytterbium doped glass fiber systems, which can be widely used in industrial processing. Nonlinear interaction between high concentration active ions or the co upconversion effect will degrade these system performances. Our numerical model considers the nonlinear transition in the high concentration doped system and may be used to calculate the threshold power and output power.
Chapter 6 proposes several schemes for all wave fiber transmission systems, including doubly doped fiber amplifiers such as erbium thulium co doped and erbium praseodymium co doped fiber amplifiers and triply doped fiber amplifiers such as erbium thulium praseodymium co doped fiber amplifiers, and presents their numerical models and calculates the dependence of gains at different wavelength on fiber and pump parameters.
Chapter 7 introduces the spectral conversion mechanisms of multi rare earth co doped glass waveguides including the setting up of rate equations and power propagation equations model of several codoped systems. These kinds of photonic glass waveguides are simple applications of spectral downconversion and quantum cutting for enhancing performance of cSi solar cells. The power conversion efficiency and quantum conversion efficiency of the codoped systems are analyzed and the enhanced performances of a scSi solar cell model are evaluated.
Chapter 8 establishes photonic glass waveguide systems for white light generation and presents their numerical models. White light generation has important applications in lighting and display areas. In this chapter, the energy level, electron transition process, and numerical models are proposed and the fluorescence intensity of the system is calculated. Optimal active concentrations are proposed to enable system to emit red, blue, and green light, which are mixed to generate white light.
Some topics in this book appear as color reprints of authors published articles taken, with permission, from various journals, including Journal of Solid State Chemistry, Journal of Luminescence, Material Letters, IEEE Journal of Quantum Electronics, Journal of Optics Society of America, Applied Physics B, IEEE Photonics Journal, and Applied Optics, and so on.
Finally, the writing of this book would not have been possible without the help and encouragement of our many colleagues. It is our great pleasure to thank these people. Especial thanks are given to Mr. Xu Wenbin for his contribution to the part of Chapter 8. Special thanks are given to Ms. Jin Li for her contribution to the part of numerical technique, and to Ms. Xu Wenhui and Mr. Lin Yaming for their contribution to the parts of Chapter 6. We also thank our editors for their encouragement of this project. We thank you, the reader, for your time and effort spent reading this book. Though we tried to cleanse this text of conceptual and typographical errors, we apologize in advance for those that have slipped through. No book is perfect and we can only improve the text with your comments and suggestions.
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