1Fundamental Mathematics of Nonlinear Emission Photonic Glass Fiber and Waveguide Devices1

1.1Introduction1

1.2Newton Iteration Algorithm for Nonlinear Rate Equation Solution1

1.2.1Single��Variable1

1.2.2Multi��Variable3

1.3RungeKutta Algorithm for Power��Propagation Equation Solution4

1.3.1Single��Function4

1.3.2Multi��Functions6

1.4Two��Point Boundary Problem for Power��Propagation 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 Ytterbium��Doped��Glasses16

3.1Introduction16

3.2Formation Region of Yb2O3Containing Glasses16

3.3Laser Performance Parameters of Ytterbium��Doped��Glasses17

3.3.1Minimum Fraction of Excited State Ions17

3.3.2Saturation Pump Intensity18

3.3.3Minimum Pump Intensity18

3.3.4Storage��Energy 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 Energy��Level Structure of Yb3����on Glass Systems51

3.11Cooperative Upconversion of Yb3����Ion Pairs53

3.11.1Cooperative Upconversion Luminescence53

3.11.2Concentration��Quenching 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 Short��Length��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 Rare��Earth��Doped Fiber Lasers80

5.3.1Configuration and Power��Propagation Equations of Fiber Laser80

5.3.2Output Power of a Two��Level Fiber Laser81

5.3.3Output Power of a Three��Level Fiber Laser83

5.3.4Output Power of a Four��Level Fiber Laser84

5.3.5Output Power of Yb3��Doped Fiber Laser85

References906Broadband Fiber Amplifiers and Sources91

6.1Introduction91

6.2Pr3��Tm3��Er3��Co��Doped Fiber System92

6.2.1General Rate and Power��Propagation 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��Co��Doped Fiber System131

6.3.1Rate and Power��Propagation Equations131

6.3.2Dependence of Gain on Fiber Parameters134

6.4WDM Transmission System Cascaded with Tm3��Er3��Co��Doped 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

ContentsixxContents7.3Doubly��Doped System 148

7.3.1Energy Transfer Model 149

7.3.2Quantum Efficiency of Photonic Glass Waveguide 152

7.4Triply��Doped System 159

7.4.1Energy Transfer Model 159

7.4.2Quantum Efficiency of Photonic Glass Waveguide 163

7.5Performance Evaluation of sc��Si��Solar Cell with Photonic Glass Waveguides 171

References1748Photonic Glass Waveguide for White��Light Generation177

8.1Introduction 177

8.2White��Light Glasses 178

8.2.1Tm3+Tb3+Eu3+Co��Doped System 178

8.2.2Yb3+Er3+Tm3+Co��Doped System 185

8.3Emission��Tunable Glasses194

8.3.1Tb3+Sm3+Dy3+Co��Doped System 194

8.3.2Tm3+Yb3+Ho3+Co��Doped 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 Power��Propagation

Equation Group of a Three��Active Ions��Co��Doped 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 Power��Propagation Equations of a Laser

Cavity with Four��Level System225Index228