تقویت‌کننده‌های فیبر با دوز اریبیم: اصول و فناوری (اپتیک و فوتونیک)

**Erbium Fiber Amplifiers is a comprehensive introduction to the increasingly important topic of optical amplification. Written by three Bell Labs pioneers, the book stresses the importance of the interrelation of materials properties, optical properties, and systems aspects of optical fiber amplifiers. The floppy disk included with the book contains a PC based educational version of the sophisticated commercial amplifier simulation package OASIX (sold by the Specialty Fiber Group of Lucent Technologies). This powerful numerical simulation software allows one to simulate the performance of a real erbium fiber amplifier, and obtain its properties such as signal gain and noise generated. Several parameter sets are included, each of which represents a commercially available type of erbium doped fiber usedin different kinds of amplifiers (e.g. preamplifiers and power amplifiers). The user can vary, via Windows based input screens, various amplifier characteristics such as fiber length, pump power, signal power, and additional signals. The output is savedin a file which can be read by any spreadsheet or plotting package for graphical representation of the results. The software allows the reader to explore on his or her own the concepts of amplifier performance discussed in the book, and gain a more intuitive and interactive educational experience leading to a richer understanding of erbium-doped fiber amplifiers and their applications. Key Features \* Includes a software disk with a PC-based amplifier simulation tool derived from a sophisticated commercial package (OASIX), which allows the reader to gain an interactive educational experience using parameters for commercially available erbium-doped fibers \* Explains the theory of noise in optically amplified systems in an intuitive way \* The book contains a discussion of components used in amplifier fabrication and of the attendant technologies used in real systems \* The book provides basic tools for amplifier design as well as systems engineering, including the latest developments in WDM and soliton systems \* The book discusses the fundamentals of rare earth ions for the reader desiring more depth in the topic \* The book is for either the novice of experienced reader \* The chapter have links between them to allow the reader to understand the relationship between the amplifier characteristics, noise, and systems applications \* The book contains extensive references** CONTENTS 6 Foreword 11 Preface 14 Acknowledgements 16 1 INTRODUCTION 18 1.1 Long Haul Fiber Networks 18 1.2 Historical Development of Erbium-Doped Fiber Amplifiers 22 1.3 From Glass to Systems – Outline 0 2 OPTICAL FIBER FABRICATION 30 2.1 Introduction 30 2.2 Conventional Communication Fiber 31 2.3 Rare Earth Doped Fibers 33 2.3.1 Rare Earth Vapor Phase Delivery Methods 33 2.3.2 Rare Earth Solution-Doping Methods 38 2.3.3 Rod and Tube Methods 40 2.4 Pump-Signal Interaction Methods 42 2.4.1 Evanescent Field 42 2.4.2 Double Clad Fiber Design 43 2.5 Compositions 44 2.6 Physical Properties 46 2.6.1 Fiber Refractive Index and Composition Profile 46 2.6.2 Strength and Reliability 47 2.6.3 Alternate Glass Host Fabrication 47 3 COMPONENTS AND INTEGRATION 60 3.1 Introduction 60 3.2 Fiber Connectors 60 3.3 Fusion Splicing 65 3.4 Pump and Signal Combiners 67 3.5 Isolators 69 3.6 Circulators 70 3.7 Filters 72 3.8 Fiber Gratings 72 3.8.1 Introduction 72 3.8.2 Applications of Bragg Gratings 74 3.8.3 Long Period Gratings 76 3.9 Signal Multiplexers and Demultiplexers 78 3.10 Signal Add/Drop Components 79 3.11 Dispersion Compensation Components 80 3.12 Integrated Components 83 3.13 Pump Lasers 83 4 RARE EARTH IONS – INTRODUCTORY SURVEY 0 4.1 Introduction 104 4.2 Atomic Physics of the Rare Earths 104 4.2.1 Introduction – The 4f Electron Shell 0 4.2.2 The "Puzzle" of 4f Electron Optical Spectra 0 4.2.3 Semiempirical Atomic and Crystal Field Hamiltonians 109 4.2.4 Energy Level Fitting 111 4.3 Optical Spectra of Rare Earth Ions 112 4.3.1 The Character of 4f[sup(N)] – 4f[sup(N)] Optical Transitions 0 4.3.2 Intensities of One-Photon Transitions – Judd-Ofelt Theory 0 4.4 Fundamental Properties 116 4.4.1 Transition Cross Sections 116 4.4.2 Lifetimes 122 4.4.3 Linewidths and Broadening 125 4.5 Spectroscopy of the Er[sup(3+)] Ion 127 4.5.1 Lifetimes 128 4.5.2 Er[sup(3+)] Spectra, Cross Sections, and Linewidths 131 4.6 Er[sup(3+)] -Er[sup(3+)] Interaction Effects 137 5 ERBIUM-DOPED FIBER AMPLIFIERS – AMPLIFIER BASICS 0 5.1 Introduction 148 5.2 Amplification in Three-Level Systems–Basics 0 5.2.1 Three-Level Rate Equations 148 5.2.2 The Overlap Factor 157 5.3 Reduction of the Three-Level System to the Two-Level System 161 5.3.1 Validity of the Two-Level Approach 161 5.3.2 Generalized Rate Equations 163 5.4 Amplified Spontaneous Emission 164 5.5 Analytical Solutions to the Two-Level System 166 6 ERBIUM-DOPED FIBER AMPLIFIERS – MODELING AND COMPLEX EFFECTS 0 6.1 Introduction 170 6.2 Absorption and Emission Cross Sections 170 6.3 Gain and ASE Modeling 173 6.3.1 Model Equations – Homogeneous Broadening 0 6.3.2 Average Inversion Relationship 175 6.3.3 Inhomogeneous Broadening 176 6.4 Amplifier Simulations 178 6.4.1 Signal Gain, ASE Generation, and Population Inversion 178 6.4.2 Gain as a Function of Fiber Length 186 6.4.3 Spectral Profile of the ASE 186 6.4.4 Small Signal Spectral Gain and Noise Modeling 188 6.4.5 Saturation Modeling – Signal Gain and Noise Figure 0 6.4.6 Power Amplifier Modeling 192 6.4.7 Effective Parameter Modeling 195 6.5 Transverse Mode Models – Erbium Confinement Effect 0 6.6 Excited–State Absorption Effects 0 6.6.1 Model Equations 203 6.6.2 Modeling Results in the Presence of ESA 205 6.6.3 800 nm Band Pumping 205 6.7 Er[sup(3+)] -Er[sup(3+)] Interaction Effects 208 6.7.1 Upconversion Effects on Amplifier Performance 210 6.7.2 Pair Induced Quenching 212 7 OPTICAL AMPLIFIERS IN FIBER OPTIC COMMUNICATION SYSTEMS – THEORY 0 7.1 Introduction 218 7.2 Optical Noise: Device Aspects 219 7.2.1 Classical Derivation of Optical Amplifier Noise 219 7.2.2 Noise at the Output of an Optical Amplifier 222 7.2.3 Comparison of Optical Amplifier Devices 227 7.3 Optical Noise: System Aspects 229 7.3.1 Receivers 230 7.3.2 Bit Error Rate Calculations - Direct Detection 231 7.3.3 Optical Preamplifiers – Noise Figure and Sensitivity 0 7.3.4 Optical Inline Amplifiers - Amplifier Chains 243 7.3.5 Noise in Optical Power Amplifiers 252 7.3.6 Nonlinearity Issues 253 7.3.7 Analog Applications 257 8 AMPLIFIER CHARACTERIZATION AND DESIGN ISSUES 268 8.1 Introduction 268 8.2 Basic Amplifier Measurement Techniques 268 8.2.1 Gain Measurements 268 8.2.2 Power Conversion Efficiency 274 8.2.3 Noise Figure Measurements 275 8.3 Amplifier Design Issues 280 8.3.1 Copropagating and Counterpropagating Pumping Issues 282 8.3.2 Choice of Fiber Lengths and Geometries for Various Applications 285 8.3.3 Multistage Amplifiers 290 8.3.4 Bidirectional Amplifiers 294 8.3.5 Power Amplifiers 297 8.3.6 WDM Amplifier Design Issues 301 8.3.7 Distributed Amplifiers 312 8.3.8 Waveguide Amplifiers 319 9 SYSTEM IMPLEMENTATIONS OF AMPLIFIERS 338 9.1 Introduction 338 9.2 System Demonstrations and Issues 340 9.2.1 Preamplifiers 340 9.2.2 Inline Amplifiers - Single Channel Transmission 344 9.2.3 Mine Amplifiers - WDM Transmission 352 9.2.4 Repeaterless Systems 362 9.2.5 Remote Pumping 363 9.2.6 Analog Applications 368 9.2.7 Gain Peaking and Self-Filtering 371 9.2.8 Polarization Issues 376 9.2.9 Transient Effects 380 9.3 Soliton Systems 384 9.3.1 Principles 384 9.3.2 System Results and Milestones 391 10 FOUR LEVEL FIBER AMPLIFIERS FOR 1.3 μM AMPLIFICATION 0 10.1 Introduction 418 10.1.1 Gain in a Four-Level System 418 10.2 Pr[sup(3+)] -doped Fiber Amplifiers 421 10.2.1 Introduction 421 10.2.2 Spectroscopic Properties 422 10.2.3 Gain Results for Pr[sup(3+)] -doped Fiber Amplifiers 423 10.2.4 Modeling of the Pr[sup(3+)] -doped Fiber Amplifier Gain 429 10.2.5 System Results 433 10.3 Nd[sup(3+)] -Doped Fiber Amplifiers 435 10.3.1 Introduction 435 10.3.2 Gain Results for Nd[sup(3+)] -Doped Fiber Amplifiers 436 10.3.3 Modeling of the Nd[sup(3+)] -Doped Fiber Amplifier Gain 437 Appendix A 446 A.1 OASIX® Amplifier Simulation Software 0 A.2 Introduction 446 A.2.1 System Requirements 446 A.2.2 Installing OASIX® 0 A.2.3 Starting OASIX® 0 A.2.4 What to do next 447 A.3 A Quick Overview and Tour 447 A.3.1 Fibers and Modeling Parameters 447 A.3.2 Saving a Simulation Configuration 448 A.3.3 Device Types Simulated 448 A.3.4 Data Entry and Device Conventions 449 A.3.5 Screens and Menus 449 A.3.6 Simulation Looping and Output Modes 450 A.4 Screen Contents and Simulation Methodology 451 A.4.1 Main/Entry Screen 451 A.4.2 Single-Stage Setup Screen 452 A.4.3 Additional Signals Screen 452 A.4.4 Output Setup Screen 453 A.4.5 Simulation Status Box 454 A.5 Simulation Looping Structure 455 A.5.1 Specifying Loop Parameters 455 A.5.2 Choosing Loop Order 455 A.5.3 Linear or Logarithmic Looping 456 A.5.4 Multiple Parameters Varied in a Loop 456 A.5.5 Influence on Output Format 457 A.5.6 Output Modes 457 A.6 Sample Simulations 459 A.6.1 Single-Run, Single-Stage EDFA 459 A.6.2 Multiple-Run, Single-Stage EDFA 460 A.6.3 Other simulations to try 460 A.7 Computation of Signal Related Quantities 460 A.8 Computation of ASE Related Quantities 461 A.9 Basic Operating Principles 462 A.9.1 Simulation Speed and the Number of Waves 463 A.9.2 Causes and Remedies for Convergence Failure 464 A.10 Comment on the treatment of losses 465 INDEX 468 A 468 B 469 C 470 D 470 E 470 F 471 G 471 H 472 I 472 J 472 K 472 L 473 M 473 N 473 O 473 P 474 Q 475 R 475 S 475 T 476 U 476 V 476 W 476 Y 477 Z 477 CONTENTS......Page 6 Foreword......Page 11 Preface......Page 14 Acknowledgements......Page 16 1.1 Long Haul Fiber Networks......Page 18 1.2 Historical Development of Erbium-Doped Fiber Amplifiers......Page 22 A.2.3 Starting OASIX®......Page 0 2.1 Introduction......Page 30 2.2 Conventional Communication Fiber......Page 31 2.3.1 Rare Earth Vapor Phase Delivery Methods......Page 33 2.3.2 Rare Earth Solution-Doping Methods......Page 38 2.3.3 Rod and Tube Methods......Page 40 2.4.1 Evanescent Field......Page 42 2.4.2 Double Clad Fiber Design......Page 43 2.5 Compositions......Page 44 2.6.1 Fiber Refractive Index and Composition Profile......Page 46 2.6.3 Alternate Glass Host Fabrication......Page 47 3.2 Fiber Connectors......Page 60 3.3 Fusion Splicing......Page 65 3.4 Pump and Signal Combiners......Page 67 3.5 Isolators......Page 69 3.6 Circulators......Page 70 3.8.1 Introduction......Page 72 3.8.2 Applications of Bragg Gratings......Page 74 3.8.3 Long Period Gratings......Page 76 3.9 Signal Multiplexers and Demultiplexers......Page 78 3.10 Signal Add/Drop Components......Page 79 3.11 Dispersion Compensation Components......Page 80 3.13 Pump Lasers......Page 83 4.2 Atomic Physics of the Rare Earths......Page 104 4.2.3 Semiempirical Atomic and Crystal Field Hamiltonians......Page 109 4.2.4 Energy Level Fitting......Page 111 4.3 Optical Spectra of Rare Earth Ions......Page 112 4.4.1 Transition Cross Sections......Page 116 4.4.2 Lifetimes......Page 122 4.4.3 Linewidths and Broadening......Page 125 4.5 Spectroscopy of the Er[sup(3+)] Ion......Page 127 4.5.1 Lifetimes......Page 128 4.5.2 Er[sup(3+)] Spectra, Cross Sections, and Linewidths......Page 131 4.6 Er[sup(3+)] -Er[sup(3+)] Interaction Effects......Page 137 5.2.1 Three-Level Rate Equations......Page 148 5.2.2 The Overlap Factor......Page 157 5.3.1 Validity of the Two-Level Approach......Page 161 5.3.2 Generalized Rate Equations......Page 163 5.4 Amplified Spontaneous Emission......Page 164 5.5 Analytical Solutions to the Two-Level System......Page 166 6.2 Absorption and Emission Cross Sections......Page 170 6.3 Gain and ASE Modeling......Page 173 6.3.2 Average Inversion Relationship......Page 175 6.3.3 Inhomogeneous Broadening......Page 176 6.4.1 Signal Gain, ASE Generation, and Population Inversion......Page 178 6.4.3 Spectral Profile of the ASE......Page 186 6.4.4 Small Signal Spectral Gain and Noise Modeling......Page 188 6.4.6 Power Amplifier Modeling......Page 192 6.4.7 Effective Parameter Modeling......Page 195 6.6.1 Model Equations......Page 203 6.6.3 800 nm Band Pumping......Page 205 6.7 Er[sup(3+)] -Er[sup(3+)] Interaction Effects......Page 208 6.7.1 Upconversion Effects on Amplifier Performance......Page 210 6.7.2 Pair Induced Quenching......Page 212 7.1 Introduction......Page 218 7.2.1 Classical Derivation of Optical Amplifier Noise......Page 219 7.2.2 Noise at the Output of an Optical Amplifier......Page 222 7.2.3 Comparison of Optical Amplifier Devices......Page 227 7.3 Optical Noise: System Aspects......Page 229 7.3.1 Receivers......Page 230 7.3.2 Bit Error Rate Calculations - Direct Detection......Page 231 7.3.4 Optical Inline Amplifiers - Amplifier Chains......Page 243 7.3.5 Noise in Optical Power Amplifiers......Page 252 7.3.6 Nonlinearity Issues......Page 253 7.3.7 Analog Applications......Page 257 8.2.1 Gain Measurements......Page 268 8.2.2 Power Conversion Efficiency......Page 274 8.2.3 Noise Figure Measurements......Page 275 8.3 Amplifier Design Issues......Page 280 8.3.1 Copropagating and Counterpropagating Pumping Issues......Page 282 8.3.2 Choice of Fiber Lengths and Geometries for Various Applications......Page 285 8.3.3 Multistage Amplifiers......Page 290 8.3.4 Bidirectional Amplifiers......Page 294 8.3.5 Power Amplifiers......Page 297 8.3.6 WDM Amplifier Design Issues......Page 301 8.3.7 Distributed Amplifiers......Page 312 8.3.8 Waveguide Amplifiers......Page 319 9.1 Introduction......Page 338 9.2.1 Preamplifiers......Page 340 9.2.2 Inline Amplifiers - Single Channel Transmission......Page 344 9.2.3 Mine Amplifiers - WDM Transmission......Page 352 9.2.4 Repeaterless Systems......Page 362 9.2.5 Remote Pumping......Page 363 9.2.6 Analog Applications......Page 368 9.2.7 Gain Peaking and Self-Filtering......Page 371 9.2.8 Polarization Issues......Page 376 9.2.9 Transient Effects......Page 380 9.3.1 Principles......Page 384 9.3.2 System Results and Milestones......Page 391 10.1.1 Gain in a Four-Level System......Page 418 10.2.1 Introduction......Page 421 10.2.2 Spectroscopic Properties......Page 422 10.2.3 Gain Results for Pr[sup(3+)] -doped Fiber Amplifiers......Page 423 10.2.4 Modeling of the Pr[sup(3+)] -doped Fiber Amplifier Gain......Page 429 10.2.5 System Results......Page 433 10.3.1 Introduction......Page 435 10.3.2 Gain Results for Nd[sup(3+)] -Doped Fiber Amplifiers......Page 436 10.3.3 Modeling of the Nd[sup(3+)] -Doped Fiber Amplifier Gain......Page 437 A.2.1 System Requirements......Page 446 A.3.1 Fibers and Modeling Parameters......Page 447 A.3.3 Device Types Simulated......Page 448 A.3.5 Screens and Menus......Page 449 A.3.6 Simulation Looping and Output Modes......Page 450 A.4.1 Main/Entry Screen......Page 451 A.4.3 Additional Signals Screen......Page 452 A.4.4 Output Setup Screen......Page 453 A.4.5 Simulation Status Box......Page 454 A.5.2 Choosing Loop Order......Page 455 A.5.4 Multiple Parameters Varied in a Loop......Page 456 A.5.6 Output Modes......Page 457 A.6.1 Single-Run, Single-Stage EDFA......Page 459 A.7 Computation of Signal Related Quantities......Page 460 A.8 Computation of ASE Related Quantities......Page 461 A.9 Basic Operating Principles......Page 462 A.9.1 Simulation Speed and the Number of Waves......Page 463 A.9.2 Causes and Remedies for Convergence Failure......Page 464 A.10 Comment on the treatment of losses......Page 465 A......Page 468 B......Page 469 E......Page 470 G......Page 471 K......Page 472 O......Page 473 P......Page 474 S......Page 475 W......Page 476 Z......Page 477 In the past few years, the use of erbium-doped fiber amplifiers has increased the capacity of fiber optics transmission systems by more than a hundred-fold. These amplifiers allow for the amplification of transmission signals in all optical ways without the need for electronic processing of the signal, which limits the capacity of optical systems. With the recent explosive growth in optical transmission networks, the fiber amplifier has become an essential building block for these networks. Understanding it provides great insight into today's high-capacity fiber networks, their design, and their future evolution.Erbium-Doped Fiber Amplifiers has been written by early pioneers in the development of fiber amplifier technology and optically amplified systems. The book guides the reader from the most fundamental aspects of fiber amplifiers all the way to system design and applications. The fundamental chapters address the important aspects of noise theory, design, and understanding of optically amplified systems. The coverage is such that the book will be of interest to researchers, practitioners, and students new to the field.The book can be read as a sequence of linked chapters which build on each other. Since each chapter is relatively self-contained, the reader can also jump in at the desired point of interest and refer to other chapters as needed. Many figures are used to present concepts in an intuitive and understandable way. Numerous references are provided for the reader wishing to delve further into any of the topics covered. With the continued soaring demand for optical transmission networks, the book provides an important base for understanding the technicalunderpinnings of such networks.

Erbium Fiber Amplifiers is a comprehensive introduction to the increasingly important topic of optical amplification. Written by three Bell Labs pioneers, the book stresses the importance of the interrelation of materials properties, optical properties, and systems aspects of optical fiber amplifiers.

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Key Features
* Explains the theory of noise in optically amplified systems in an intuitive way
* The book contains a discussion of components used in amplifier fabrication and of the attendant technologies used in real systems
* The book provides basic tools for amplifier design as well as systems engineering, including the latest developments in WDM and soliton systems
* The book discusses the fundamentals of rare earth ions for the reader desiring more depth in the topic
* The book is for either the novice of experienced reader
* The chapter have links between them to allow the reader to understand the relationship between the amplifier characteristics, noise, and systems applications
* The book contains extensive references Erbium-Doped Fiber Amplifiers, Fundamentals and Technology guides the reader from the most fundamental aspects of fiber amplifiers all the way to system design and applications. The fundamental chapters address the important issues of erbium ion properties, amplifiers fabrication, components for amplifiers, gain performance, and noise theory. The systems chapters cover the amplifier design issues and transmission achievements resulting from the use of erbium-doped fiber amplifiers in undersea and terrestrial systems, both single channel and WDM. The coverage is such that the book is of interest to researchers, practitioners, and students new to the field.