MATLAB仿真指南：导波光子学基础与应用

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"导波光子学matlab仿真.pdf" 导波光子学是光学领域的一个重要分支，主要研究光在特定结构（如光纤、光波导等）中的传播和操控。MATLAB是一款强大的数学计算软件，广泛应用于科学计算、数据分析、算法开发以及图形可视化等领域。在导波光子学中，MATLAB可以用于模拟光波的传播特性，设计和优化光子器件，以及分析实验数据。本书"GuidedWave Photonics Fundamentals and Applications with MATLAB"由Le Nguyen Binh撰写，是导波光子学与MATLAB结合的实用教程。书中详细介绍了导波光子学的基础理论，包括光的传播原理、光波导的模式分析、光与材料相互作用的基本概念，以及相关的应用实例。通过MATLAB，作者提供了仿真代码，帮助读者理解和实践这些理论知识，这对于本科生和研究生深入学习导波光学具有极大的价值。书中的内容可能涵盖了以下几个方面： 1. 光波导理论：介绍光波导的形成原理，如电磁场在不同介质界面的传播条件，以及如何通过模式解析来确定光在波导中的传输特性。 2. 光纤通信：讨论光纤作为导波光子学的重要应用，包括多模和单模光纤的特性，以及光纤通信系统的信号传输和调制解调技术。 3. MATLAB仿真工具箱：介绍如何使用MATLAB的Optical Communication Toolbox或FDTD Solutions等工具进行光子器件的设计和性能评估，例如模拟光的传播、散射、耦合和损耗等现象。 4. 实验数据分析：讲解如何利用MATLAB处理和分析实验测量数据，如光谱分析、信噪比计算、误码率测试等。 5. 光子器件设计：涵盖各种光子器件的建模，如光开关、光调制器、光滤波器等，通过MATLAB实现对器件性能的预测和优化。 6. 超快光纤激光器：探讨基于MATLAB的模型，研究超快光纤激光器的工作原理和动态行为，包括脉冲压缩、锁模效应等。 7. 有机薄膜光子学：介绍有机薄膜的分子层沉积技术和它们在光子学中的应用，可能会涉及到MATLAB在材料性质计算和器件模拟中的应用。通过阅读本书，读者不仅可以掌握导波光子学的基本理论，还能掌握MATLAB在光子学研究中的实际应用技巧，提高其在光学工程领域的实践能力。值得注意的是，书中虽然使用了MATLAB商标，但并不意味着MATLAB公司对书中的内容或练习提供了官方保证。读者应独立验证书中提供的仿真结果和理论分析。

Contents xv

9. Integrated Guided-Wave Photonic Transmitters .........................................................457

9.1 Introduction ...............................................................................................................457

9.2 Optical Modulators ...................................................................................................458

9.2.1 Phase Modulators ........................................................................................458

9.2.2 Intensity Modulators ...................................................................................460

9.2.2.1 Phasor Representation and Transfer Characteristics ..............460

9.2.2.2 Bias Control ...................................................................................462

9.2.2.3 Chirp Free Optical Modulators .................................................. 462

9.2.2.4 Structures of Photonic Modulators ............................................464

9.2.2.5 Typical Operational Parameters .................................................464

9.3 Traveling Wave Electrodes for Integrated Modulators........................................465

9.3.1 Introduction ..................................................................................................466

9.3.2 Numerical Formulation ..............................................................................467

9.3.2.1 Discrete Fields and Potentials ....................................................467

9.3.2.2 Electrode Line Capacitance, Characteristic Impedance

and Microwave Effective Index ..................................................469

9.3.2.3 Electric Fields E

and E

and the Overlap Integral ..................471

9.3.3 Electrode Simulation and Discussions .....................................................471

9.3.3.1 Grid Allocation and Modeling Performance ...........................471

9.3.3.2 Model Accuracy ............................................................................ 474

9.3.4 Electro-Optic Overlap Integral, Γ .............................................................. 476

9.3.5 Tilted Wall Electrode ...................................................................................478

9.3.6 Frequency Responses of Phase Modulation by Single Electrode ......... 481

9.3.7 Remarks .........................................................................................................484

9.4 Lithium Niobate Optical Modulators: Devices and Applications .....................485

9.4.1 Mach-Zehnder Interferometric Modulator and Ultra-High Speed

Advanced Modulation Formats .................................................................485

9.4.1.1 Amplitude Modulation................................................................486

9.4.1.2 Phase Modulation ........................................................................486

9.4.1.3 Frequency Modulation ................................................................486

9.4.2 LiNbO

MZIM Fabrication .........................................................................487

9.4.3 Effects of Angled-Wall Structure on RF Electrodes ................................488

9.4.4 Integrated Modulators and Modulation Formats ...................................490

9.4.5 Remarks .........................................................................................................492

9.5 Generation and Modulation of Optical Pulse Sequences ...................................492

9.5.1 Return-to-Zero Optical Pulses ...................................................................492

9.5.1.1 Generation .....................................................................................492

9.5.1.2 Phasor Representation .................................................................493

9.5.2 Differential Phase Shift Keying .................................................................498

9.5.2.1 Background ...................................................................................498

9.5.2.2 Optical Differential Phase Shift Keying Transmitter .............499

9.6 Generation of Modulation Formats ........................................................................500

9.6.1 Amplitude Shift Keying .............................................................................500

9.6.1.1 Amplitude–Modulation Amplitude Shift Keying-Non-

Return-to-Zero and Amplitude Shift Keying-Return-to-Zero .... 500

9.6.1.2 Amplitude–Modulation on-off Keying Return-to-Zero

Formats ..........................................................................................501

9.6.1.3 Amplitude–Modulation Carrier-Suppressed Return-to-

Zero Formats .................................................................................501

xvi Contents

9.6.2 Discrete Phase–Modulation Non-Return-to-Zero Formats ...................503

9.6.2.1 Differential Phase Shift Keying .................................................503

9.6.2.2 Differential Quadrature Phase Shift Keying ...........................504

9.6.2.3 M-Ary Amplitude Differential Phase Shift Keying ................505

9.6.3 Continuous Phase-Modulation (PM)-Non-Return-to-Zero Formats....506

9.6.3.1 Linear and Nonlinear Minimum Shift Keying ........................509

9.6.3.2 Minimum Shift Keying as a Special Case of Continuous

Phase Frequency Shift Keying ................................................... 511

9.6.3.3 Minimum Shift Keying as Offset Differential Quadrature

Phase Shift Keying ....................................................................... 512

9.6.3.4 Conguration of Photonic Minimum Shift Keying

Transmitter Using Two Cascaded Electro-Optic Phase

Modulators .................................................................................... 512

9.6.3.5 Conguration of Optical Minimum Shift Keying

Transmitter Using Mach-Zehnder Intensity Modulators:

I-Q Approach ................................................................................ 514

9.6.4 Single Side Band (SSB) Optical Modulators ............................................. 514

9.7 Problems ..................................................................................................................... 515

References ............................................................................................................................. 518

10. Nonlinearity in Guided Wave Devices .......................................................................... 521

10.1 Nonlinear Effects in Integrated Optical Waveguides for Photonic Signal

Processing ..................................................................................................................521

10.1.1 Introductory Remarks ................................................................................. 521

10.1.2 Third-Order Nonlinearity and Parametric Four-Wave Mixing

Process ...........................................................................................................522

10.1.2.1 Nonlinear Wave Equation ...........................................................522

10.1.2.2 Four-Wave Mixing Coupled-Wave Equations ......................... 523

10.1.2.3 Phase Matching ............................................................................ 524

10.1.3 Transmission Models and Nonlinear Guided Wave Devices ...............525

10.1.4 System Applications of Third-Order Parametric Nonlinearity in

Optical Signal Processing ...........................................................................526

10.1.4.1 Parametric Ampliers .................................................................526

10.1.4.2 Wavelength Conversion and Nonlinear Phase

Conjugation ............................................................................. 530

10.1.4.3 High-Speed Optical Switching...................................................533

10.1.4.4 Triple Correlation .........................................................................537

10.1.5 Application of Nonlinear Photonics in Advanced

Telecommunications ....................................................................................542

10.1.6 Remarks .........................................................................................................548

10.2 Nonlinear Effects in Actively Mode-locked Fiber Lasers ...................................549

10.2.1 Introductory Remarks .................................................................................549

10.2.2 Laser Model ..................................................................................................549

10.2.2.1 Modeling of the Fiber ..................................................................550

10.2.2.2 Modeling of the Er:Doped Fiber Ampliers ............................550

10.2.2.3 Modeling of the Optical Modulator ..........................................550

10.2.2.4 Modeling of the Optical Filter .................................................... 551

10.2.3 Nonlinear Effects in Actively Mode-Locked Fiber Lasers .....................551

10.2.3.1 Zero Detuning .............................................................................. 551

Contents xvii

10.2.3.2 Detuning in Actively Mode-Locked Fiber Laser with

Nonlinearity Effect.......................................................................553

10.2.3.3 Pulse Amplitude Equalization in Harmonic Mode-Locked

Fiber Laser ....................................................................................... 555

10.2.4 Experiments ..................................................................................................556

10.2.4.1 Experimental Setup .....................................................................556

10.2.4.2 Mode-Locked Pulse Train with 10 GHz Repetition Rate ....... 557

10.2.4.3 Pulse Shortening and Spectrum Broadening under

Nonlinearity Effect.......................................................................559

10.2.5 Remarks .........................................................................................................559

10.3 Nonlinear Photonic Pre-Processing for Bispectrum Optical Receivers ............560

10.3.1 Introductory Remarks .................................................................................560

10.3.2 Bispectrum Optical Receiver ..................................................................... 561

10.3.3 Triple Correlation and Bispectra ................................................................ 561

10.3.3.1 Denition ....................................................................................... 561

10.3.3.2 Gaussian Noise Rejection ............................................................562

10.3.3.3 Encoding of Phase Information .................................................562

10.3.3.4 Eliminating Gaussian Noise .......................................................562

10.3.4 Bispectral Optical Structures .....................................................................563

10.3.4.1 Principles .......................................................................................564

10.3.4.2 Technological Implementation ..................................................564

10.3.5 Four-Wave Mixing in Highly Nonlinear Media .....................................565

10.3.6 Third Harmonic Conversion ......................................................................565

10.3.7 Conservation of Momentum ......................................................................565

10.3.8 Estimate of Optical Power Required for Four-Wave Mixing ................565

10.3.9 Mathematical Principles of Four-Wave Mixing and the Wave

Equations .......................................................................................................566

10.3.9.1 Phenomena of Four-Wave Mixing .............................................566

10.3.9.2 Coupled Equations and Conversion Efciency .......................567

10.3.9.3 Evolution of Four-Wave Mixing along the Nonlinear

Waveguide Section .......................................................................568

10.3.10 Transmission and Detection .......................................................................568

10.3.10.1 Optical Transmission Route and Simulation Platform ...........568

10.3.10.2 Four-Wave Mixing and Bispectrum Receiving ........................569

10.3.10.3 Performance ..................................................................................569

10.3.11 Remarks .........................................................................................................572

10.4 Raman Effects in Microstructure Optical Fibers or Photonic Crystal

Fibers ................................................................................................................... 573

10.4.1 Introductory Remarks ................................................................................. 573

10.4.2 Raman Gain in Photonic Crystal Fibers ................................................... 575

10.4.2.1 Measurement of Raman Gain ....................................................575

10.4.2.2 Effective Area and Raman Gain Coefcient ............................ 576

10.4.3 Remarks .........................................................................................................582

10.5 Raman Gain of Segmented Core Prole Fibers ....................................................582

10.5.1 Segmented-Core Fiber Design for Raman Amplication ......................583

10.5.2 Advantages of Dispersion Compensating Fiber as a Lumped/

Discrete Raman Amplier (DRA) .............................................................583

10.5.3 Spectrum of Raman Amplication ...........................................................584

10.5.4 Key Equations for Deducing the Raman Gain of Ge-Doped Silica ......584

xviii Contents

10.5.5 Design Methodology for Dispersion Compensating Fiber—

Discrete Raman Ampliers ........................................................................586

10.5.6 Design Steps .................................................................................................589

10.5.7 Sampled Prole Design ...............................................................................590

10.5.8 Remarks ......................................................................................................... 591

10.6 Summary ....................................................................................................................592

References .............................................................................................................................595

Appendix 1 Coordinate System Transformations ............................................................601

Appendix 2 Models for Couplers in FORTRAN ..............................................................607

Appendix 3 Overlap Integral ................................................................................................633

Appendix 4 Coupling Coefcients ......................................................................................637

Appendix 5 Additional Coupling Coefcients .................................................................639

Appendix 6 Elliptic Integral .................................................................................................641

Appendix 7 Integrated Photonics: Fabrication Processes for LiNbO

Ultra-Broadband Optical Modulators ..........................................................643

Appendix 8 Planar Waveguides by Finite Difference Method—FORTRAN

PROGRAMS ......................................................................................................665

Appendix 9 Interdependence between Electric and Magnetic Fields and

Electromagnetic Waves ....................................................................................729

xix

Preface

This book presents the theory and simulation of optical waveguides and wave propaga-

tions in a guided environment, the guided wave photonics. It consists of a unied treat-

ment of three distinct but related topics of formulation of wave equations in the transverse

plane and time-dependent propagation directions, the coupling of the guided wave sys-

tems, and nonlinear behavior of the guided waves in such waveguiding systems.

A departure from the convention followed by most books in the eld is the omission of

introductory chapters on the fundamentals of the theory of guided waves. Rather, the book

as a whole is aimed at readers with a background on the propagation of electromagnetic

waves, offered in a semester course covering essential matters on the guiding of light-

waves in waveguide structures. However, essential background materials are given in the

appendices. These guided wave devices play the most important roles in the engineering

of optical communications transmission at ultra-high speed.

Therefore, guiding of lightwaves in planar and three-dimensional structures is described

in Chapters 2 and 3, while Chapters 4 and 5 describe the guiding of lightwaves in circular

optical waveguides, the single-mode optical bers. Chapters 6 and 7 describe the coupling

phenomena via the scalar and full coupled-mode theories. Chapter 8 gives a brief treatment

of nonlinear optical waveguides and Chapter 10 a treatment of optical bers and their appli-

cations in performing a number of photonic manipulating functions such as phase conju-

gation and time demultiplexing in optical transmission systems. Nonlinear effects in such

guided wave devices are also treated, wherever appropriate in sections of the chapters.

The motivation and materials for this book have been provided mainly by research

conducted in the University of Western Australia, Monash University, Siemens Central

Research Laboratories at Otto Hahn Ring, Munich, Germany and Nortel Networks

Advanced Technology Research Centers at Harlow, England with which the author has

been associated as a technical and academic member.

Many other people contributed signicantly to this book. Research students at Monash

University contributed over the years; in particular, my research scholars and doctoral

graduates Dr. Su-Vun Chung, Dr. Shu Zheng, Dr. Wenn Jing Lai, Dr. X. Wang and Dr.

Nguyen Duc Nhan. Undergraduate students attending the courses in advanced photo-

nics and optical ber communications and electromagnetic wave propagations of the

Department of Electrical and Computer Systems Engineering of Monash University,

Faculty of Engineering of the Christian Albrechts University of Kiel, Germany and

Network Technology Research Center of Nanyang Technological University of Singapore,

have questioned and challenged several aspects of wave guiding in optical waveguides, I

thus thank them for their exchanges of ideas and curiosity.

I wish to thank Ashley Gasque of CRC Press for her encouragement and assistance in the

formulation of this book. I extend special thanks to the wife Nguyen Thi Phuong and my

son Le Nguyen Lam for putting up with the intrusion on family time as a result of all the

days and nights spent on the chapters of this book. Last and not least, I thank my mother

Nguyen Thi Huong and late father for giving their children the best education philosophy

over many years and their teaching of “learning for life.”

Le Nguyen Binh

Glen Iris, Australia

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