Edited by

Rich P. Mildren

and James R. Rabeau

Optical Engineering of Diamond

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Optical Engineering of Diamond

Edited by Rich P. Mildren and James R. Rabeau

The Editors

Assoc. Prof. Rich P. MildrenMacquarie University,MQ Photonics Research CentreDepartment of Physics and AstronomySydney, NSW 2109Australia

Assoc. Prof. James R. RabeauMacquarie University (Honorary Fellow)Department of Physics and AstronomySydney, NSW 2109Australia(currently at Deloitte Touche Tohmatsu, Australia)

Cover PictureConcept image of diamond photonic nanowire arrays with embedded nitrogen-vacancy color centers. By applying large-scale semiconductor manufacturing techniques to single-crystal diamond, we may utilize its unique and exceptional material properties in diverse areas of quantum science, optics and photonics, and nanotechnology. The work was performed by researchers at the Harvard University and Texas A&M. Created by Jay Penni, used with permission of Marko Loncar and Thomas Babinec.

All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate.

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Contents

Foreword XV Preface XVII ListofContributors XXI

1 IntrinsicOpticalPropertiesofDiamond 1 RichP.Mildren1.1 Transmission 21.2 Lattice Absorption 31.2.1 The Two-Phonon Region 41.2.2 Absorption at Wavelengths Longer than 5 µm 71.2.3 Temperature Dependence 81.2.4 Isotopic Content 91.3 UV Edge Absorption 111.4 Refractive Index 131.4.1 Temperature Dependence of the Refractive Index 141.5 Verdet Constant 161.6 First-Order Raman Scattering 161.6.1 Wavelength Dependence 201.6.2 Raman Linewidth 211.6.3 Temperature Dependence 221.6.4 Isotopic Content 231.7 Stimulated Raman Scattering 241.8 Brillouin Scattering 251.9 Electronic Nonlinearity 271.9.1 Nonlinear Refractive Index 291.9.2 Two-Photon Absorption 29 Acknowledgments 30 References 31

2 OpticalQualityDiamondGrownbyChemicalVaporDeposition 35 IanFriel2.1 Introduction 352.2 CVD Diamond Growth Principles 36

V

VI Contents

2.2.1 Fundamentals of Growth 362.2.2 Morphology and Texture 422.3 Properties of Optical Quality CVD Diamond 432.3.1 Absorption 442.3.2 Nonoptical Wavelengths 472.3.3 Isotopic Purity 492.3.4 Strain-Induced Birefringence 492.3.5 Scatter 522.3.6 Other Properties of CVD Diamond 542.3.6.1 Thermal Properties  542.3.6.2 Strength  562.4 Optical Applications of CVD Diamond 602.4.1 Applications of Polycrystalline Diamond 602.4.2 Applications of Single-Crystal Diamond 612.5 Summary 632.6 Acknowledgments 64 References 64

3 PolishingandShapingofMonocrystallineDiamond 71 JonathanR.Hird3.1 Introduction: Background and Historical Overview 713.2 Shaping Diamond: Cleaving, Bruting, and Sawing 733.3 Practical Aspects of Diamond Polishing 743.3.1 Apparatus and Preparation 743.3.2 Directional Dependence of Polishing: Wear Anisotropy 753.4 The Science of Mechanical Polishing 773.4.1 Wear Anisotropy 793.4.2 Velocity Dependence 793.4.3 Diamond Polishing Wear Debris 813.4.4 The Polished Diamond Surface 823.4.5 Subsurface Damage 843.4.6 The Scaife: Its Surface and Preparation 843.4.7 Atmosphere Dependence 883.4.8 Triboluminescence 883.4.9 Wear Mechanism 893.5 Tribological Behavior of Diamond 923.5.1 Slow-Speed Sliding of Diamond against Diamond 923.5.2 Sliding of Diamond against Other Materials 953.6 Other Polishing Methods 963.6.1 Wear of Diamond by Other Materials 963.6.2 Hot Metal Polishing 973.6.3 Chemical–Mechanical Planarization 973.7 Producing High-Quality Planar Surfaces on Diamond 983.7.1 Cleaving 983.7.2 Post-Mechanical Polishing Treatment 99

Contents VII

3.7.3 Dry Chemical Etching 993.8 Nonplanar and Structured Geometries 1013.9 Summary 102 References 103

4 RefractiveandDiffractiveDiamondOptics 109 FredrikNikolajeffandMikaelKarlsson4.1 Introduction 1094.2 Windows and Domes 1104.3 Refractive Devices 1124.3.1 Lenses 1124.3.2 Prisms 1184.3.3 Other Devices 1184.4 Diffractive Components 1194.5 Polishing 1264.6 Micromachining 1284.7 Coatings 1334.8 Applications 1344.9 Conclusions and Outlook 137 References 138

5 Nitrogen-VacancyColorCentersinDiamond:Properties,Synthesis,andApplications 143

CarloBradac,TorstenGaebel,andJamesR.Rabeau5.1 Introduction 1435.2 Defects in Diamond 1445.2.1 Intrinsic and Extrinsic Defects 1445.2.2 Nitrogen-Related Defects in Diamond 1455.2.2.1 C-Center  1465.2.2.2 A-Center  1475.2.2.3 B-Center  1475.2.2.4 Platelets  1475.2.2.5 Other Nitrogen-Vacancy Complexes  1475.2.3 Nitrogen-Vacancy (NV) Center 1485.2.3.1 Structure  1495.2.3.2 Charge State  1505.2.3.3 Energy Level Scheme  1525.2.4 Optical and Spin Properties of NV− Centers in Diamond 1535.2.4.1 Polarization  1535.2.4.2 Control  1555.2.4.3 Measurement  1565.2.4.4 Relaxation Time  1565.3 Synthesis of Diamond 1595.3.1 High-Pressure, High-Temperature (HPHT) Synthesis 1595.3.2 Chemical Vapor Deposition (CVD) Synthesis 160

VIII Contents

5.3.3 Detonation 1615.3.4 Enhancement of Color Center Concentration 1625.3.4.1 Irradiation  1625.3.4.2 Ion Implantation  1635.3.4.3 Incorporation during CVD Growth  1635.4 Applications of Color Centers in Diamond 1635.4.1 Quantum Information Technology 1645.4.2 Life Sciences 1655.4.3 High-Resolution Magnetometry 1655.5 Feasibility of NV Center-Based Nanotechnologies 1655.5.1 Fabricating Ultrasmall (

Contents IX

7.3.2 Implication of Surface Functional Changes on Luminescent Properties of NV Centers Implanted to Different Depths 216

7.4 Formation of Variously Charged NV Centers in Diamond 2177.4.1 Introduction of Vacancies to the Diamond Lattice: Different

Irradiation Strategies  2207.4.1.1 Creation of Vacancies: GR1 versus ND1  2207.4.1.2 Resulting NV PL of Variously Irradiated NDs  2217.4.2 Formation of NV Centers: An Annealing Study 2237.5 Transfer Doping Effects: Luminescent Properties of NV Centers in

Variously Terminated Nanodiamonds 2257.5.1 Quenching of NV-Luminescence on ND Particles 2267.5.2 Surface and Size Effects in the Variously Terminated

Nanodiamond 2287.5.2.1 Fluorinated NDs  2287.5.2.2 Size Dependence of NV Luminescence on Variously Terminated

ND  2297.5.3 Fluorescent Nanodiamond Particles as a Sensor of Charged

Molecules 2317.5.3.1 Interactions with Charged Polymers  2317.5.4 NDs for Biology: Monitoring of Transfection by ND Carriers 2327.6 Conclusions 235 References 236

8 DiamondRamanLaserDesignandPerformance 239 RichardP.Mildren,AlexanderSabella,OndrejKitzler,DavidJ.Spence,

andAaronM.McKay8.1 Introduction and Background 2398.1.1 Crystalline Raman Laser Principles 2428.1.1.1 Basic SRS Theory  2438.1.1.2 Raman Laser Design and Modeling  2458.2 Optical, Thermal, and Physical Properties of Diamond 2468.2.1 Raman Gain Coefficient 2488.2.1.1 Dependence on Polarization  2508.2.1.2 Dependence on Pump Linewidth  2538.2.2 Thermal Properties 2548.2.2.1 Thermal Lens Strength  2558.2.2.2 Thermally Induced Stress Birefringence  2558.2.2.3 Thermal Stress Fracture  2568.2.3 Laser Damage Threshold 2568.2.4 Design Implications for CVD-Grown Material 2578.3 Diamond Raman Laser Development 2588.3.1 External Cavity Wavelength Conversion 2588.3.2 Intracavity Diamond Raman Lasers 2618.3.3 Synchronously Pumped Mode-Locked Lasers 2628.4 Extending the Capability of Raman Lasers Using Diamond 264

X Contents

8.4.1 Long-Wavelength Generation 2648.4.2 Deep Ultraviolet Generation 2658.4.3 High Average Power 2678.5 Conclusions and Outlook 270 Acknowledgments 271 References 272

9 QuantumOpticalDiamondTechnologies 277 PhilippNeumannandJörgWrachtrup9.1 Introduction 2779.1.1 Single Quantum Systems 2779.1.2 The Nitrogen-Vacancy (NV) Center in Diamond 2789.1.3 The Present Situation 2789.2 The NV Center’s Electron Spin as a Master Qubit 2799.3 Nuclear Spins as a Qubit Resource 2809.3.1 Interaction of a Single Electron Spin with nearby Nuclear Spins 2829.3.1.1 Nuclear spin Hamiltonian 2829.3.1.2 Secular Approximation and Nonsecular Terms 2839.3.1.3 Examples of Nearby Nuclear Spins 2849.3.1.4 Quantum Gates Using Nuclear Spins 2879.3.1.5 The Nuclear Spin Bath 2889.3.2 Nonlocal States: The Heart of a Quantum Processor 2939.3.2.1 Two Nearest-Neighbor 13C Nuclear Spins 2939.3.2.2 Characterization of the Qubit System 2959.3.2.3 Generation and Detection of Entanglement 2969.4 Summary and Outlook 303 References 305

10 Diamond-BasedOpticalWaveguides,Cavities,andOtherMicrostructures 311

SnjezanaTomljenovic-Hanic,TimothyJ.Karle,AndrewD.Greentree,BrantC.Gibson,BarbaraA.Fairchild,AlastairStacey,andStevenPrawer

10.1 Introduction 31110.1.1 Motivation: Applications of Fluorescent Diamond Devices 31110.1.1.1 Sensing 31210.1.1.2 Single-Photon Sources for Quantum Key Distribution and Quantum

Metrology 31310.1.1.3 Quantum Information Processing with NV Diamond  31510.2 Optical Properties 31810.3 Design of Diamond-Based Optical Structures 31910.4 Single-Crystal Diamond 32110.4.1 Lift-Off of Thin and Ultra-Thin Single-Crystal Diamond Films 32210.4.1.1 Lift-Off  32210.4.1.2 Lift-Out  32210.4.2 Fabrication: Lithography and Etching 323

Contents XI

10.4.2.1 Photolithography 32510.4.2.2 E-Beam Lithography 32510.4.2.3 FIB Milling 32510.4.2.4 Ga Hard Mask 32610.4.2.5 Reactive Ion Etching: A Scalable Process 32610.4.2.6 Etching of Bulk Diamond: Microlenses  32710.4.3 Optical Waveguiding in Single-Crystal Diamond 32710.4.3.1 Waveguides: FIB Lithography 32810.4.3.2 RIE-Fabricated Waveguides 33010.4.3.3 Light Guiding in Ion-Implanted Diamond  33010.4.4 Surface Emission: Solid Immersion Lenses and Nanopillars 33010.4.4.1 Solid Immersion Lenses 33110.4.4.2 Nanopillars  33210.4.5 Cavities 33310.4.5.1 Nanobeams 33310.4.5.2 Two-Dimensional Photonic Crystals 33310.4.5.3 Ring Resonators  33410.5 Polycrystalline Thin Films 33510.5.1 Properties 33510.5.2 Optical Structures in Polycrystalline Films 33710.5.2.1 Ring Resonators 33710.5.2.2 Two-Dimensional Photonic Crystals  33710.6 Hybrid Approaches 33810.6.1 Nanomanipulation of Nanodiamond 33810.7 Conclusions and Outlook 340 Acknowledgments 343 References 343

11 ThermalManagementofLasersandLEDsUsingDiamond 353 AlanJ.Kemp,John-MarkHopkins,JenniferE.Hastie,StephaneCalvez,

YanfengZhang,ErdanGu,MartinD.Dawson,andDavidBurns11.1 Introduction 35311.1.1 The Requirement for Thermal Management of Lasers and LEDs 35311.1.2 The Advantages of Diamond: Thermal Conductivity and Rigidity 35411.2 The Use of Diamond in Lasers: A Brief Review 35511.2.1 Diamond as a Sub-Mount for Lasers 35511.2.2 Intracavity Applications of Diamond for Thermal Management 35511.2.3 Direct Exploitation of Diamond as a Laser Gain Material 35611.3 Exploiting the Extreme Properties of Diamond 35711.3.1 Intracavity versus Extracavity Use of Diamond 35711.3.2 Material Requirements for Intracavity Applications 36011.4 Current Uses of Diamond: Semiconductor Disk Lasers 36011.4.1 Semiconductor Disk Lasers: Basic Principles 36011.4.2 Thermal Management Strategies for Semiconductor Disk Lasers 36211.4.2.1 Approaches to the Use of Diamond 362

XII Contents

11.4.2.2 Intracavity and Extracavity Approaches to the Use of Diamond 36311.4.2.3 Intracavity Diamond Heat Spreaders for Wavelength Diversity 36711.4.3 A Review of Progress to Date, and Future Prospects 36811.5 Current Uses of Diamond: Doped-Dielectric Disk Lasers 36911.5.1 Doped-Dielectric Disk Lasers: Diamond Sub-Mounting for Mechanical

Rigidity 36911.5.2 Intracavity Use of Diamond in Doped-Dielectric Disk Lasers 37111.5.3 Future Prospects 37411.6 Current Uses of Diamond: Light-Emitting Diodes 37511.6.1 Introduction 37511.6.2 Diamond as a Heat Spreader in LEDs 37511.6.3 Monolithic Structures and the Epitaxy of Gallium Nitride on

Diamond 37611.6.4 Diamond LEDs 37611.7 Conclusions and Future Directions 376 Acknowledgments 378 References 378

12 LaserMicro-andNanoprocessingofDiamondMaterials 385 VitalyI.Konov,TarasV.Kononenko,andVitaliV.Kononenko12.1 Introduction 38512.2 Laser-Induced Surface Graphitization 38812.2.1 Mechanisms of Diamond Surface Graphitization 38812.2.2 Experimental Data 38912.3 Laser Ablation 39412.3.1 Vaporization Ablation 39512.3.2 Nanoablation 40212.3.3 Photoionization of Diamond 40612.4 Bulk Graphitization of Diamond 41012.4.1 Threshold Conditions 41012.4.2 Laser-Induced Graphitization Waves 41212.4.3 Three-Dimensional (3-D) Laser Writing in Diamond 41412.5 Diamond Laser Processing Techniques 41912.5.1 Laser Polishing 42012.5.2 Formation of Conductive Structures in Diamond 42412.5.3 Surface Structuring 42812.5.4 Diamond Optics 43112.6 Conclusions 438 Acknowledgments 438 References 438

13 FluorescentNanodiamondsandTheirProspectsinBioimaging 445 NitinMohanandHuan-ChengChang13.1 Introduction 44513.2 Color Centers 446

Contents XIII

13.3 Red Fluorescent Nanodiamonds 44813.3.1 Mass Production 44813.3.2 Fluorescence Spectra 45113.3.3 Photostability 45113.3.4 Fluorescence Lifetimes 45313.4 Smaller FNDs 45413.5 Biological Applications 45813.5.1 Fluorescence Resonance Energy Transfer 45813.5.2 Cellular Uptake and Fluorescence Imaging 45913.5.3 Two-Photon Excited Fluorescence Imaging 46013.5.4 Fluorescence Lifetime Imaging 46113.5.5 Super Resolution Imaging 46313.5.6 Single Particle Tracking 46413.5.7 In Vivo Imaging in Caenorhabditis elegans 46513.5.8 Other Imaging Techniques 46713.6 Conclusion 469 References 469

Index 473 ColorPlates 489

Foreword

Practically every publication on research involving diamond materials begins by touting the extreme and unique physical and chemical properties of diamond. It is for this reason that research and applications involving diamond materials has expanded tremendously during the past 25 years. This expansion has been driven by improvements in the synthesis of diamond materials, achieving purity, quality, uniformity, and morphologies that are unattainable in geologically mined dia-monds, and thus enabling many new technological applications.

Today, engineered diamond materials are available in many forms, ranging from single-crystal gems and plates, through a range of polycrystalline plates and shapes with varying grain sizes and morphologies, to films and coatings with nano- to micro-crystalline grain sizes, and nanocrystalline powders. This diversity in diamond materials has attracted research and applications in many fields, including optics and lasers, quantum computing and communication, biology, high-energy and high-pressure physics, thermal management, tribology, electro-chemistry, electronics, micro-electromechanical systems (MEMS), chemical sens-ing, and corrosion resistance.

The primary driver behind this blossoming of diamond materials is the rapid improvements and expansion in diamond synthesis achieved via by chemical vapor deposition (CVD). Improvements in diamond synthesis by high-pressure, high-temperature (HPHT) processes, and of nanopowders by detonation processes, have also contributed to the diverse research and applications of diamond.

Our expanding knowledge base on diamond materials, and their properties and processing, requires that we expand upon the existing array of books and reviews in the field. Given the intense interest in the applications of the many forms of diamond to optics and optical applications, this new book – Optical Engineering of Diamond – is a welcome and valuable addition to the field. The book will immediately assist many of the exciting and important developments employing diamond materials and their optical properties that are about to happen. Examples of the fields which will be impacted are quantum devices, lasers, infrared sensing, radiation detection, synchrotron and accelerator technologies, fusion research, biological research and drug delivery, jewelry and gems, and high-power and high-voltage electronics.

XV

XVI Foreword

This book contains 13 chapters written by the leading experts in their subfields. The chapters compile and review a knowledge base that is not available anywhere else, and provide guidance for the processing, forming, shaping, and building of devices and structures from diamond materials. As such, Optical Engineering of Diamond will become a valuable reference work for researchers and technologists working with diamond materials.

J.E. ButlerRetired

U.S. Naval Research Laboratory, Washington, DCCubic Carbon Ceramics, Huntingtown, MD

Preface

If one were to carry out a survey on the most important materials in optics that come to mind, the responses might include silica, yttrium aluminum garnet, and gallium arsenide. Over and above core optical properties such as transparency and luminescence, other important considerations come into play including dura-bility, ease of manufacture, and thermal conductivity. But what if a material existed that displayed all of these properties on a vastly superior scale? A material of exceptional hardness, thermal conductivity, and transparency, that was also cheap, and easy to fabricate and modify? It is well known that diamond exhibits some of these properties and is indeed often touted as a being a “super material”; however, it also has a reputation for being expensive and difficult to synthesize, and still maintains the perception of being reserved for the wealthy. Nevertheless, the synthesis of diamond has advanced enormously in recent years, with diamonds of sizes spanning from several nanometers to multiple centimeters now routinely produced with qualities that often exceed that of natural diamond. This capability has come after innumerable failed attempts to make diamond, and we can now consider ourselves privileged to witness and participate in this “golden” age of diamond optics and photonics.

Today, considerable research efforts are underway in diverse areas such as diamond optics, photonics, lasers, quantum computing, and biomedicine. In quantum technologies for example, it is the room-temperature rigidity of the crystal lattice that is being harnessed to study quantum effects in an ideal isolated environment. The possibilities are multiplied with ground-breaking parallel devel-opments in nanoscale imaging and manipulation, enabling the use of ultra-small diamonds in unique bioimaging technologies. Science magazines, general media, and blogs continuously report new developments, and some have already led to commercially available products. Just as the unique aesthetic properties of diamond have fascinated over millennia, so the fascination continues with renewed inten-sity for properties which have always resided just below the surface.

By capturing the state of the art in diamond optical engineering, this book aims to provide a resource in a convenient and accessible form to support further research and development. Written by 39 experts from 12 leading research groups, the book includes chapters on detailed optical properties, fabrication, and engineering techniques of diamond, and reviews several of its topical optical

XVII

XVIII Preface

applications. By way of introduction, Chapter 1 provides an in-depth review of the linear and nonlinear optical properties intrinsic to diamond. Six subsequent chap-ters deal with growth and shaping methods, and with engineering the content of diamond. In Chapter 2, I. Friel reviews diamond growth by chemical vapor deposi-tion, and includes descriptions of the growth principles and of properties and applications of high-optical-quality material. In Chapter 3, J.R. Hird describes the fascinating history of diamond polishing, and reviews in detail modern polishing techniques and the associated wear mechanisms and surface properties. This chapter also includes a description of techniques used to achieve surface rough-nesses approaching atomic dimensions. In Chapter 4, written by F. Nikolajeff and M. Karlsson, techniques used to create refractive elements such as domes, diffrac-tive optics, and lens arrays are reviewed. Recipes for plasma based-techniques for producing micro-structures are a valuable feature of this chapter. In Chapter 5, C. Bradac, T. Gaebel, and J.R. Rabeau, review the properties, synthesis, and applica-tions of nitrogen-vacancy color centers in diamond, a vitally important topic that underpins a large focus of present-day diamond optical research. The possibility of creating diamond light-emitting diodes and laser diodes was one of the early drivers for diamond synthesis, and progress in this challenging task is reviewed in Chapter 6 by S. Koizumi and T. Makino, who also discuss in detail the electro-optical properties of n-doped diamond. Surface optics is a topic of growing impor-tance; hence, in Chapter 7, V. Petrakova, M. Ledvina, and M. Nesladek report experimental and modeling results on the effects of the surface proximity and the lattice termination on the properties of color centers. The applications for this phenomenon in areas such as biosensing are also discussed in this chapter.

The chapters in the final section of the book provide a comprehensive review of the major and topical optical applications. In Chapter 8, R.P. Mildren, A. Sabella, O. Kitzler, D.J. Spence, and A.M. McKay review the recent progress of diamond Raman lasers, and discuss the highly promising outlook for creating high-power devices of broad wavelength reach. In Chapter 9, P. Neumann and J. Wrachtrup provide a detailed description of the optical and spin properties of the nitrogen vacancy center and discuss the important application area in quantum information processing. Subsequently, in Chapter 10, S. Tomljenovic-Hanic, T.J. Karle, A.D. Greentree, B.C. Gibson, B.A. Fairchild, A. Stacey, and S. Prawer describe applications for fluorescent diamond in quantum key distribution and metrology, and compre-hensively review the methods used to create the enabling photonic structures such as waveguides and optical cavities. The use of diamond as heat-spreaders in optical systems such as high-average-power lasers and light-emitting diodes is reviewed in Chapter 11 by A.J. Kemp, J.-M. Hopkins, J.E. Hastie, S. Calvez, Y. Zhang, E. Gu, M.D. Dawson, and D. Burns. This chapter includes model results that highlight design considerations and optical applications in which diamond provides striking advantages. Direct write laser fabrication is a highly practical method for manipu-lating the surface and bulk of diamond, and in Chapter 12, V.I. Konov, T.V. Kononenko, and V.V. Kononenko report extensively on the principles of laser processing; these authors also discuss in detail a large range of applications such as laser polishing, the fabrication of diffractive optics, and direct-write of conduc-

Preface XIX

tive structures in the bulk. Finally, in Chapter 13, N. Mohan and H.-C. Chang review the applications of fluorescent nanodiamond in biomedicine. This chapter describes the properties of nanoprobes, the challenges involved in their mass production, and the numerous ways that they are being used in vivo and in vitro for particle tracking and bioimaging.

This book constitutes important milestones in the fields of optical device engi-neering and diamond science. We are very grateful to the contributing authors, who all responded enthusiastically to our invitation and produced extremely valu-able chapters. We also acknowledge the contributions of numerous colleagues who have shared our enthusiasm for this project, and the editorial staff at Wiley for their assistance, in particular Valerie Moliere and Anja Tschörtner. Many thanks to Andy Edmonds, Stefania Castelletto, and Torston Gaebel for their assistance in proofing manuscripts. We are grateful to Jim Butler for supporting the book concept from the outset, providing expert advice along the way, and for contribut-ing the Foreword. The future of diamond optics is bright, and we look forward to the exciting developments ahead.

Rich P. Mildren and James R. RabeauSydney, August 2012

List of Contributors

Carlo BradacMacquarie UniversityDepartment of Physics and AstronomySydney, NSW 2109Australia

David BurnsUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NWUK

Stephane CalvezUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NWUK

Huan-Cheng ChangAcademia SinicaInstitute of Atomic and Molecular SciencesTaipei 106 Taiwan

Martin D. DawsonUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NWUK

XXI

Barbara A. FairchildUniversity of MelbourneSchool of PhysicsParkville, Vic 3010Australia

Ian FrielElement SixKing’s Ride ParkAscot SL5 8BPUK

Torsten GaebelMacquarie UniversityDepartment of Physics and AstronomySydney, NSW 2109Australia

Brant C. GibsonUniversity of MelbourneSchool of PhysicsParkville, Vic 3010Australia

Andrew D. GreentreeUniversity of MelbourneSchool of PhysicsParkville, Vic 3010Australia

XXII ListofContributors

Erdan GuUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NWUK

Jennifer E. HastieUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NWUK

Jonathan R. HirdUniversity of CaliforniaLos AngelesDepartment of Physics and AstronomyLos Angeles, CA 90095-1547USA

John-Mark HopkinsUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NWUK

Timothy J. KarleUniversity of MelbourneSchool of PhysicsParkville, Vic 3010Australia

Mikael KarlssonUppsala UniversityThe Ångström LaboratoryP.O. Box 534751 21 UppsalaSweden

Alan J. KempUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NWUK

Ondrej KitzlerMacquarie UniversityMQ Photonics Research CentreSydney, NSW 2109Australia

Satoshi KoizumiNational Institute for Materials ScienceWide Bandgap Materials Group1-1 NamikiTsukuba 305-0044Japan

Taras V. KononenkoGeneral Physics InstituteNatural Sciences CenterVavilova Street, 38Moscow 119991Russia

Vitali V. KononenkoGeneral Physics InstituteNatural Sciences CenterVavilova Street, 38Moscow 119991Russia

Vitaly I. KonovGeneral Physics InstituteNatural Sciences CenterVavilova Street, 38Moscow 119991Russia

ListofContributors XXIII

Miroslav LedvinaInstitute of Organic Chemistry and BiochemistryAcademy of Sciences of the Czech Republicv.v.i., Flemingovo n. 2166 10 Prague 6Czech Republic

Toshiharu MakinoNational Institute of Advanced Industrial Science and TechnologyEnergy Technology Research Institute1-1-1 UmezonoTsukuba 305-8568Japan

Aaron M. McKayMacquarie UniversityMQ Photonics Research CentreSydney, NSW 2109Australia

Richard P. MildrenMacquarie UniversityMQ Photonics Research CentreSydney, NSW 2109Australia

Nitin MohanAcademia SinicaInstitute of Atomic and Molecular SciencesTaipei 106, Taiwan

Milos NesladekUniversity HasseltInstitute for Materials ResearchIMECIMOMEC DivisionWetenschapspark 13590 DiepenbeekBelgium

Philipp NeumannUniversität StuttgartPhysikalisches Institut70569 StuttgartGermany

Fredrik NikolajeffUppsala UniversityThe Ångström LaboratoryP.O. Box 534751 21 UppsalaSweden

Vladimira PetrakovaInstitute of PhysicsAcademy of Sciences of the Czech Republicv.v.i., Na Slovance 2182 21 Prague 8Czech RepublicandCzech Technical University in PragueFaculty of Biomedical EngineeringSítná sq. 3105272 01 KladnoCzech Republic

Steven PrawerUniversity of MelbourneSchool of PhysicsParkville, Vic 3010Australia

James R. RabeauMacquarie UniversityDepartment of Physics and AstronomySydney, NSW 2109Australia

XXIV ListofContributors

Alexander SabellaMacquarie UniversityMQ Photonics Research CentreSydney, NSW 2109AustraliaandDefence Science and Technology OrganisationEdinburgh, South Australia 5111Australia

David J. SpenceMacquarie UniversityMQ Photonics Research CentreSydney, NSW 2109Australia

Alastair StaceyUniversity of MelbourneSchool of PhysicsParkville, Vic 3010Australia

Snjezana Tomljenovic-HanicUniversity of MelbourneSchool of PhysicsParkville, Vic 3010Australia

Jörg WrachtrupUniversität StuttgartPhysikalisches Institut70569 StuttgartGermany

Yanfeng ZhangUniversity of StrathclydeInstitute of Photonics106 RottenrowGlasgow G4 0NWUK

1

IntrinsicOpticalPropertiesofDiamondRichP.Mildren

Diamond comprises the lowest mass element that can form a stable covalently bonded crystal lattice, and this lattice is highly symmetric and tightly bound. Its resulting extreme properties, along with the recent developments in its synthesis, have led to an explosion of interest in the material for a diverse range of optical technologies including sensors, sources, and light manipulators. The optical prop-erties in many respects sit well apart from those of other materials, and therefore offer the tantalizing prospect of greatly enhanced capability. A detailed knowledge base of the interaction of electromagnetic radiation with the bulk and the surface of diamond is of fundamental importance in assisting optical design.

For any material, the dataset characterizing optical performance is large and diamond is no exception despite its inherent lattice simplicity. The properties of interest extend over a large range of optical frequencies, intensities and environ-mental parameters, and for many variants of the diamond form including defect and impurity levels, crystal size, and isotopic composition. Over and above the fascination held for this ancient material, its highly symmetric structure and pure natural isotopic content (98.9% 12C) provides an outstanding example for under-pinning solid-state theory. As a result, diamond has been extensively studied and its optical properties are better known than most other materials.

Many excellent reviews of optical properties have been reported previously (see e.g. Refs [1–3]). These concentrate mainly on linear optical properties, often focus on extrinsic phenomena, and are written from perspectives outside of the field of optics, such as electronics and solid-state physics. Consequently, there is a need to consolidate the data from the perspective of optical design. Furthermore, the nonlinear optical properties of diamond have not to date been comprehensively reviewed. The aim of this chapter is to do this, with emphasis placed on the intrin-sic properties of single-crystal diamond (i.e., pure Type IIa diamond1)). The chapter

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Optical Engineering of Diamond, First Edition. Edited by Rich P. Mildren and James R. Rabeau.© 2013 Wiley-VCH Verlag GmbH & Co. KGaA. Published 2013 by Wiley-VCH Verlag GmbH & Co. KGaA.

1) Type IIa represents the most pure form; other categories (Types Ia, Ib, and IIb) have substantial levels of nitrogen (Type Ia and Ib) and/or boron impurity (Type IIb). Note that the delineations between types are not well defined. Type IIa are rarely found as

large homogeneous crystals in nature as nitrogen aids the formation process. It is thus for historical reasons that nitrogen-doped diamonds, which provide the major source of natural gemstones, are categorized as Type I.

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also includes the dependence of optical properties on basic variables such as wavelength, temperature, and isotopic composition. Although the scope is limited to bulk intrinsic properties, the intention is to stimulate a further expansion of the knowledge base as the limits of measurement resolution and performance are extended, and as more detailed investigations emerge into areas such as surface optics, crystal variants, and nano-optical effects.

The chapter focuses on the optical properties spanning from ultraviolet (UV) to infrared (IR). It should be noted that, throughout the chapter, Système Interna-tionale (SI) units have been used, apart from some exceptions to stay with conven-tions. The data provided refer to diamond with the naturally occurring isotopic ratio, unless specifically stated otherwise.

1.1Transmission

Diamond has a wide bandgap and lacks first-order infrared absorption, which makes it one of the most broadly transmitting of all solids. As shown in Figure 1.1, the transmission spectrum for a diamond window is featureless for wave-lengths longer than approximately 225 nm (α < 1 cm−1 for λ > 235 nm), apart from a moderate absorption in the range 2.6 to 6.2 µm and extending weakly outside each side. Indeed, there is no absorption in the long-wavelength limit, which is a characteristic of the Group IV elements (e.g., Si and Ge) that share the diamond

Figure1.1 Transmission spectrum for a Type IIa diamond window (“Type IIIa,” Element 6) of 1 mm thickness. The spectrum was measured using a Cary 5000 spectrom-eter (UV-near IR) and Bruker Zertex 80 (>2 µm; resolution 4 cm−1). The transmission for Fresnel loss only (dashed curve) was

calculated using the relation described in the text and in Equation (1.6). The small difference between the dashed and measured curves in the regions away from the UV-edge and lattice absorption is largely attributed to the combination of spectrometer calibration error and scatter in the sample.

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lattice symmetry. UV-edge absorption, infrared lattice absorption and Fresnel reflection dominate the wavelength dependence for transmission. The Fresnel reflection at each diamond–air interface is approximately 17% in the visible (R = 17.1% at 632 nm), and when accounting for multiple reflections between each surface this leads to a maximum transmission of (1 − R)2/(1 − R2) = 70.8%. Using dispersion data for the refractive index (see Section 1.4), the transmission upper limit (no absorption) is shown as a function of wavelength (dashed line in Figure 1.1).

1.2LatticeAbsorption

The absorption in the mid-IR, which is most prominent in the range 2.6 to 6.2 µm, arises due to the coupling of radiation with the movement of nuclei, and is often referred to as “lattice” or “multiphonon” absorption. The magnitude and shape of the absorption spectrum is a consequence of the vibrational properties of the crystal lattice, which are governed by the forces between neighboring atoms and the symmetry of collective vibrations. The theoretical framework that most suc-cessfully describes the spectrum has been developed since the 1940s, stimulated by the pioneering work of Sir C.V. Raman on diamond’s optical properties and Max Born on the quantum theory of crystals. It is interesting to note that, although diamond’s lattice is one of the most simple, there have been substantial contro-versies in explaining the spectrum (see e.g., Ref. [4]) and there are on-going chal-lenges to thoroughly explain some of the features.

A brief and qualitative summary of the theory of lattice absorption is provided here to assist in an understanding of the IR spectrum’s dependence on important material and environmental parameters such as impurity levels, isotopic content, and temperature. A greatly simplifying and important aspect is that there is no one-phonon absorption in pure, defect-free diamond (which would appear most strongly near 7.5 µm for diamond), as also for other monatomic crystals with inversion symmetry such as Si and Ge. The movement of nuclei in vibrational modes of the lattice are countered by equal and opposite movement of neighbors, so that no dipole moment for coupling with radiation is induced. One-phonon absorption may proceed by spoiling the local symmetry through, for example, lattice imperfections (impurities and defects) or by the application of electric field. Dipole moments may also be induced in the crystal via interaction of the incident photon with more than one phonon, although with reduced oscillator strength; this is the origin of lattice absorption in pure diamond. From a classical viewpoint, the absorption mechanism can be qualitatively understood as one phonon inducing a net charge on atoms, and a second phonon (or more) vibrating the induced charge to create a dipole moment [5]. The maximum phonon fre-quency that can be transmitted by the lattice is 1332 cm−1 (which corresponds to the zero-momentum optical phonon and the Raman frequency), and integer multiples of this frequency at 3.75 µm (2665 cm−1) and 2.50 µm (3997 cm−1) mark

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the short-wavelength limits for two- and three-phonon absorption regions. The demarcations between two- and three-phonon absorption are clearly evident in the transmission spectrum of Figure 1.1 and the logarithmic plot of lattice absorption in Figure 1.2 [6]. Between wavelengths 3.75 and 6 µm, the lattice absorption at room temperature is strongest with a peak of approximately 10 cm−1 at 4.63 µm, and is primarily attributable to two-phonon absorption.

1.2.1 TheTwo-PhononRegion

Absorption may involve the creation and destruction of phonons, which are con-strained to certain energies and wavevectors as a result of the symmetry and interatomic forces. For two-phonon creation, the absorption at a given frequency is proportional to the number of pairs of modes of the created phonons and a transition probability that takes into consideration allowed phonon combinations (e.g., longitudinal or transverse) and the transition oscillator strength. The number of allowed combinations of a given energy is usually highest for phonon wavevec-tors along directions of high symmetry in the lattice, and with momenta that

Figure1.2 Two-, three-, and four-phonon lattice absorption bands. The underlying figure showing the calculated (smooth solid curve) and measured absorption spectra is

reprinted with permission from Ref. [6]; © 1994, SPIE. The measurements were collated from several sources, as detailed in the reference.

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