Optical Properties of Materials and Their Applications
Description
Featuring contributions by noted experts in the field of electronic and optoelectronic materials and photonics, this book looks at the optical properties of materials as well as their physical processes and various classes. Taking a semi-quantitative approach to the subject, it presents a summary of the basic concepts, reviews recent developments in the study of optical properties of materials and offers many examples and applications.
Optical Properties of Materials and Their Applications, 2nd Edition starts by identifying the processes that should be described in detail and follows with the relevant classes of materials. In addition to featuring four new chapters on optoelectronic properties of organic semiconductors, recent advances in electroluminescence, perovskites, and ellipsometry, the book covers: optical properties of disordered condensed matter and glasses; concept of excitons; photoluminescence, photoinduced changes, and electroluminescence in noncrystalline semiconductors; and photoinduced bond breaking and volume change in chalcogenide glasses. Also included are chapters on: nonlinear optical properties of photonic glasses; kinetics of the persistent photoconductivity in crystalline III-V semiconductors; and transparent white OLEDs. In addition, readers will learn about excitonic processes in quantum wells; optoelectronic properties and applications of quantum dots; and more.
* Covers all of the fundamentals and applications of optical properties of materials
* Includes theory, experimental techniques, and current and developing applications
* Includes four new chapters on optoelectronic properties of organic semiconductors, recent advances in electroluminescence, perovskites, and ellipsometry
* Appropriate for materials scientists, chemists, physicists and electrical engineers involved in development of electronic materials
* Written by internationally respected professionals working in physics and electrical engineering departments and government laboratories
Optical Properties of Materials and Their Applications, 2nd Edition is an ideal book for senior undergraduate and postgraduate students, and teaching and research professionals in the fields of physics, chemistry, chemical engineering, materials science, and materials engineering.
More details
Other editions
Additional editions
Person
Edited by
Jai Singh, AM, PhD, College of Engineering, IT and Environment, Charles Darwin University, Darwin, Australia.
Series Editors
Arthur Willoughby University of Southampton, Southampton, UK
Peter Capper formerly of Ex-Leonardo M. W. Ltd, Southampton, UK
Safa Kasap University of Saskatchewan, Saskatoon, Canada
Content
List of Contributors xv
Series Preface xvii
Preface xix
1 Fundamental Optical Properties of Materials I 1
S.O. Kasap, W.C. Tan, Jai Singh, and Asim K. Ray
1.1 Introduction 1
1.2 Optical Constants n and K 2
1.2.1 Refractive Index and Extinction Coefficient 2
1.2.2 n and K, and Kramers-Kronig Relations 5
1.3 Refractive Index and Dispersion 7
1.3.1 Cauchy Dispersion Relation 7
1.3.2 Sellmeier Equation 8
1.3.3 Refractive Index of Semiconductors 10
1.3.3.1 Refractive Index of Crystalline Semiconductors 10
1.3.3.2 Bandgap and Temperature Dependence 11
1.3.4 Refractive Index of Glasses 11
1.3.5 Wemple-DiDomenico Dispersion Relation 14
1.3.6 Group Index 15
1.4 The Swanepoel Technique: Measurement of n and ¿¿¿¿ for Thin Films on Substrates 16
1.4.1 Uniform Thickness Films 16
1.4.2 Thin Films with Non-uniform Thickness 22
1.5 Transmittance and Reflectance of a Partially Transparent Plate 25
1.6 Optical Properties and Diffuse Reflection: Schuster-Kubelka-Munk Theory 27
1.7 Conclusions 31
Acknowledgments 31
References 32
2 Fundamental Optical Properties of Materials II 37
S.O. Kasap, K. Koughia, Jai Singh, Harry E. Ruda, and Asim K. Ray
2.1 Introduction 37
2.2 Lattice or Reststrahlen Absorption and Infrared Reflection 40
2.3 Free Carrier Absorption (FCA) 42
2.4 Band-to-Band or Fundamental Absorption (Crystalline Solids) 45
2.5 Impurity Absorption and Rare-Earth Ions 48
2.6 Effect of External Fields 54
2.6.1 Electro-Optic Effects 54
2.6.2 Electro-Absorption and Franz-Keldysh Effect 55
2.6.3 Faraday Effect 56
2.7 Effective Medium Approximations 58
2.8 Conclusions 61
Acknowledgments 61
References 62
3 Optical Properties of Disordered Condensed Matter 67
Koichi Shimakawa, Jai Singh, and S.K. O'Leary
3.1 Introduction 67
3.2 Fundamental Optical Absorption (Experimental) 69
3.2.1 Amorphous Chalcogenides 69
3.2.2 Hydrogenated Nano-Crystalline Silicon (nc-Si:H) 72
3.3 Absorption Coefficient (Theory) 74
3.4 Compositional Variation of the Optical Bandgap 79
3.4.1 In Amorphous Chalcogenides 79
3.5 Conclusions 80
References 80
4 Optical Properties of Glasses 83
Andrew Edgar
4.1 Introduction 83
4.2 The Refractive Index 84
4.3 Glass Interfaces 86
4.4 Dispersion 88
4.5 Sensitivity of the Refractive Index 90
4.5.1 Temperature Dependence 90
4.5.2 Stress Dependence 91
4.5.3 Magnetic Field Dependence-The Faraday Effect 92
4.5.4 Chemical Perturbations-Molar Refractivity 94
4.6 Glass Color 95
4.6.1 Coloration by Colloidal Metals and Semiconductors 95
4.6.2 Optical Absorption in Rare-Earth-Doped Glass 96
4.6.3 Absorption by 3d Metal Ions 99
4.7 Fluorescence in Rare-Earth-Doped Glass 102
4.8 Glasses for Fiber Optics 104
4.9 Refractive Index Engineering 106
4.10 Glass and Glass-Fiber Lasers and Amplifiers 109
4.11 Valence Change Glasses 111
4.12 Transparent Glass Ceramics 114
4.12.1 Introduction 114
4.12.2 Theoretical Basis for Transparency 116
4.12.3 Rare-Earth-Doped Transparent Glass Ceramics for Active Photonics 120
4.12.4 Ferroelectric Transparent Glass Ceramics 121
4.12.5 Transparent Glass Ceramics for X-ray Storage Phosphors 121
4.13 Conclusions 124
References 124
5 Concept of Excitons 129
Jai Singh, Harry E. Ruda, M.R. Narayan, and D. Ompong
5.1 Introduction 129
5.2 Excitons in Crystalline Solids 130
5.2.1 Excitonic Absorption in Crystalline Solids 133
5.3 Excitons in Amorphous Semiconductors 135
5.3.1 Excitonic Absorption in Amorphous Solids 137
5.4 Excitons in Organic Semiconductors 139
5.4.1 Photoexcitation and Formation of Excitons 140
5.4.1.1 Photoexcitation of Singlet Excitons Due to Exciton-Photon Interaction 141
5.4.1.2 Excitation of Triplet Excitons 142
5.4.2 Exciton Up-Conversion 147
5.4.3 Exciton Dissociation 148
5.4.3.1 Conversion from Frenkel to CT Excitons 151
5.4.3.2 Dissociation of CT Excitons 152
5.5 Conclusions 153
References 154
6 Photoluminescence 157
Takeshi Aoki
6.1 Introduction 157
6.2 Fundamental Aspects of Photoluminescence (PL) in Materials 158
6.2.1 Intrinsic Photoluminescence 159
6.2.2 Extrinsic Photoluminescence 160
6.2.3 Up-Conversion Photoluminescence (UCPL) 162
6.2.4 Other Related Optical Transitions 163
6.3 Experimental Aspects 164
6.3.1 Static PL Spectroscopy 164
6.3.2 Photoluminescence Excitation Spectroscopy (PLE) and Photoluminescence Absorption Spectroscopy (PLAS) 167
6.3.3 Time Resolved Spectroscopy (TRS) 168
6.3.4 Time-Correlated Single Photon Counting (TCSPC) 171
6.3.5 Frequency-Resolved Spectroscopy (FRS) 172
6.3.6 Quadrature Frequency Resolved Spectroscopy (QFRS) 173
6.4 Photoluminescence Lifetime Spectroscopy of Amorphous Semiconductors by QFRS Technique 175
6.4.1 Overview 175
6.4.2 Dual-Phase Double Lock-in (DPDL) QFRS Technique 176
6.4.3 Exploring Broad PL Lifetime Distribution in a-Si:H by Wideband QFRS 178
6.4.3.1 Effects of Excitation Intensity, Excitation, and Emission Energies 179
6.4.3.2 Temperature Dependence 184
6.4.3.3 Effect of Electric and Magnetic Fields 185
6.4.4 Residual PL Decay of a-Si:H 189
6.5 QFRS on Up-Conversion Photoluminescence (UCPL) of RE-Doped Materials 192
6.6 Conclusions 197
Acknowledgments 198
References 198
7 Photoluminescence, Photoinduced Changes, and Electroluminescence in Noncrystalline Semiconductors 203
Jai Singh
7.1 Introduction 203
7.2 Photoluminescence 205
7.2.1 Radiative Recombination Operator and Transition Matrix Element 206
7.2.2 Rates of Spontaneous Emission 211
7.2.2.1 At Nonthermal Equilibrium 212
7.2.2.2 At Thermal Equilibrium 214
7.2.2.3 Determining E0 215
7.2.3 Results of Spontaneous Emission and Radiative Lifetime 216
7.2.4 Temperature Dependence of PL 222
7.2.5 Excitonic Concept 223
7.3 Photoinduced Changes in Amorphous Chalcogenides 225
7.3.1 Effect of Photo-Excitation and Phonon Interaction 226
7.3.2 Excitation of a Single Electron-Hole Pair 228
7.3.3 Pairing of Like Excited Charge Carriers 229
7.4 Radiative Recombination of Excitons in Organic Semiconductors 232
7.4.1 Rate of Fluorescence 233
7.4.2 Rate of Phosphorescence 233
7.4.3 Organic Light Emitting Diodes (OLEDs) 234
7.4.3.1 Second- and Third-Generation OLEDs: TADF 235
7.5 Conclusions 236
Acknowledgments 236
References 237
8 Photoinduced Bond Breaking and Volume Change in Chalcogenide Glasses 241
Sandor Kugler, Rozália Lukács, and Koichi Shimakawa
8.1 Introduction 241
8.2 Atomic-Scale Computer Simulations of Photoinduced Volume Changes 243
8.3 Effect of Illumination 244
8.4 Kinetics of Volume Change 245
8.4.1 a-Se 245
8.4.2 a-As2Se3 246
8.5 Additional Remarks 248
8.6 Conclusions 249
References 249
9 Properties and Applications of Photonic Crystals 251
Harry E. Ruda and Naomi Matsuura
9.1 Introduction 251
9.2 PC Overview 252
9.2.1 Introduction to PCs 252
9.2.2 Nanoengineering of PC Architectures 253
9.2.3 Materials Selection for PCs 255
9.3 Tunable PCs 255
9.3.1 Tuning PC Response by Changing the Refractive Index of Constituent Materials 256
9.3.1.1 PC Refractive Index Tuning Using Light 256
9.3.1.2 PC Refractive Index Tuning Using an Applied Electric Field 256
9.3.1.3 Refractive Index Tuning of Infiltrated PCs 257
9.3.1.4 PC Refractive Index Tuning by Altering the Concentration of Free Carriers (Using Electric Field or Temperature) in Semiconductor-Based PCs 257
9.3.2 Tuning PC Response by Altering the Physical Structure of the PC 258
9.3.2.1 Tuning PC Response Using Temperature 258
9.3.2.2 Tuning PC Response Using Magnetism 258
9.3.2.3 Tuning PC Response Using Strain 258
9.3.2.4 Tuning PC Response Using Piezoelectric Effects 259
9.3.2.5 Tuning PC Response Using MEMS Actuation 260
9.4 Selected Applications of PC 260
9.4.1 Waveguide Devices 261
9.4.2 Dispersive Devices 262
9.4.3 Add/Drop Multiplexing Devices 262
9.4.4 Applications of PCs for Light-Emitting Diodes (LEDs) and Lasers 263
9.5 Conclusions 265
Acknowledgments 265
References 265
10 Nonlinear Optical Properties of Photonic Glasses 269
Keiji Tanaka
10.1 Introduction 269
10.2 Photonic Glass 271
10.3 Nonlinear Absorption and Refractivity 272
10.3.1 Fundamentals 272
10.3.2 Two-Photon Absorption 275
10.3.3 Nonlinear Refractivity 278
10.4 Nonlinear Excitation-Induced Structural Changes 280
10.4.1 Fundamentals 280
10.4.2 Oxides 281
10.4.3 Chalcogenides 283
10.5 Conclusions 285
10.A Addendum: Perspectives on Optical Devices 286
References 288
11 Optical Properties of Organic Semiconductors 295
Takashi Kobayashi and Hiroyoshi Naito
11.1 Introduction 295
11.2 Molecular Structure of p-Conjugated Polymers 296
11.3 Theoretical Models 298
11.4 Absorption Spectrum 300
11.5 Photoluminescence 304
11.6 Non-Emissive Excited States 306
11.7 Electron-Electron Interaction 309
11.8 Interchain Interaction 314
11.9 Conclusions 320
References 321
12 Organic Semiconductors and Applications 323
Furong Zhu
12.1 Introduction 323
12.1.1 Device Architecture and Operation Principle 324
12.1.2 Technical Challenges and Process Integration 325
12.2 Anode Modification for Enhanced OLED Performance 327
12.2.1 Low-Temperature High-Performance ITO 327
12.2.1.1 Experimental Methods 328
12.2.1.2 Morphological Properties 329
12.2.1.3 Electrical Properties 331
12.2.1.4 Optical Properties 333
12.2.1.5 Compositional Analysis 336
12.2.2 Anode Modification 339
12.2.3 Electroluminescence Performance of OLEDs 340
12.3 Flexible OLEDs 345
12.3.1 Flexible OLEDs on Ultrathin Glass Substrate 346
12.3.2 Flexible Top-Emitting OLEDs on Plastic Foils 347
12.3.2.1 Top-Emitting OLEDs 348
12.3.2.2 Flexible TOLEDs on Plastic Foils 350
12.4 Solution-Processable High-Performing OLEDs 353
12.4.1 Performance of OLEDs with a Hybrid MoO3-PEDOT:PSS Hole Injection Layer (HIL) 353
12.4.2 Morphological Properties of the MoO3-PEDOT:PSS HIL 361
12.4.3 Surface Electronic Properties of MoO3-PEDOT:PSS HIL 363
12.5 Conclusions 368
References 369
13 Transparent White OLEDs 373
Choi Wing Hong and Furong Zhu
13.1 Introduction-Progress in Transparent WOLEDs 373
13.2 Performance of WOLEDs 374
13.2.1 Optimization of Dichromatic WOLEDs 374
13.2.2 J-L-V Characteristics of WOLEDs 377
13.2.3 Electron-Hole Current Balance in Transparent WOLEDs 384
13.3 Emission Behavior of Transparent WOLEDs 386
13.3.1 Visible-Light Transparency of WOLEDs 386
13.3.2 L-J Characteristics of Transparent WOLEDs 390
13.3.3 Angular-Dependent Color Stability of Transparent WOLEDs 395
13.4 Conclusions 400
References 400
14 Optical Properties of Thin Films 403
V.-V. Truong, S. Tanemura, A. Haché, and L. Miao
14.1 Introduction 403
14.2 Optics of Thin Films 404
14.2.1 An Isotropic Film on a Substrate 404
14.2.2 Matrix Methods for Multi-Layered Structures 406
14.2.3 Anisotropic Films 407
14.3 Reflection-Transmission Photoellipsometry for Determination of Optical Constants 408
14.3.1 Photoellipsometry of a Thick or a Thin Film 408
14.3.2 Photoellipsometry for a Stack of Thick and Thin Films 410
14.3.3 Remarks on the Reflection-Transmission Photoellipsometry Method 412
14.4 Application of Thin Films to Energy Management and Renewable-Energy Technologies 412
14.4.1 Electrochromic Thin Films 413
14.4.2 Pure and Metal-Doped VO2 Thermochromic Thin Films 414
14.4.3 Temperature-Stabilized V1-xWxO2 Sky Radiator Films 417
14.4.4 Optical Functional TiO2 Thin Film for Environmentally Friendly Technologies 420
14.5 Application of Tunable Thin Films to Phase and Polarization Modulation 424
14.6 Conclusions 430
References 430
15 Optical Characterization of Materials by Spectroscopic Ellipsometry 435
J. Mistrík
15.1 Introduction 435
15.2 Notions of Light Polarization 436
15.3 Measureable Quantities 438
15.4 Instrumentation 441
15.5 Single Interface 442
15.6 Single Layer 448
15.7 Multilayer 454
15.8 Linear Grating 458
15.9 Conclusions 462
Acknowledgments 463
References 463
16 Excitonic Processes in Quantum Wells 465
Jai Singh and I.-K. Oh
16.1 Introduction 465
16.2 Exciton-Phonon Interaction 466
16.3 Exciton Formation in QWs Assisted by Phonons 467
16.4 Nonradiative Relaxation of Free Excitons 474
16.4.1 Intraband Processes 475
16.4.2 Interband Processes 479
16.5 Quasi-2D Free-Exciton Linewidth 485
16.6 Localization of Free Excitons 491
16.7 Conclusions 499
References 500
17 Optoelectronic Properties and Applications of Quantum Dots 503
Jørn M. Hvam
17.1 Introduction 503
17.2 Epitaxial Growth and Structure of Quantum Dots 504
17.2.1 Self-Assembled Quantum Dots 504
17.2.2 Site-Controlled Growth on Patterned Substrates 505
17.2.3 Natural or Interface Quantum Dots 506
17.2.4 Quantum Dots in Nanowires 507
17.3 Excitons in Quantum Dots 508
17.3.1 Quantum-Dot Bandgap 509
17.3.2 Optical Transitions 510
17.4 Optical Properties 513
17.4.1 Radiative Lifetime, Oscillator Strength, and Internal Quantum Efficiency 514
17.4.2 Linewidth, Coherence, and Dephasing 516
17.4.3 Transient Four-Wave Mixing 517
17.5 Quantum Dot Applications 520
17.5.1 Quantum Dot Lasers and Optical Amplifiers 520
17.5.1.1 Gain Dynamics 522
17.5.1.2 Homogeneous Broadening and Dephasing 524
17.5.1.3 Long-Wavelength Lasers 526
17.5.1.4 Nano Lasers 527
17.5.2 Single-Photon Emitters 527
17.5.2.1 Micropillars and Nanowires 530
17.5.2.2 Photonic Crystal Waveguide 531
17.6 Conclusions 533
Acknowledgments 534
References 534
18 Perovskites - Revisiting the Venerable ABX3 Family with Organic Flexibility and New Applications 537
Junwei Xu, D.L. Carroll, K. Biswas, F. Moretti, S. Gridin, and R.T.Williams
18.1 Introduction 537
18.1.1 Review 537
18.1.2 The Structures 538
18.1.2.1 Simple Cubic Frameworks 538
18.1.2.2 The Multiplicity of Hybrids 539
18.1.2.3 Structural Variation 540
18.2 Hybrid Perovskites in Photovoltaics 544
18.2.1 Review 544
18.2.2 The Phenomena Characterized as "Defect Tolerance" 548
18.3 Light-Emitting Diodes Using Solution-Processed Lead Halide Perovskites 549
18.3.1 Review 549
18.3.2 Construction and Characterization of LEDs Utilizing CsPbBr3 Nano-Inclusions in Cs4PbBr6 as the Electroluminescent Medium 553
18.4 Ionizing Radiation Detectors Using Lead Halide Perovskite Materials: Basics, Progress, and Prospects 562
18.5 Conclusions 582
Acknowledgments 583
References 583
19 Optical Properties and Spin Dynamics of Diluted Magnetic Semiconductor Nanostructures 589
Akihiro Murayama and Yasuo Oka
19.1 Introduction 589
19.2 Quantum Wells 591
19.2.1 Spin Injection 591
19.2.2 Study of Spin Dynamics by Pump-Probe Spectroscopy 594
19.3 Fabrication of Nanostructures by Electron-Beam Lithography 596
19.4 Self-Assembled Quantum Dots 599
19.5 Hybrid Nanostructures with Ferromagnetic Materials 604
19.6 Conclusions 607
Acknowledgments 608
References 609
20 Kinetics of the Persistent Photoconductivity in Crystalline III-V Semiconductors 611
Ruben Jeronimo Freitas and Koichi Shimakawa
20.1 Introduction 611
20.2 A Review of PPC in III-V Semiconductors 613
20.3 Key Physical Terms Related to PPC 615
20.3.1 Dispersive Reaction 615
20.3.2 SEF and Power Law 616
20.3.3 Waiting Time Distribution 617
20.4 Kinetics of PPC in III-V Semiconductors 617
20.5 Conclusions 623
Acknowledgments 623
20.A On the Reaction Rate Under the Uniform Distribution 623
References 625
Index 627
1
Fundamental Optical Properties of Materials I
S.O. Kasap1, W.C. Tan2, Jai Singh3, and Asim K. Ray4
1Department of Electrical and Computer Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Canada
2Department of Electrical & Computer Engineering, National University of Singapore, Kent Ridge, Singapore
3College of Engineering, IT and Environment, Purple 12, Charles Darwin University, Ellengowan Drive, Darwin, Australia
4Department of Electrical & Computer Engineering, Brunel University London, Kingston Lane, Uxbridge, UK
CHAPTER MENU
- Introduction
- Optical Constants n and K
- Refractive Index and Dispersion
- The Swanepoel Technique: Measurement of n and a for Thin Films on Substrates
- Transmittance and Reflectance of a Partially Transparent Plate
- Optical Properties and Diffuse Reflection: Schuster-Kubelka-Munk Theory
- Conclusions
- References
1.1 Introduction
Optical properties of a material change or affect the characteristics of light passing through it by modifying its propagation vector or intensity. Two of the most important optical parameters are the refractive index n and the extinction coefficient K, which are generically called optical constants, although some authors include other optical coefficients within this terminology. The latter is related to the attenuation or absorption coefficient a. In Part I, in this chapter, we present the complex refractive index, the frequency or wavelength dependence of n and K, so-called dispersion relations, how n and K are inter-related, and how n and K can be determined by studying the transmission as a function of wavelength through a thin film of the material. Physical insights into n and K are provided in Part II (Chapter 2). In addition, there has been a strong research interest in characterizing the optical properties of inhomogeneous media, such as porous media, in which both light absorption and scattering take place so that the reflectance is not specular but diffuse. The latter problem is now included in this second edition.
The optical properties of various materials, with n and K being the most important, are available in the literature in one form or another, either published in journals, books, and handbooks, or posted on websites of various researchers, organizations (e.g. NIST), or companies (e.g. Schott Glass). Nonetheless, the reader is referred to the works of Greenway and Harbeke [1], Wolfe [2], Klocek [3], Palik [4,5], Ward [6], Efimov [7], Palik and Ghosh [8], Nikogosyan [9], and Weaver and Frederikse [10] for the optical properties of a wide range of materials. Adachi's books on the optical constants of semiconductors are highly recommended [11-13], along with Madelung's third edition of Semiconductors: Data Handbook [14]. There are, of course, other books and handbooks that also contain optical constants in various chapters; see, for example, references [15-20]. There are also various books that describe optical properties of solids at the senior undergraduate and introductory graduate levels, such as those by Tanner [21], Jimenez and Tomm [22], Stenzel [23], Fox [24], Simmons and Potter [25], Toyozawa [26], Wooten [27], and Abeles [28], which are highly recommended.
A number of experimental techniques are available for measuring n and K, some of which have been summarized by Simmons and Potter [25]. For example, ellipsometry measures changes in the polarization of light incident on a sample to sensitively characterize surfaces and thin films (see Chapter 23 in this volume). The interaction of incident polarized light with the sample causes a polarization change in the light, which may then be measured by analyzing the light reflected from the sample. Collins has also provided an extensive in-depth review of ellipsometry for optical measurements [29]. One of the most popular and convenient optical experiments involves a monochromatic light passing through a thin sample, and measuring the transmitted intensity as a function of wavelength, T(?), using a simple spectrophotometer. For thin samples on a thick transparent substrate, the transmission spectrum shows oscillations in T(?) with the wavelength due to interferences within the thin film. Swanepoel's technique uses the T(?) measurement to determine n and K, as described in Section 1.4.
1.2 Optical Constants n and K
One of the most important optical constants of a material is its refractive index, which in general depends on the wavelength of the electromagnetic (EM) wave, through a relationship called dispersion. In materials where an EM wave loses its energy during its propagation, the refractive index becomes complex. The real part is usually the refractive index, n, and the imaginary part is called the extinction coefficient, K. In this section, the refractive index and extinction coefficient will be presented in detail, along with some common dispersion relations. A more practical and a semiquantitative approach is taken along the lines in [30] rather than a full dedication to rigor and mathematical derivations. More analytical approaches can be found in other texts, such as [25,26].
1.2.1 Refractive Index and Extinction Coefficient
The refractive index of an optical or dielectric medium, n, is the ratio of the velocity of light c in vacuum to its velocity v in the medium; n = c/v. Using this and Maxwell's equations, one obtains the well-known Maxwell's formula for the refractive index of a substance as , where er is the static dielectric constant or relative permittivity and µr the relative magnetic permeability of the medium. As µr = 1 for nonmagnetic substances, one gets , which is very useful in relating the dielectric properties to optical properties of materials at any particular frequency of interest. As er depends on the wavelength of light, the refractive index also depends on the wavelength of light, and this dependence is called dispersion. In addition to dispersion, an EM wave propagating through a lossy medium experiences attenuation, which means it loses its energy, due to various loss mechanisms such as the generation of phonons (lattice waves), photogeneration, free carrier absorption, scattering, etc. In such materials, the refractive index becomes a complex function of the frequency of the light wave. The complex refractive index in this chapter is denoted by n*, with real part n, and imaginary part K, called the extinction coefficient, is related to the complex relative permittivity, , by,
(1.1a)where and are, respectively, the real and imaginary parts of er. Eq. (1.1a) gives:
(1.1b)In explicit terms, n and K can be obtained as
(1.2a) (1.2b)Some books (particularly in electrical engineering) use and n* = n - iK instead of and n* = n + iK. The preference lies in what was assumed for the propagating electric field, whether it is represented by expi(?t - kx) or expi(kx - ?t), where k is the propagation constant. In a lossy medium, the imaginary part of n* must lead to a traveling wave whose amplitude decays. Notice that, for , and -that is, the refractive index is essentially determined by the real part of er and K is determined by the imaginary part of er, which is known to represent losses in a dielectric medium.
The extinction coefficient K represents loss from the energy carried by the propagating EM wave by conveniently including this loss as the imaginary part in the complex refractive index. The optical attenuation coefficient a gauges the rate of this loss from the propagating EM wave. In the absence of scattering, the attenuation would be due to absorption within the medium. For an EM wave that is propagating along x with an intensity I, a is defined by
(1.3)We can relate a and K quite easily by taking a plane wave traveling along x for which the electric field in the wave propagates as E = Eoexpi(kx - ?t), where Eo is a constant, ? is the angular frequency and k is the complex propagation constant in the medium, related to n* by its definition k = n*?/c = (n + iK)(?/c). In free space...
