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ОбложкаMcCall M.W. Birefringent thin films and polarizing elements / M.W.McCall, I.J.Hodgkinson, Q.Wu. - 2nd ed. - London: Imperial College Press, 2015. - xxxv, 431 p.: ill., tab. - Bibliogr.: p.411-421. - Ind.: p.423-431. - ISBN 978-1-78326-535-0
Шифр: (И/В34-M44) 02
 

Место хранения: 02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents
 
Preface to the Second Edition ................................. vii
List of Figures ............................................... xix
List of Tables .............................................. xxvii
Glossary ..................................................... xxix

1  Introduction ................................................. 1
   1.1  Structural Classification of Crystals ................... 2
   1.2  Optical Classification of Crystals ...................... 2
   1.3  Structure of Birefringent Films ......................... 4
   1.4  Optical Classification of Birefringent Films ............ 4
   1.5  Layout of the Book ...................................... 5

Part 1. Propagation in Biaxial Media ............................ 9

2  Propagation Equations ....................................... 11
   2.1  Maxwell's Equations .................................... 11
   2.2  Propagation in Free Space. Mathematical Methods ........ 12
        2.2.1  SI units ........................................ 16
   2.3  Propagation in Isotropic Media ......................... 17
   2.4  Propagation in Anisotropic Media ....................... 18
   2.5  Energy Flow ............................................ 21
   2.6  Notation for Biaxial Media ............................. 22
        2.6.1  Material axes ................................... 22
        2.6.2  Propagation axes ................................ 23
        2.6.3  Rotations ....................................... 23
        2.6.4  Computations .................................... 25
   2.7  Propagation in a Common Direction in a Biaxial Medium .. 26
        2.7.1  Maxwell's equations ............................. 26
        2.7.2  Fresnel's equation .............................. 27
        2.7.3  Eigenequations for normalized fields ............ 27
3  Basis Vectors ............................................... 31
   3.1  Partially Coherent States .............................. 32
        3.1.1  Coherence ....................................... 32
        3.1.2  Stokes parameters ............................... 33
        3.1.3  Stokes vectors .................................. 34
        3.1.4  Degree of polarization .......................... 35
        3.1.5  Unpolarized light ............................... 35
        3.1.6  Partially polarized light ....................... 35
        3.1.7  Polarized light ................................. 35
        3.1.8  Basis vectors ................................... 36
   3.2  Coherent States ........................................ 37
        3.2.1  Jones vectors ................................... 37
        3.2.2  Elliptical polarization ......................... 37
        3.2.3  Circular polarization ........................... 39
        3.2.4  Linear polarization ............................. 40
        3.2.5  Basis vectors ................................... 40
        3.2.6  Photons ......................................... 41
        3.2.7  Ellipsometric parameters ........................ 41
   3.3  Propagation in Layered Biaxial Media ................... 42
        3.3.1  Fresnel's quartic equation ...................... 43
        3.3.2  Propagation in the deposition plane ............. 44
        3.3.3  Uniaxial media .................................. 45
        3.3.4  Isotropic media ................................. 45
        3.3.5  Basis travelling wave fields .................... 46
        3.3.6  Power ........................................... 48
        3.3.7  Change of basis ................................. 48
4  Transfer Matrices ........................................... 51
   4.1  Mueller Calculus ....................................... 52
        4.1.1  Rotated elements ................................ 52
        4.1.2  Elements in series .............................. 54
        4.1.3  Characterization of reflecting surfaces ......... 55
        4.1.4  Mueller calculus computations ................... 55
   4.2  Jones Calculus ......................................... 55
        4.2.1  Linear polarizer ................................ 56
        4.2.2  Retardation plate ............................... 56
        4.2.3  Quarter-wave plate .............................. 57
        4.2.4  Rotated elements ................................ 57
        4.2.5  Elements in series .............................. 58
        4.2.6  Periodic arrangements ........................... 58
        4.2.7  Jones calculus computations ..................... 59
   4.3  Relationship of Mueller Calculus and Jones Calculus .... 59
   4.4  Berreman Calculus ...................................... 59
        4.4.1  Field matrix F .................................. 60
        4.4.2  Field coefficients a ............................ 61
        4.4.3  Total field m ................................... 61
        4.4.4  Phase matrix Ad ................................. 62
        4.4.5  Characteristic matrix M ......................... 62
        4.4.6  System matrix A ................................. 64
        4.4.7  Properties of M ................................. 65
        4.4.8  Computation of film parameters from M ........... 66
   4.5  Abeles and Heavens Calculus ............................ 68
        4.5.1  Isotropic layer ................................. 68
        4.5.2  Deposition plane ................................ 70
   4.6  Film and Toolbox Structures ............................ 72
        4.6.1  PS coatings ..................................... 72
        4.6.2  Interfaces ...................................... 74
        4.6.3  Application of the BTF Toolbox .................. 75
        4.6.4  Chiral coatings ................................. 76
   4.7  Relationship of Jones and Berreman Calculus ............ 78
        4.7.1  Jones matrix with interference .................. 78
        4.7.2  Jones matrix with reflections but without
               interference .................................... 79
5  Reflection and Transmission ................................. 81
   5.1  General Case - All Media Biaxial ....................... 81
        5.1.1  Crystal-crystal interface ....................... 84
   5.2  Sorting Columns of F ................................... 84
   5.3  Isotropic Cover and Substrate .......................... 88
        5.3.1  Amplitude reflection and transmission
               coefficients .................................... 90
        5.3.2  Irradiance reflectance coefficients ............. 90
   5.4  All Media Isotropic .................................... 91
        5.4.1  Phase changes on reflection and transmission .... 92
   5.5  Computations Using the BTF Toolbox ..................... 92
        5.5.1  Conservation of energy .......................... 93
   5.6  Stokes Vectors and Mueller Matrices for Optical
        Coatings ............................................... 93
        5.6.1  Retrieval of remittances &om Mueller matrices ... 95
   5.7  Remittance Coefficients for Partially Polarized Light .. 95
        5.7.1  Illumination by unpolarized light ............... 96
        5.7.2  Polarization gamut .............................. 96
6  Guided Waves ......................................... 99
   6.1  Modal Condition ........................................ 99
        6.1.1  General case .................................... 99
        6.1.2  Isotropic cover and substrate .................. 101
        6.1.3  Uncoupled modes ................................ 102
        6.1.4  Poles and zeros of R ........................... 104
        6.1.5  Examples ....................................... 104
   6.2  Modal Cutoffs ......................................... 104
   6.3  Modal Contours ........................................ 106
   6.4  Modal Field Structure ................................. 107
   6.5  Modal Polarization .................................... 109
   6.6  Modal Overlap ......................................... 110
   6.7  Modal Order ........................................... 110
   6.8  Power Flow ............................................ 114
   6.9  Prism Couplers ........................................ 117

Part 2. Characterization of Anisotropic Films ................. 121

7  Deposition of Basic Nanostructures ......................... 123
   7.1  Computer Modelling of Deposition ...................... 124
        7.1.1  Serial deposition of hard spheres .............. 124
        7.1.2  Visual analysis of simulations ................. 124
        7.1.3  Radial distribution function ................... 125
        7.1.4  Two-dimensional angular distribution ........... 126
        7.1.5  Column angle ................................... 127
        7.1.6  Birefringence .................................. 128
        7.1.7  Conclusions from simulations of deposition ..... 128
   7.2  Apparatus for Depositing Anisotropic Coatings ......... 128
        7.2.1  Deposition conditions .......................... 129
   7.3  Basic Columnar Nanostructures Characterized by
        Electron Microscopy ................................... 130
        7.3.1  TC biaxial media ............................... 131
        7.3.2  NC biaxial media ............................... 132
        7.3.3  NC uniaxial Media .............................. 133
        7.3.4  Biaxial media with all axes inclined ........... 133
        7.3.5  Zig-zag and wavy anisotropic media ............. 135
        7.3.6  Tilted-columnar chiral media ................... 137
        7.3.7  Normal-columnar chiral media ................... 137
        7.3.8  Natural chiral media - scarab beetle cuticle ... 140
        7.3.9  Notes on electron microscopy images ............ 141
   7.4  Optical Characterization of the Basic Nanostructures .. 142
8  Form Birefringence ......................................... 145
   8.1  Measurement of In-Plane Birefringence ................. 145
        8.1.1  Perpendicular incidence ellipsometry ........... 146
        8.1.2  Computation of ellipsometric parameters ........ 146
        8.1.3  Computation of An .............................. 147
   8.2  Measurement of Principal Refractive Indices ........... 149
        8.2.1  Use of narrowband filters ...................... 150
        8.2.2  Photometric method ............................. 151
        8.2.3  Waveguide method ............................... 151
        8.2.4  Half-wave plate method ......................... 151
        8.2.5  Multiple-angle ellipsometry .................... 151
   8.3  Modelling Form Birefringence .......................... 154
        8.3.1  Bragg-Pippard equations ........................ 154
        8.3.2  Inversion of the Bragg-Pippard equations ....... 157
   8.4  Empirical Model for Form Birefringence ................ 158
        8.4.1  Comparison of TC and NC films .................. 159
9  Handed Media ............................................... 163
   9.1  Nanoengineered Chiral Media ........................... 163
        9.1.1  Continuous-chiral and discrete-chiral media .... 164
        9.1.2  Optical activity ............................... 165
        9.1.3  The circular Bragg resonance ................... 169
        9.1.4  Real-time display of the Bragg resonance ....... 170
        9.1.5  Polarization response maps ..................... 171
        9.1.6  Coordinates of the Bragg resonance ............. 171
        9.1.7  Index-matched chiral media ..................... 172
        9.1.8  Antireflection coatings for chiral media ....... 172
        9.1.9  Origin of the remittances ...................... 173
        9.1.10 Approximate expressions for remittances ........ 175
        9.1.11 Ambichiral media ............................... 176
        9.1.12 Structurally perturbed chiral media ............ 178
   9.2  Natural Chiral Media .................................. 183
        9.2.1  Surface texture ................................ 183
        9.2.2  Colour of chiral films ......................... 185
        9.2.3  Mueller spectroscopic ellipsometry ............. 187
        9.2.4  Models for beetle chiral architecture .......... 192
        9.2.5  Advantages of chiral architecture .............. 194
10 Continuum Methods .......................................... 195
   10.1 Statement of the Problem .............................. 195
   10.2 Oseen Transformation .................................. 198
        10.2.1 Reflectances and transmittances ................ 200
   10.3 Coupled Wave Theory ................................... 201
        10.3.1 Derivation of the coupled wave equations ....... 201
        10.3.2 Solution to the coupled wave equations ......... 205
        10.3.3 Grating reflection and transmission
               coefficients ................................... 205
   10.4 Derivation of Remittances from a SCM .................. 207
   10.5 From Multilayer to Continuum .......................... 212
11 Effective Media ............................................ 217
   11.1 Herpin Indices for PS Layers - Medium-Wavelength
   and Long-Wavelength Regimes ................................ 217
   11.2 Herpin Indices for Isotropic Layers ................... 220
   11.3 TC Biaxial Layers with a Common Deposition Plane ...... 222
        11.3.1 A and В NC uniaxial ............................ 222
        11.3.2 A and В parallel, TC ........................... 224
        11.3.3 A and В coplanar, TC with ψА = -ψB ............. 225
        11.3.4 Biaxial layers deposited in different planes ... 227
   11.4 Herpin Indices for NC Chiral Media .................... 229
12 Anisotropic Scatter ........................................ 233
   12.1 Scatter into the Air .................................. 233
   12.2 Scatter Patterns Formed on the Film ................... 235
   12.3 Scatter into the Substrate ............................ 237
   12.4 In Situ Measurement of Scatter ........................ 237
        12.4.1 Dependence of haze on Δ ........................ 238
        12.4.2 Haze from herring-bone stacks .................. 238
   12.5 Simple Theory of Scatter .............................. 239
   12.6 Stress and Scatter From Stress-Related Cracks ......... 241
13 Fluid Transport ............................................ 245
   13.1 Fluid Patches ......................................... 245
        13.1.1 Recording fluid patches ........................ 246
        13.1.2 MDM narrowband filters ......................... 247
   13.2 Scatter from Fluid Patches ............................ 249
        13.2.1 Scatter anisotropy ............................. 249
        13.2.2 Theory of scatter .............................. 250
   13.3 Influence on Birefringence ............................ 253
        13.3.1 Change of birefringence in fluid patches ....... 253
        13.3.2 Principal refractive indices ................... 255
        13.3.3 Cooling and venting ............................ 256
   13.4  Sealing Biaxial Nanostructures ....................... 256
14 Metal Films ................................................ 261
   14.1 Growth and Post-Deposition Sputter Etching ............ 261
   14.2 Direct Recording of Optical Anisotropies .............. 264
        14.2.1 Silver, gold and aluminium ..................... 265
        14.2.2 Aging .......................................... 268
        14.2.3 Argon ion sputter etching ...................... 268
   14.3 Computer Modelling of Anisotropy in Metals ............ 269
        14.3.1 Bulk metals .................................... 271
        14.3.2 Depolarization factors ......................... 273
        14.3.3 Isotropic resonance ............................ 273
        14.3.4 Anisotropic resonance .......................... 274
   14.4 Modelling Deposition and Etching ...................... 276
        14.4.1 Simulated deposition of gold ................... 277
        14.4.2 Simulated deposition of silver ................. 278
        14.4.3 Simulated deposition/etch paths ................ 278
   14.5 Summary ............................................... 280

Part 3. Applications of Birefringent Media .................... 283

15 Linear Polarizers .......................................... 285
   15.1 Real Polarizers ....................................... 285
   15.2 Dichroic Polarizers ................................... 287
   15.3 Tilted Plate and Thin Film Polarizers ................. 289
        15.3.1 Plate polarizers ............................... 289
        15.3.2 Coated-plate polarizers ........................ 289
        15.3.3 Embedded thin film polarizers .................. 291
        15.3.4 Birefringent Fabry-Perot polarizing filter ..... 292
   15.4 Crystalline Prism Polarizers .......................... 297
        15.4.1 Glan-Foucault prism ............................ 297
        15.4.2 Feussner polarizer ............................. 298
        15.4.3 Wollaston prism ................................ 299
        15.4.4 Rochon prism ................................... 299
   15.5 Birefringent Thin Film Analogues ...................... 300
16 Phase Retarders ............................................ 301
   16.1 Crystalline Wave Plates ............................... 301
        16.1.1 Quartz and magnesium fluoride .................. 301
        16.1.2 Multiple-order wave plates ..................... 302
        16.1.3 Zero-order wave plates ......................... 304
        16.1.4 Achromatic wave plates ......................... 305
        16.1.5 Wide-field elements ............................ 307
        16.1.6 Variable phase compensators .................... 310
   16.2 Birefringent Thin Film Analogues ...................... 313
        16.2.1 Thin film wave plates .......................... 313
        16.2.2 Thin film zero-order wave plates ............... 314
        16.2.3 Thin film achromatic wave plates ............... 314
        16.2.4 Thin film Babinet compensator .................. 316
        16.2.5 Thin film Soleil-Babinet compensator ........... 317
        16.2.6 Thin film Berek compensator .................... 317
        16.2.7 Patterning thin film retarders ................. 318
17 Birefringent Filters ....................................... 321
   17.1 Polarization State Filters ............................ 321
        17.1.1 Linear polarizer ............................... 321
        17.1.2 Circular polarizer ............................. 322
        17.1.3 Rotator ........................................ 322
        17.1.4 Depolarizer .................................... 323
   17.2 Wavelength Filters .................................... 324
        17.2.1 Lyot-Ohman filter .............................. 324
        17.2.2 Sole filters ................................... 328
        17.2.3 Filters for tuning dye lasers .................. 329
18 Coating Architectures ...................................... 335
   18.1 Isotropic Architectures ............................... 335
   18.2 Birefringent Architectures ............................ 336
        18.2.1 General birefringent coating ................... 336
        18.2.2 PS coatings .................................... 337
        18.2.3 Design considerations for PS coatings .......... 338
        18.2.4 Examples of PS coatings ........................ 338
        18.2.5 Normal and hybrid monitoring ................... 343
   18.3 Chiral Architectures .................................. 344
        18.3.1 Chiral photonic flake .......................... 344
   18.4 Isotropic-Birefringent-Chiral Architectures ........... 347
Appendix A  PS Sampler ........................................ 349
   A.l  Anisotropic Antireflection Coating .................... 351
   A.2  Anisotropic Reflector ................................. 353
   A.3  Anisotropic-Phase Reflector ........................... 355
   A.4  Achromatic Antireflection Coating ..................... 357
   A.5  Achromatic Fifty Percent Reflector .................... 359
   A.6  Single-Cavity Narrowband Filter ....................... 361
   A.7  Multi-Cavity Narrowband Filter ........................ 363
   A.8  Edge Filter ........................................... 365
   A.9  Common-Index Thin Film Polarizer ...................... 367
   A 10 Multi-Cavity Linear Polarizer ......................... 369
Appendix В  Birefringent Thin Films Toolbox ................... 371
   B l  Quick Reference ....................................... 373
   B.2  Commands and Functions ................................ 377

Bibliography .................................................. 411
Index ......................................................... 423

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