 | McCall 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
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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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