Birefringent Thin Films And Polarizing Elements

by Ian J Hodgkinson, Hong Wu Qi

Overview

This book describes the propagation of light in biaxial media, the properties of biaxial thin films, and applications such as birefringent filters for tuning the wavelength of dye lasers.A novel feature of the first part is the parallel treatment of Stokes, Jones, and Berreman matrix formalisms in a chapter-by-chapter development of wave equations, basis vectors, transfer matrices, reflection and transmission equations, and guided waves. Computational tools for MATLAB are included.The second part focuses on an emerging planar technology in which anisotropic microstructures are formed by oblique deposition in vacuum. Methods for characterizing dielectric and metal films are discussed. Topics such as form birefringence, effective medium theory, anisotropic scatter and anisotropic fluid transport are discussed in detail.Practical applications of bulk and layered birefringent media are considered in the final part. Separate chapters are devoted to linear polarizers, phase retarders, and birefringent filters. Traditional bulk-media polarizing elements are included and compared with thin film designs.

Product Details

ISBN-13:	9789810229061
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	02/12/1998
Pages:	412
Product dimensions:	6.36(w) x 8.54(h) x 1.03(d)

Table of Contents

	List of Tables	xv
	List of Figures	xvii
	Glossary	xxiii
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	5
1.5	Layout of the Book	7
I	Propagation in Biaxial Media	9
2	Propagation Equations	11
2.1	Maxwell's Equations	12
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	24
2.6.3	Rotations	24
2.6.4	Computations	26
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	28
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	36
3.1.8	Basis Vectors	36
3.2	Coherent States	38
3.2.1	Jones Vectors	38
3.2.2	Elliptical Polarization	38
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	43
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
4	Transfer Matrices	49
4.1	Mueller Calculus	50
4.1.1	Rotated Elements	50
4.1.2	Elements in Series	51
4.1.3	Mueller Calculus Computations	52
4.2	Jones Calculus	52
4.2.1	Linear Polarizer	54
4.2.2	Retardation Plate	54
4.2.3	Quarter-Wave Plate	54
4.2.4	Rotated Elements	55
4.2.5	Elements in Series	55
4.2.6	Periodic Arrangements	56
4.2.7	Jones Calculus Computations	56
4.3	Relationship of Mueller and Jones Calculus	56
4.4	Berreman Calculus	57
4.4.1	Field Matrix F	57
4.4.2	Field Coefficients a	58
4.4.3	Total Field m	59
4.4.4	Phase Matrix A[subscript d]	59
4.4.5	Characteristic Matrix M	60
4.4.6	System Matrix A	62
4.4.7	Properties of M	62
4.4.8	Computation of Film Parameters from M	63
4.5	Abeles and Heavens Calculus	65
4.5.1	Isotropic Layer	65
4.5.2	Deposition Plane	67
4.5.3	Berreman Calculus Computations	69
4.6	Relationship of Jones and Berreman Calculus	74
4.6.1	Jones Matrix with Interference	74
4.6.2	Jones Matrix with Reflections but without Interference	75
5	Reflection and Transmission	77
5.1	General Case - All Media Biaxial	78
5.1.1	Crystal-Crystal Interface	81
5.2	Sorting Columns of F	81
5.3	Isotropic Cover and Substrate	85
5.3.1	Amplitude Reflection and Transmission Coefficients	87
5.3.2	Irradiance Reflectance Coefficients	88
5.4	All Media Isotropic	89
5.4.1	Phase Changes on Reflection and Transmission	90
5.5	Computations Using the BTF Toolbox	90
5.5.1	General Birefringent Coating	90
5.5.2	PS Coatings	91
6	Guided Waves	93
6.1	Modal Condition	94
6.1.1	General Case	94
6.1.2	Isotropic Cover and Substrate	95
6.1.3	Uncoupled Modes	97
6.1.4	Poles of R	98
6.1.5	Examples	98
6.2	Modal Cutoffs	100
6.3	Modal Contours	100
6.4	Modal Field Structure	104
6.5	Modal Polarization	106
6.6	Modal Overlap	108
6.7	Modal Order	111
6.8	Power Flow	111
6.9	Prism Couplers	112
II	Characterization of Anisotropic Films	115
7	Deposition of Microstructures	117
7.1	Vacuum Deposition	118
7.1.1	Apparatus	118
7.1.2	Deposition Parameters	119
7.2	Columnar Structures and Effective Media	119
7.2.1	Uniaxial Media	119
7.2.2	Biaxial Media	119
7.2.3	Effective Anisotropic Media	123
7.2.4	Zig-Zag and Wavy Anisotropic Media	123
7.2.5	Helical Microstructures	125
7.3	Computer Modelling of Deposition	127
7.3.1	Serial Deposition of Hard Spheres	127
7.3.2	Visual Analysis of Simulations	127
7.3.3	Radial Distribution Function	128
7.3.4	Two-Dimensional Angular Distribution	131
7.3.5	Column Angle	131
7.3.6	Birefringence	131
7.3.7	Conclusions from Simulations of Deposition	131
8	Form Birefringence	135
8.1	Perpendicular Incidence Ellipsometry	136
8.1.1	Computation of Ellipsometric Parameters	136
8.1.2	Characteristic Ellipsometric Curves	138
8.1.3	Experimental Values	144
8.2	Measurement of Principal Refractive Indices	144
8.2.1	In Situ Measurements	145
8.2.2	Use of Narrowband Filters	146
8.2.3	Photometric Method	147
8.2.4	Waveguide Method	147
8.3	Modelling Form Birefringence	149
8.3.1	Bragg-Pippard Equations	149
8.3.2	Inversion of the Bragg-Pippard Equations	151
9	Effective Media	153
9.1	Herpin Indices for Isotropic Layers	154
9.2	Biaxial Layers with a Common Deposition Plane	155
9.2.1	A and B Normal Columnar	157
9.2.2	A and B Parallel, Tilted Columnar	159
9.2.3	A and B Coplanar, Tilted Columnar with [psi subscript A] = -[psi subscript B]	162
9.3	Biaxial Layers Deposited in Different Planes	164
10	Anisotropic Scatter	167
10.1	Scatter into the Air	168
10.2	Scatter From Stress-Related Cracks	169
10.3	Scatter Patterns Formed on the Film	174
10.4	Scatter into the Substrate	175
10.5	In Situ Measurement of Scatter	175
10.5.1	Dependence of Haze on [Delta]	177
10.5.2	Haze from Herring-Bone Stacks	177
10.6	Simple Theory of Scatter	180
11	Fluid Transport	183
11.1	Fluid Patches	184
11.1.1	Recording Fluid Patches	185
11.1.2	MDM Narrowband Filters	185
11.2	Scatter from Fluid Patches	188
11.2.1	Scatter Anisotropy	188
11.2.2	Theory of Scatter	191
11.2.3	General AR Coating	194
11.2.4	High Reflectance Coating	194
11.2.5	Narrowband Interference Filter	194
11.3	Influence on Birefringence	197
11.3.1	Change of Birefringence in Fluid Patches	197
11.3.2	Principal Refractive Indices	201
11.3.3	Cooling and Venting	202
12	Metal Films	203
12.1	Growth and Post-Deposition Sputter Etching	204
12.2	Direct Recording of Optical Anisotropies	206
12.2.1	Silver and Gold	209
12.2.2	Aluminium	209
12.2.3	Aging	216
12.2.4	Argon Ion Sputter Etching	217
12.3	Computer Modelling of Anisotropy in Metals	217
12.3.1	Bulk Metals	221
12.3.2	Depolarization Factors	222
12.3.3	Isotropic Resonance	223
12.3.4	Anisotropic Resonance	225
12.4	Modelling Deposition and Etching	227
12.4.1	Simulated Deposition of Gold	228
12.4.2	Simulated Deposition of Silver	231
12.4.3	Simulated Deposition of Aluminium	231
12.4.4	Simulated Deposition / Etch Paths	231
12.5	Summary	236
III	Applications of Birefringent Media	237
13	Linear polarizers	239
13.1	Real Polarizers	240
13.2	Dichroic Polarizers	241
13.3	Tilted Plate and Thin Film Polarizers	243
13.3.1	Plate Polarizers	243
13.3.2	Coated-Plate Polarizers	244
13.3.3	Embedded Thin Film Polarizers	246
13.3.4	Birefringent Fabry-Perot Polarizing Filter	247
13.4	Crystalline Prism Polarizers	251
13.4.1	Glan-Foucault Prism	252
13.4.2	Wollaston Prism	253
13.4.3	Rochon Prism	253
14	Phase Retarders	255
14.1	Crystalline Wave Plates	256
14.1.1	Quartz and Magnesium Fluoride	256
14.1.2	Multiple-Order Wave Plates	257
14.1.3	Zero-Order Wave Plate	259
14.1.4	Achromatic Wave Plates	259
14.1.5	Wide-Field Elements	264
14.1.6	Variable Phase Compensators	265
14.2	Birefringent Thin Film Analogues	267
14.2.1	Thin Film Wave Plates	267
14.2.2	Thin Film Babinet Compensator	270
14.2.3	Thin Film Soleil-Babinet Compensator	270
14.2.4	Thin Film Berek Compensator	271
15	Birefringent Filters	273
15.1	Polarization State Filters	274
15.1.1	Linear Polarizer	274
15.1.2	Circular Polarizer	274
15.1.3	Rotator	274
15.1.4	Depolarizer	275
15.2	Wavelength Filters	276
15.2.1	Lyot-Ohman Filter	276
15.2.2	Solc Filters	279
15.2.3	Filters for Tuning Dye Lasers	282
16	Birefringent Coatings	289
16.1	Isotropic Coatings	290
16.2	General Birefringent Coating	290
16.3	PS Coatings	294
16.4	Design Considerations for PS Coatings	294
16.4.1	Making an Anisotropic Version	296
16.4.2	Replacing an Intermediate Index	299
16.4.3	Identical Response Profiles Separated in Wavelength	299
16.4.4	Spoiling the s-response	299
16.5	Normal and Hybrid Monitoring	300
16.6	PS Sampler	302
16.6.1	Anisotropic Antireflection Coating	302
16.6.2	Anisotropic Reflector	304
16.6.3	Anisotropic-Phase Reflector	306
16.6.4	Achromatic Antireflection Coating	308
16.6.5	Achromatic Fifty Percent Reflector	310
16.6.6	Single-Cavity Narrowband Filter	312
16.6.7	Multi-Cavity Narrowband Filter	314
16.6.8	Edge Filter	316
16.6.9	Common-Index Thin Film Polarizer	318
16.6.10	Multi-Cavity Linear Polarizer	320
A	Birefringent Thin Films Toolbox	323
A.1	Quick Reference	324
A.2	Commands and Functions	327
	Notes and References	365
	Index	371