Glossary x

Fundamentals of Thin Film Optics 1

Optical Basic Concepts 1

Internal Angles in Thin Films 2

Reflection 3

Reflections 4

Example Reflection Calculations 5

Graphics for Visualization of Coating Behavior 6

Reflectance as Vector Addition 6

Reflectance Amplitude Diagram 7

Admittance Diagram 8

Electric Field in a Coating 9

Admittance versus Reflectance Amplitude Diagrams 10

Triangle Diagram 11

Behavior of Some Simple AR Coating Types 12

Single-Layer Antireflection Coating 12

Two-Layer AR Amplitude Diagram Example 13

Wavelength Effects 14

Broad-Band AR Coating 17

Two V-Coat Possibilities 18

Index of Refraction Simulations and Approximations 19

Effective Index of Refraction 19

Complex Effective Index Plot 20

Simulating One Index With Two Others 21

Herpin Equivalent Layers 22

Approximations of One Index with Others 23

The QWOT Stack, a Coating Building Block 24

QWOT Stack Reflectors 25

QWOT Stack Properties 26

Width of the Block Band 28

Applications of the QWOT Stack 29

Absentee Layer 30

Narrow Band Pass Filter 31

Optical Density and Decibels (db) 32

NBP Filter Design 33

Multiple-Cavity NBP 34

Rabbit Ears 36

Coatings at Non-Normal Angles of Incidence 37

Polarization Effects 37

Wavelength Shift with Angle of Incidence 38

Angle of Incidence Effects in Coatings 39

Polarizing Beamsplitters 40

Polarization as Viewed in Circle Diagrams 41

Non-Polarizing Beamsplitters in General 43

A Non-Polarizing Beamsplitter Design Procedure 44

Non-Polarizing BS's Found & Rules-of-Thumb 46

Coatings with Absorption 47

Various Metals on Triangle Diagrams 47

Chromium Metal Details 48

A Design Example Using Chromium 50

Potential Transmittance 52

Understanding Behavior and Estimating a Coating's Potential 53

Estimating What Can Be Done Before Designing 53

Effects of Last Layer Index on BBAR Coatings 54

Effects of Index Difference (H-L) on BBAR Coatings 55

Bandwidth Effects on BBAR Coatings 56

Bandwidth Effects Background 57

Estimating the Rave of a BBAR 59

Estimating the Minimum Number of Layers in a BBAR 60

Bandpass and Blocker Coatings 61

Mirror Estimating Example Using ODBWP 63

Estimating Edge Steepness in Bandpass Filters 64

Estimating Bandwidths of Narrow Bandpass Filters 65

Blocking Bands at Higher Harmonics of a QWOT Stack 68

Insight Gained from Hypothetical Cases 71

'Step-Down' Index of Refraction AR Coatings 71

Too Much Overall Thickness in a Design 74

Inhomogeneous Index of Refraction Designs 75

Possibility of Synthesizing Designs 77

Fourier Concepts 77

Fourier Background 78

Fourier Examples 80

Fourier Limitations 82

Designing Various Types of Coatings 84

Designing a New Coating 84

Designing BBAR Coatings 85

Tails in BBAR Coatings 87

Designing Edge Filters, High Reflectors, Polarizing

and Non-Polarizing Beamsplitters 89

Designing Beamsplitters in General 90

Designing to a Spectral Shape & Computer Optimization 91

Performance Goals and Weightings 92

Constraints 93

Global vs. Local Minima 94

Some Optimizing Concepts 94

Damped Least Squares Optimization 95

Needle Optimization 95

Flip-Flop Optimization 96

Appendix

Equation Summary 97

Bibliography 101

Index 102

Preface

The principles of optical thin films are reviewed and applications shown of various useful graphical tools (or methods) for optical coating design: the reflectance diagram, admittance diagram, and triangle Diagram. It is shown graphically how unavailable indices can be approximated by two available indices of higher and lower values than the one to be approximated. The basis of ideal antireflection coating design is shown empirically. The practical approximation of these inhomogeneous index profiles is demonstrated. Much of the discussions center on AR coatings, but most other coating types are seen in the perspective of the same graphics and underlying principles. Reflection control is the basis of essentially all dielectric optical coatings; and transmittance, optical density, etc., are byproducts of reflection (and absorption). The best insight is gained by the study of reflectance. It is also shown that AR coatings, high reflectors, and edge filters are all in the same family of designs. The graphical tools described are found to be useful as an aid to understanding and insight with respect to how optical coatings function and how they might be designed to meet given requirements.