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This front matter contains an introduction, table of contents, and symbol glossary.

Library of Congress Cataloging-in-Publication Data

Willey, Ronald R., 1936-

Field guide to optical thin films / Ronald R. Willey.

p. cm. -- (SPIE field guides; v. FG07)

Includes bibliographical references and index.

1. Optical coatings. 2. Thin films. 3. Optical films. I. Title. II. Series: SPIE field guides; FG07.

TS517.2.W535 2006

681′.4--dc22 2005037922

Published by

SPIE—The International Society for Optical Engineering

P.O. Box 10

Bellingham, Washington 98227-0010 USA

Phone: +1360 676 3290

Fax: +1 360 647 1445



The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.

Printed in the United States of America.


Introduction to the Series

Welcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.

Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.

The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at

John E. Greivenkamp, Series Editor

Optical Sciences Center

The University of Arizona

The Field Guide Series

Keep information at your fingertips with all of the titles in the Field Guide Series:

Field Guide to Geometrical Optics, John E. Greivenkamp (FG01)

Field Guide to Atmospheric Optics, Larry C. Andrews (FG02)

Field Guide to Adaptive Optics, Robert K. Tyson & Benjamin W. Frazier (FG03)

Field Guide to Visual and Ophthalmic Optics, Jim Schwiegerling (FG04)

Field Guide to Polarization, Edward Collett (FG05)

Field Guide to Optical Lithography, Chris A. Mack (FG06)

Field Guide to Optical Thin Films, Ronald R. Willey (FG07)

Field Guide to Optical Thin Films

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.

Ronald R. Willey

Table of Contents

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 25

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 97

Equation Summary 97

Bibliography 101

Index 102


Frequently used variables, symbols, and terms:


Absorptance intensity

absentee layer

Layer of an even number of QWOTs thickness at the design wavelength

angle matched

PT of layer adjusted to be QWOT at an angle


Angle of incidence to surface normal


Antireflection (coating)


Broad band AR coating






Speed of light in vacuum


A spacer of HWOT (or multiples) with high reflectors on either side


Wavenumbers, number of waves per cm.


Decibel (= −10 OD)


Design of experiments methodology


Dense wavelength division multiplexing


Gigahertz, 109 cycles per second


High-efficiency AR coating


Half-wave optical thickness


Imaginary, in complex numbers




Extinction coefficient


Layer pair (H and L)


Long wavelength pass (filter)


Metal-dielectric-metal coating


Multiple internal reflection


Multilayer antireflection (coating)


Matching layer(s)


Real part of the index of refraction


Complex refractive index. N = n − ik


Effective index of refraction


Narrow band pass (filter)


Optical density (= log10(1/T))


Optical density bandwidth product


Optical thickness


Prism diagram


Physical thickness


Quarter-half-quarter wave OT design of AR coating


Quarter wave optical thickness


Reflectance amplitude coefficient


Reflectance intensity (R = rr*)

Rabbit ears

High reflectance in the pass band of a NBP the spectral appearance is like rabbit ears


Average reflectance over a spectral region


Index versus thickness profile of rippled or corrugated form rather than square wave


Single-layer antireflection (coating)


Short wavelength pass (filter)




Transmittance, intensity


Total internal reflection




Speed of light in medium


Number of wavelengths per centimeter in vacuum




Optical axis


Absorption coefficient


Angle of incidence, refraction, or reflection




Frequency of the light


Number of wavelengths per centimeter




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