Edmund Optics(cid:15)(cid:3)(cid:44)(cid:81)(cid:70)(cid:17)(cid:3)
`(cid:40)(cid:91)(cid:75)(cid:76)(cid:69)(cid:76)(cid:87)(cid:3)(cid:20)(cid:19)11(cid:3)
`
`0001
`
`

`
`ISBN: 0-8247-0849-0
`
`"rec paper.
`
`Headquarters
`Marcel Dekker, Inc.
`270 Madison Avenue, New York, NY 10016
`tel: 212-696-9000; fax: 212-685-4540
`
`Eastern Hemisphere Distribution
`Marcel Dekker AG
`
`Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland
`tel: 41-61-261-8482; fax: 41-61—26l—8896
`
`World Wide Web
`
`http://www.dekker.com
`
`The publisher offers discounts on this book when ordered in bulk quantities. For more infor-
`mation, write to Special Sales/Professional Marketing at the headquarters address above.
`
`Copyright © 2002 by Marcel Dekker, inc. All Rights Reserved.
`
`Neither this book nor any part may be reproduced or transmitted in any fomi or by any
`means, electronic or mechanical, including photocopying, microfilming, and recording, or
`by any information storage and retrieval system, without permission in writing from the
`publisher.
`
`Current printing (last digit):
`10 9 8 7 6 5 4 3 2
`
`
`
`0002
`
`

`
`Contents
`
`Preface to the Second Edition
`Preface to the First Edition
`
`iii
`v
`
`1 Fundamentals of Thin Film Optics and the
`Use of Graphical Methods in Thin Film Design......................l
`
`INTRODUCTION ........................................................................................... .. 1
`1.1.
`1.2. REVIEW OF THIN FILM OPTICS PRINCIPLES ........................................ ..5
`1.3. REFLECTANCE DIAGRAMS ........................................................................ ..8
`1.3.1. Low Reflectors, Antireflection Coatings ............................................ .. 10
`1.3.2. High Reflectors .................................................................................. ..19
`1.3.3. Narrow Bandpass Pass Filters ........................................................... ..22
`1.3.4. Beamsplitters ....................................................................................... ..30
`1.3.5. Three-Layer AR Coating on Germanium, Example ............................ .. 34
`1.3.6. Example Four-Layer Broad Band AR Coating in the Visible ............. .. 36
`1.3.7. Physical Thickness versus Optical Thickness...................................... ..36
`1.4. ADMITTANCE DIAGRAMS ........................................................................ ..36
`1.5. TRIANGLE DIAGRAMS .............................................................................. ..39
`1.5.1. Designing Coatings with Absorbing Materials.................................... ..40
`1.6. APPROXIMATIONS OF INDICES AND DESIGNS ................................... ..6l
`1.7. INHOMOGENEOUS INDEX FUNCTIONS ................................................ ..65
`1.7.1. Low Index Limitations ........................................................................ ..74
`1.7.2. A Fourier Approach ............................................................................ ..77
`1.8. OPTIMIZATION ........................................................................................... .. 83
`1.8.1. Perfonnance Goals and Weightings .................................................... .. 84
`
`vii
`
`
`
`0003
`
`

`
`viii
`
`Contents
`
`1.8.2. Constraints ......................................................................................... ..85
`1.8.3. Global versus Local Minima ............................................................... ..85
`
`¢
`‘
`
`1.8.4. Some Optimizing Concepts ................................................................. ..86
`1.9. SUMMARY ................................................................................................... ..88
`1.10. REFERENCES ............................................................................................. ..88
`
`2 Estimating What Can Be Done Before Designing......... ......91
`
`INTRODUCTION .......................................................................................... ..91
`2.1.
`2.2. ANTIREFLECTION COATINGS ................................................................. ..91
`2.2.1. Procedure ............................................................................................ ..92
`2.2.2. The Fonnula ...................................
`................................................... ..93
`2.2.3. Results ................................................................................................. ..95
`
`2.2.4. Summary of Antireflection Coating Estimation ................................ .. 101
`2.3. BANDPASS AND BLOCKER COATINGS ............................................... .. 101
`
`2.3.1. Estimating the Width ofa Blocking Band ......................................... .. 102
`2.3.2. Estimating the Optical Density ofa Blocking Band .......................... .. 104
`2.3.3. Estimating the Number of Layers and Thickness Needed ................. .. 105
`2.3.4. Estimating More Complex Coatings ............................................ .. 105
`2.3.5. Estimating Edge Filter Passband Reflection Losses .......................... .. 11 I
`2.4. DICHROIC REFLECTION COATINGS
`................................................. .. 121
`2.5. DWDM FILTERS ........................................................................................ ..123
`2.6. SUMMARY ................................................................................................. .. 127
`2.7. REFERENCES ............................................................................................ .. I28
`
`3 Fourier Viewpoint of Optical Coatings..............................129
`
`INTRODUCTION ....................................................................................... .. 129
`3.1.
`3.2. FOURIER CONCEPTS ............................................................................... ..129
`
`3.2.1. Background ....................................................................................... ..130
`3.2.2. Some Limitations .............................................................................. ..134
`
`3.2.3. A Method to Determine the Multiple Reflections ............................. ..137
`3.2.4. Overcoming Low Index Limitations with Thickness ......................... .. 139
`3.3. DESIGNING A VERY BROAD BAND AR COATING ............................. ..147
`3.4. CONCLUSIONS .......................................................................................... ..148
`3.5. REFERENCES ............................................................................................ ..149
`
`4 Typical Equipment for Optical Coating Production ........]50
`
`4.1.
`
`INTRODUCTION ........................................................................................ .. I50
`
`
`
`0004
`
`

`
`Estimating Before Designing
`
`12]
`
`2.4. DICI-IROIC REFLECTION COATINGS
`
`The estimation of general coating spectral shapes such as color correction filters
`may be reasonably approximated by the above methods in most cases. In the case
`of dichroic filters for color separation, etc.,
`the above approach should be
`satisfactory. However, it is also of great interest to know how many layers are
`needed to achieve a certain edge slope between the pass and block ba.nds. This is
`often the determining factor rather than OD in such filters.
`The steepness of the side of an edge filter is in inverse proportion to the
`number of layers or pairs. The spectral distance from the high to the low
`transmittance region is usually the important factor for the designer. This might
`be from 80% to 20% T (about .1 to .7 OD) or some other choice of limits. If we
`call the spectral distance dg and the peak density at the QWOT wavelength ODP,
`the effect of steepness may be approximated by Eqn. 2.7. We know the Ag from
`Eqn. 22 and the ODP from Eqn. 2.3.
`
`dg ~
`
`N l[ Ag
`ODPL74
`
`2
`
`] ~ 1
`
`2
`
`arcsin ((nH — nL)/(nH + n,)
`1:
`log % ((nH/nlf + (nL/nH)P)
`
`(2.7)
`
`The 1/2 factor (found empirically) would need to be changed if the specific OD
`range from high to low transmittance or reflectance were changed from the 80%
`to 20% used above. Since we know that the peak OD is directly proportional to
`the number of layers in the stack, the dg will be inversely proportional to the
`number of layers (to some power). This shows how adding layers for steepness
`has a strong effect at a low total number of layers. but a weak effect if there are
`already many layers. The wavelength of the edge multiplied by dg gives the
`approximate change of wavelength from 20 to 80% reflectance. Figure 2.31
`illustrates this for 5, I0- 15 and 20 layer pairs of L and H indices of l.45 and 2.25
`on a spectral plot. Figure 2.32 shows actual data measured from Fig. 2.3 l plotted
`for comparison with a curve generated by the formula. The formula estimates a
`slope which is less steep than the real case for many layers and more steep for less
`than seven (7) layer pairs. However, it does show clearly the great number of
`layers needed for a steep edge and the “point of diminishing returns.” 1n the
`region of 10 to 20 layers, this should be an adequate engineering estimate of
`performance before designing.
`
`
`
`0005
`
`

`
`122
`
`Chapter 2
`
`EDGE STEEPNESS
`
`“I.
`
`Reflectance
`
`Wavelength (nm)
`
`
`
`
`
`Fig. 2.31 Spectra of filter edge for 5, 10, 15 and 20 layer pairs of indices 1.45/2.25.
`
`NM dg VERSUS # PAIRS
`
`NMFROM20TO80%
`
`
`FORMULA
`
`NUMBER OF LAYER PAIRS
`
`Fig. 2.32 Actual data measured from Fig. 2.31 plotted for comparison with a curve
`generated by Eqn. 2.7.
`
`
`
`0006