Basics of OPTICS OF MULTILAYER SYSTEMS hBcklI
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Contents
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Preface……………………………………………………………………….………..……….4 =%> E8)Jb
Chapter 1 -;HZ!Lf
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: < 0S\P=\
THEORY……………………………………………………………………………………….5 $ntC{a>&
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 yDe*-N\'W
1.1.1 Layered medium electromagnetic field equations………………………………...5 VC Ay~,
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 qT4`3nH:
1.1.3 The Fresnel formulas ……………………………………………………………18 0|0IIgy
1.1.4 Other ways of determining amplitude transmittance and reflectance of the 8Jp?@qt=$
layered medium…………………………………………………………………..19 z5<&}Vh;P
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 nSZp,?^
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 9WQ'"wyAQ
1.2.1 Matrix calculating method ………………………………………………………22 FcOrA3tt
1.2.2 Description of optical coating and presentation of calculation results…………..28 h]|2b0
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 (tzAUrC
1.2.4 Approximate formulas…………………………………………………………...33 7<2?NLE8*
1.2.5 Other recurrent methods…………………………………………………………34 ,g|ht%"
1.2.6 The admittance phase plane……………………………………………………...38 %)^0NQv
1.3 Some common properties of multilayer coatings…………………………………….46 6 {3q l:
1.3.1 The relation between the characteristic matrix and spectral coefficients of a #a8i($k{e
multilayer coating ……………………………………………………………….47 -A:'D8o#f
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 CJ#Y u3}
1.3.3 Transmittance and reflectance of the combination of two multilayer xBw ua;
subsystems ……………………………………………………………………....54 lfw BUb
1.4 The multilayer coatings optical properties: impact of variations in the layer SokU9n!
parameters……………………………………………………………………………...58 {@-tRm&
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… )D]LPC d[
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral 5: EE%(g9
coefficients: probability assessment method ……………………….…………...63 )^E6VD&6
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter f|yq~3x)
variations ………………………………………………………………………...66 REk^pZ3B
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 X Fww|SG$
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 Fy_~~nI0
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 x^pHP|<3`
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 tf9a- s
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the n.P $E
central wavelength ………………………………………………………………80 #so"p<7 R
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 >Y:veEa6v6
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 lgHzI (
1.6.1 Common expressions for spectral coefficients of filter-type systems near central n{c-3w.uD
wavelength ………………………………………………………………………88 IF?
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 K5+ONA<c
Chapter 2 )L, Nh~
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 K*j1Fy:
2.1 Synthesis methods based on merit function optimization …………………………...98 /"1[qT\F
2.1.1 Merit function selection …………………………………………………………98 e#tWQM3
2.1.2 Merit function optimization ……………………………………………………101 #Z_f/@b
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 VZA>Er B
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 |q_Hiap#a
2.2.1 Needle-like variations of the refractive index ………………………………….115 7{f{SIB
2.2.2 The principal idea of the method ………………………………………………119 s!
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2.2.3 Description of the method ……………………………………………………...124 :Ui'x8yt
Bibliography …...………………………………………….……………….………..……130
