Basics of OPTICS OF MULTILAYER SYSTEMS
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Contents MMr7 ,?,$
Preface……………………………………………………………………….………..……….4 tc2GI6]e'
Chapter 1 =bg&CZV T
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: ?_j6})2zY
THEORY……………………………………………………………………………………….5 -+_aL4.
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 Tocdh.H|
1.1.1 Layered medium electromagnetic field equations………………………………...5
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1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 2CgIY89O
1.1.3 The Fresnel formulas ……………………………………………………………18
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1.1.4 Other ways of determining amplitude transmittance and reflectance of the sr@Xum T
layered medium…………………………………………………………………..19 mS&\m#s <
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 fX$4TPy(h
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 C(*@-N pf[
1.2.1 Matrix calculating method ………………………………………………………22 -LK(C`gB
1.2.2 Description of optical coating and presentation of calculation results…………..28 o4'4H y
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 V;]V wsZ"
1.2.4 Approximate formulas…………………………………………………………...33 e27CbA{_w
1.2.5 Other recurrent methods…………………………………………………………34 uvv-lAbjw
1.2.6 The admittance phase plane……………………………………………………...38 C^=gZ
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1.3 Some common properties of multilayer coatings…………………………………….46 <\>ak7m
1.3.1 The relation between the characteristic matrix and spectral coefficients of a |b~g^4
multilayer coating ……………………………………………………………….47 m:Cx~
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 :XZom+>2n
1.3.3 Transmittance and reflectance of the combination of two multilayer \lIHC{V\
subsystems ……………………………………………………………………....54 &`Z)5Ww
1.4 The multilayer coatings optical properties: impact of variations in the layer &Wz:-G7<n
parameters……………………………………………………………………………...58 m:O2_%\l
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… {!Z_&i5
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral u,SZ-2K!7~
coefficients: probability assessment method ……………………….…………...63 Ul0<Zxv
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter E^W*'D
variations ………………………………………………………………………...66 Yn2^nT=8
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 j?hyN@ns
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 f /i,Zw
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 :BxYaAVt^
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 J7^T!7V.
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the rWpfAE)!
central wavelength ………………………………………………………………80 w/W?/ 1P>q
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 7#. PMyK9
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 QGG(I 7{-
1.6.1 Common expressions for spectral coefficients of filter-type systems near central 2#M:J gWV
wavelength ………………………………………………………………………88 K5rj!*x.o
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 ,;pX.Ob U
Chapter 2 )^#Zg8L
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 "hY^[@7 W
2.1 Synthesis methods based on merit function optimization …………………………...98 V="f)'S$
2.1.1 Merit function selection …………………………………………………………98 }(}vlL
2.1.2 Merit function optimization ……………………………………………………101 * t9qH
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 sl O9H6<
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 > 0)`uJ
2.2.1 Needle-like variations of the refractive index ………………………………….115 zGz'2, o3
2.2.2 The principal idea of the method ………………………………………………119 ; OqLNfU3y
2.2.3 Description of the method ……………………………………………………...124 @7 HBX P
Bibliography …...………………………………………….……………….………..……130
