Basics of OPTICS OF MULTILAYER SYSTEMS \#\`!L[1
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Contents A+0 T" 2
Preface……………………………………………………………………….………..……….4 BGB,Gb
Chapter 1 ",~ b2]ym
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: j}|N^A_ S
THEORY……………………………………………………………………………………….5 y\F`B0#$
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 Po Yr:=S?
1.1.1 Layered medium electromagnetic field equations………………………………...5 =w',-+@
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 "C:rTIH
1.1.3 The Fresnel formulas ……………………………………………………………18 ^H5w41
1.1.4 Other ways of determining amplitude transmittance and reflectance of the _-@ZOhw&
layered medium…………………………………………………………………..19 b :fxkQm
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 W$z#ssr
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 -!XrwQyk
1.2.1 Matrix calculating method ………………………………………………………22 /J 1S@-
1.2.2 Description of optical coating and presentation of calculation results…………..28 H{j~ihq7
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 ?JuX~{{. L
1.2.4 Approximate formulas…………………………………………………………...33 % $/=4f.j
1.2.5 Other recurrent methods…………………………………………………………34 6PiEa(
1.2.6 The admittance phase plane……………………………………………………...38 'fS?xDs-v
1.3 Some common properties of multilayer coatings…………………………………….46 .HyjL5r-
1.3.1 The relation between the characteristic matrix and spectral coefficients of a 3xBN10R#
multilayer coating ……………………………………………………………….47 / lf\
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1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 |9 +bSH9
1.3.3 Transmittance and reflectance of the combination of two multilayer , ] f) ,;=
subsystems ……………………………………………………………………....54 e ZynF<i
1.4 The multilayer coatings optical properties: impact of variations in the layer jv*Dg (
parameters……………………………………………………………………………...58 rU;
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1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… S8*^ss>?^R
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral AU0$A403
coefficients: probability assessment method ……………………….…………...63 )2) Zz +<
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter ,"@w>WL<9
variations ………………………………………………………………………...66 VKT@2HjNT`
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 jZa25Z00
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 @ L\-ZWq
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 ])N|[ |$
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 >ysriPnQ
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the h^['rmd
central wavelength ………………………………………………………………80 nA>*IU[
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 :L]-'\y
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 M_tj7Q3
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1.6.1 Common expressions for spectral coefficients of filter-type systems near central (})]H:W7
wavelength ………………………………………………………………………88 1T!cc%ah
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 e-~hS6p(
Chapter 2 b+W)2rFO
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 ;
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2.1 Synthesis methods based on merit function optimization …………………………...98 `f%&<, i
2.1.1 Merit function selection …………………………………………………………98 T48BRVX -F
2.1.2 Merit function optimization ……………………………………………………101 D._{E*vg
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 l &}piC
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 MO[c0n%
2.2.1 Needle-like variations of the refractive index ………………………………….115 +:}kZDl@ X
2.2.2 The principal idea of the method ………………………………………………119 :}^Rs9 '
2.2.3 Description of the method ……………………………………………………...124 b([:,T7
Bibliography …...………………………………………….……………….………..……130
