Basics of OPTICS OF MULTILAYER SYSTEMS "=0#pH1o
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Contents >qj Q;z[
Preface……………………………………………………………………….………..……….4 Tti]H9g_
Chapter 1 IG?044Y
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: Re3vW re
THEORY……………………………………………………………………………………….5 v Dgf}
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 LEoL6 ga
1.1.1 Layered medium electromagnetic field equations………………………………...5 __\Tv>Y
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 LHjGlBy
1.1.3 The Fresnel formulas ……………………………………………………………18 >y%*HC!G
1.1.4 Other ways of determining amplitude transmittance and reflectance of the )x1LOMe
layered medium…………………………………………………………………..19 ;6g &_6
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 ,}i`1E 1=
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 3+gp_7L
1.2.1 Matrix calculating method ………………………………………………………22 {O-,JCq /
1.2.2 Description of optical coating and presentation of calculation results…………..28 #!d@;= [\
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 5`oVyxJ<
1.2.4 Approximate formulas…………………………………………………………...33 J>(I"K%
1.2.5 Other recurrent methods…………………………………………………………34 1s4+a^ &
1.2.6 The admittance phase plane……………………………………………………...38 |cwGc \ES
1.3 Some common properties of multilayer coatings…………………………………….46 B[:-SWd
1.3.1 The relation between the characteristic matrix and spectral coefficients of a m&xyw9a
multilayer coating ……………………………………………………………….47 U$R+&@;
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 kYw k'\s
1.3.3 Transmittance and reflectance of the combination of two multilayer %xE\IRlR
subsystems ……………………………………………………………………....54 mAkR<\?iTF
1.4 The multilayer coatings optical properties: impact of variations in the layer f!;4 -.p`
parameters……………………………………………………………………………...58 RkVU^N"
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… &D, gKT~
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral "V!y"yQ
coefficients: probability assessment method ……………………….…………...63 rWKc,A[
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter zG|}| //}
variations ………………………………………………………………………...66 ;W6P$@'zs
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 'ojI _%9<
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 1df }gG
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 1?\ # hemL
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 6 <JiHVP7
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the hC@oyC(4
central wavelength ………………………………………………………………80 y#HDJ=2
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 V3O<l}ak
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 5bZf$$b
1.6.1 Common expressions for spectral coefficients of filter-type systems near central _
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wavelength ………………………………………………………………………88 b_xn80O
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 Vt-D8J\A
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Chapter 2 )En *5-1
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 YNCQPN\v`1
2.1 Synthesis methods based on merit function optimization …………………………...98 5tMp@$F\{[
2.1.1 Merit function selection …………………………………………………………98 .C fi/
2.1.2 Merit function optimization ……………………………………………………101 6]#pPk8[Z
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 >]?!c5=
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 T0xU }
2.2.1 Needle-like variations of the refractive index ………………………………….115 N:Yjz^Jt
2.2.2 The principal idea of the method ………………………………………………119 GaMiu! |,
2.2.3 Description of the method ……………………………………………………...124 ]9]cef=h#
Bibliography …...………………………………………….……………….………..……130
