Basics of OPTICS OF MULTILAYER SYSTEMS Bp:i[9w
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Contents UB&)U\hn
Preface……………………………………………………………………….………..……….4 d/3
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Chapter 1 '.&z y#
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: 8`j;v>2
THEORY……………………………………………………………………………………….5 4zw5?$YWO"
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 n gC|BLT%h
1.1.1 Layered medium electromagnetic field equations………………………………...5 2 (Ez
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1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 ]/C1p G*o
1.1.3 The Fresnel formulas ……………………………………………………………18 -+#g.1UL/
1.1.4 Other ways of determining amplitude transmittance and reflectance of the 2~BId&]
layered medium…………………………………………………………………..19 &:ib>EB03=
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 B \z4o\am%
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 d,0Yi
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1.2.1 Matrix calculating method ………………………………………………………22 Nq3q##Ut:
1.2.2 Description of optical coating and presentation of calculation results…………..28 5
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1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 "0yO~;a
1.2.4 Approximate formulas…………………………………………………………...33 ND|!U#wMNV
1.2.5 Other recurrent methods…………………………………………………………34 WF {rrU:
1.2.6 The admittance phase plane……………………………………………………...38 !b+/zXp3I
1.3 Some common properties of multilayer coatings…………………………………….46 QX$i
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1.3.1 The relation between the characteristic matrix and spectral coefficients of a _a3 ,Zuv
multilayer coating ……………………………………………………………….47 z9#iU>@
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 nS}XY
1.3.3 Transmittance and reflectance of the combination of two multilayer (8*& 42W
subsystems ……………………………………………………………………....54 , :!dq onn
1.4 The multilayer coatings optical properties: impact of variations in the layer X(;,- 7Jw
parameters……………………………………………………………………………...58 b1A8 -![
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… X)K3X:~L+
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral 1Lf :TQB
coefficients: probability assessment method ……………………….…………...63 ~+GMn[h
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter z7H[\ 4A!>
variations ………………………………………………………………………...66 . CL\``
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 * CH lg1
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 TCd1JF0
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 K8l|qe
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 =O )dHY}
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the B0^0d*8t|@
central wavelength ………………………………………………………………80 'b*
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1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 [ Yzh(a8
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 '14
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1.6.1 Common expressions for spectral coefficients of filter-type systems near central LI&+5`
wavelength ………………………………………………………………………88 1o;+.]B
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 [V5ebj:6w
Chapter 2 Ba\l`$%X
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 tCk;tu!d
2.1 Synthesis methods based on merit function optimization …………………………...98 x_JCH7-
2.1.1 Merit function selection …………………………………………………………98 hoc$aqP6pp
2.1.2 Merit function optimization ……………………………………………………101 }D7q)_g=
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 wv 2
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 'wd-!aZAd
2.2.1 Needle-like variations of the refractive index ………………………………….115 ;-d }\f ,
2.2.2 The principal idea of the method ………………………………………………119 ]Xur/ C2A
2.2.3 Description of the method ……………………………………………………...124 \V|\u= @H
Bibliography …...………………………………………….……………….………..……130
