Basics of OPTICS OF MULTILAYER SYSTEMS |)!k @?_
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Contents P"~qio-
Preface……………………………………………………………………….………..……….4 U4^p({\|-
Chapter 1 8 /RfNGY
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: -!bLMLIg
THEORY……………………………………………………………………………………….5 c9ov;Bw6S
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 5u
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1.1.1 Layered medium electromagnetic field equations………………………………...5 yG 4LQE
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 !e#I4,f n
1.1.3 The Fresnel formulas ……………………………………………………………18 P98X[0&
1.1.4 Other ways of determining amplitude transmittance and reflectance of the D<D
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layered medium…………………………………………………………………..19 JQbMw >Y
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 0,L$x*Nj5
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 WV !kA_
1.2.1 Matrix calculating method ………………………………………………………22 Vx7Dl{?{'
1.2.2 Description of optical coating and presentation of calculation results…………..28 Ei?9M^w
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 UVoLHd
1.2.4 Approximate formulas…………………………………………………………...33 hk lO:,`
1.2.5 Other recurrent methods…………………………………………………………34 _1>(GK5[
1.2.6 The admittance phase plane……………………………………………………...38 D?*sdm9r`
1.3 Some common properties of multilayer coatings…………………………………….46 [WO%rO^p
1.3.1 The relation between the characteristic matrix and spectral coefficients of a 8H%I|fm
multilayer coating ……………………………………………………………….47 u{{xnyl?
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 N`|Ab(.
1.3.3 Transmittance and reflectance of the combination of two multilayer @L>NN>?SGQ
subsystems ……………………………………………………………………....54 }JpslY*aS
1.4 The multilayer coatings optical properties: impact of variations in the layer (fk, 80
parameters……………………………………………………………………………...58 yZ(Nv $[5
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… 9^
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1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral eM1;Nl
coefficients: probability assessment method ……………………….…………...63 +{Vwz
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter ixJ20A 7
variations ………………………………………………………………………...66 \Zz= 4
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1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 2cX"#."5p
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 M:1F@\<
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 sKG ~<8M}
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 X?}GPA4 W
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the ZTPOD.:#
central wavelength ………………………………………………………………80 %6 c*dy
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 X 5oW[
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 T.m)c%]^/
1.6.1 Common expressions for spectral coefficients of filter-type systems near central p`l[cVQ<
wavelength ………………………………………………………………………88 6t mNfI34
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 '__3[D
Chapter 2 tx1m36 a"
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 divZJc
2.1 Synthesis methods based on merit function optimization …………………………...98 eS@!\H x
2.1.1 Merit function selection …………………………………………………………98 w<F;&' ;@h
2.1.2 Merit function optimization ……………………………………………………101 lTO M/^L
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 m5; [ , He
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 gq:TUvX
2.2.1 Needle-like variations of the refractive index ………………………………….115 8|-mzb&
2.2.2 The principal idea of the method ………………………………………………119 D@b<}J>0'
2.2.3 Description of the method ……………………………………………………...124 t ]I(98pY
Bibliography …...………………………………………….……………….………..……130
