Basics of OPTICS OF MULTILAYER SYSTEMS *?s/Ho &'
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Contents _8Pmv$
Preface……………………………………………………………………….………..……….4 ?#x'_2
Chapter 1 m<~>&mWr
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: n&3iz05}
THEORY……………………………………………………………………………………….5 |yuGK
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 6_x}.bkIx=
1.1.1 Layered medium electromagnetic field equations………………………………...5 iz,]%<_PE
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 ~>lOl/n 5
1.1.3 The Fresnel formulas ……………………………………………………………18 f;&` 9s| 1
1.1.4 Other ways of determining amplitude transmittance and reflectance of the /YS@[\j4
layered medium…………………………………………………………………..19 -Cg`x=G;z
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 LNWqgIq
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 &9S8al
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1.2.1 Matrix calculating method ………………………………………………………22 xq8}6Q
1.2.2 Description of optical coating and presentation of calculation results…………..28 p|xs|O 6{
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 {(8U8f<'=y
1.2.4 Approximate formulas…………………………………………………………...33 <.y;&a o
1.2.5 Other recurrent methods…………………………………………………………34
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1.2.6 The admittance phase plane……………………………………………………...38 0- 6:AHix
1.3 Some common properties of multilayer coatings…………………………………….46 2(@L Rl>:
1.3.1 The relation between the characteristic matrix and spectral coefficients of a = E##},N"
multilayer coating ……………………………………………………………….47 6tDg3`w>
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 5)h+(u C3
1.3.3 Transmittance and reflectance of the combination of two multilayer -Y5YCY!`
subsystems ……………………………………………………………………....54 g| _Hc aW
1.4 The multilayer coatings optical properties: impact of variations in the layer nNkyOaK*4
parameters……………………………………………………………………………...58 * [iity
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… j=`y
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1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral `NYF ?%
coefficients: probability assessment method ……………………….…………...63 GGYX!=]~
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter 7O;BS}Lv=
variations ………………………………………………………………………...66 =ip~J<sw &
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 jAD+:@
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 ]b5%?^Z#
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 #RCZA4>
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 WsG"x>1n
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the 8#NIs@DJ
central wavelength ………………………………………………………………80 V'Sd[*
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 S,ouj;B
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 ;$E~ZT4p
1.6.1 Common expressions for spectral coefficients of filter-type systems near central LC~CPV'F
wavelength ………………………………………………………………………88 (,d4"C
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 PEOM1oY)w
Chapter 2 [a#?}((
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 u K+9gTv
2.1 Synthesis methods based on merit function optimization …………………………...98 1R^XWAb
2.1.1 Merit function selection …………………………………………………………98 ~ z-?rW
2.1.2 Merit function optimization ……………………………………………………101 ,n
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2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 IN]`lJ
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 }.fZy& _
2.2.1 Needle-like variations of the refractive index ………………………………….115 ~Hp# 6+
2.2.2 The principal idea of the method ………………………………………………119 'qD'PLV
2.2.3 Description of the method ……………………………………………………...124 p 02nd.R6
Bibliography …...………………………………………….……………….………..……130
