Basics of OPTICS OF MULTILAYER SYSTEMS Frd` u .I
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Contents 1(4}rB3
Preface……………………………………………………………………….………..……….4 }n;. E&<[
Chapter 1 DFvj
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: L_(Y[!
THEORY……………………………………………………………………………………….5 $Ao
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1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 /8Xd2-
1.1.1 Layered medium electromagnetic field equations………………………………...5 hha!uD~ (
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 37U$9]
1.1.3 The Fresnel formulas ……………………………………………………………18 TMAart; <
1.1.4 Other ways of determining amplitude transmittance and reflectance of the U_oei3QP
layered medium…………………………………………………………………..19 *3s,~<''%
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 _u QxrB"9
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 \1[v-hvK
1.2.1 Matrix calculating method ………………………………………………………22 9X ^D(
1.2.2 Description of optical coating and presentation of calculation results…………..28 *{1]b_<
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 j@778fvM\t
1.2.4 Approximate formulas…………………………………………………………...33 ;]I~AGH:
1.2.5 Other recurrent methods…………………………………………………………34 ps&p|
1.2.6 The admittance phase plane……………………………………………………...38 ?'%9
1.3 Some common properties of multilayer coatings…………………………………….46 R uBL_Vi
1.3.1 The relation between the characteristic matrix and spectral coefficients of a @S#Ls="G
multilayer coating ……………………………………………………………….47 y|h:{<
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 >@+ r|
1.3.3 Transmittance and reflectance of the combination of two multilayer (+w.?l
subsystems ……………………………………………………………………....54 &|#z" E^-
1.4 The multilayer coatings optical properties: impact of variations in the layer - s,guW |
parameters……………………………………………………………………………...58 9{Xh wi)z
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… ~X2
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1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral ^Q baMX
coefficients: probability assessment method ……………………….…………...63 9Lp[y%{GP
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter sA1 XtO<&7
variations ………………………………………………………………………...66 nX\Q{R2
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 M7.
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1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 Ks F kC=
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 FtmI\,
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 a0*qK)gH
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the jB -wJNP/
central wavelength ………………………………………………………………80 =X u(Js-
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 -$@4e|e%a
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 e,I{+ ^P
1.6.1 Common expressions for spectral coefficients of filter-type systems near central IKVS7m
wavelength ………………………………………………………………………88 w829 8Kl
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 u .R
Chapter 2 8Ssk>M*
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 ^E| {i]j#f
2.1 Synthesis methods based on merit function optimization …………………………...98 o:nh3K/YJ
2.1.1 Merit function selection …………………………………………………………98 ]~J.YX9ST
2.1.2 Merit function optimization ……………………………………………………101 ^eHf'^Cvvu
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 ,W: Bh$%
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 }\wTV*n`X
2.2.1 Needle-like variations of the refractive index ………………………………….115 n1 +,Pe*)
2.2.2 The principal idea of the method ………………………………………………119 jSMs<ox
2.2.3 Description of the method ……………………………………………………...124 Qe;j_ BH
Bibliography …...………………………………………….……………….………..……130
