Basics of OPTICS OF MULTILAYER SYSTEMS 2Ib
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Contents iVmy|ewd
Preface……………………………………………………………………….………..……….4 K&"X7fQ
Chapter 1 ?Ho>
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: 66_=bd(9
THEORY……………………………………………………………………………………….5 I@#IXH?6
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 X V) ctF4
1.1.1 Layered medium electromagnetic field equations………………………………...5 z 61F q
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 6J$I8b#/
1.1.3 The Fresnel formulas ……………………………………………………………18 QXy= |
1.1.4 Other ways of determining amplitude transmittance and reflectance of the Y%r>=Jvu6
layered medium…………………………………………………………………..19 ) <w`:wD
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 wqzpFPk(
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 P9 q=tC3^
1.2.1 Matrix calculating method ………………………………………………………22 ''z]o#=^9
1.2.2 Description of optical coating and presentation of calculation results…………..28 RfCu5 Kn
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 l=$?#^^ /
1.2.4 Approximate formulas…………………………………………………………...33 yGX5\PSo
1.2.5 Other recurrent methods…………………………………………………………34 h b} Qt Q
1.2.6 The admittance phase plane……………………………………………………...38 G2P: |R
1.3 Some common properties of multilayer coatings…………………………………….46 NJQy*~P
1.3.1 The relation between the characteristic matrix and spectral coefficients of a axN\ZXU
multilayer coating ……………………………………………………………….47 l$R9c+L=
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 OcC|7s" ,
1.3.3 Transmittance and reflectance of the combination of two multilayer [O]rf+NZ(5
subsystems ……………………………………………………………………....54 w:=:D=xH2
1.4 The multilayer coatings optical properties: impact of variations in the layer ETdN<}m
parameters……………………………………………………………………………...58 zzd PR}VG
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… WH U l.h
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral O+=}x]q*y
coefficients: probability assessment method ……………………….…………...63 7(| f@Y ~*
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter \
*g3j
variations ………………………………………………………………………...66 J 5x ZL v
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 ^^a%Lz)U
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 ~K(mt0T )
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 % ;a B#:p6
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 ?<M x* l
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the dqFp"Xe"%
central wavelength ………………………………………………………………80 )gAqWbkB
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 \,lIPA/L
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 K\mFb
1.6.1 Common expressions for spectral coefficients of filter-type systems near central q:vGG K^
wavelength ………………………………………………………………………88 4|4[3Ye7u:
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 4.~ <|T8
Chapter 2 PO:sF]5
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 um2} XI
2.1 Synthesis methods based on merit function optimization …………………………...98 D^f;X.Qm
2.1.1 Merit function selection …………………………………………………………98 j}fSz)`i
2.1.2 Merit function optimization ……………………………………………………101 b"OH Xu
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 ln6=XD u
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 gebL6oc%
2.2.1 Needle-like variations of the refractive index ………………………………….115 J'k^(ZZ
2.2.2 The principal idea of the method ………………………………………………119 wb##|XyK<c
2.2.3 Description of the method ……………………………………………………...124 <@0S]jy
Bibliography …...………………………………………….……………….………..……130
