Basics of OPTICS OF MULTILAYER SYSTEMS 3J{vt"dS
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Contents q_ %cbAcD
Preface……………………………………………………………………….………..……….4 [ |[>}z:
Chapter 1 k6!4Zz_8
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: *:_P8G;
THEORY……………………………………………………………………………………….5 a8$kNtA
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 ,`32!i
1.1.1 Layered medium electromagnetic field equations………………………………...5 DdSSd@,x*
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 MAqLIf<G
1.1.3 The Fresnel formulas ……………………………………………………………18 Rrg8{DZhv
1.1.4 Other ways of determining amplitude transmittance and reflectance of the [iS,#w`
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layered medium…………………………………………………………………..19 w%dL 8k
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 I;7nb4]AmF
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 w\w(U
1.2.1 Matrix calculating method ………………………………………………………22 :m'+tGs
1.2.2 Description of optical coating and presentation of calculation results…………..28 A5fwAB
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 "CQw/qZw
1.2.4 Approximate formulas…………………………………………………………...33 MgJ36zM
1.2.5 Other recurrent methods…………………………………………………………34 Q6
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1.2.6 The admittance phase plane……………………………………………………...38 ,Q/Ac{C
1.3 Some common properties of multilayer coatings…………………………………….46 ~GJN@ka4%
1.3.1 The relation between the characteristic matrix and spectral coefficients of a :?Y$bX}a
multilayer coating ……………………………………………………………….47 @ {#mpDX
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 g>
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1.3.3 Transmittance and reflectance of the combination of two multilayer :jEPu3E:
subsystems ……………………………………………………………………....54 LO:fJ{ -
1.4 The multilayer coatings optical properties: impact of variations in the layer 6Pn8f
parameters……………………………………………………………………………...58 vyI%3+N@
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… \}_Yd8
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral Y[Ltrk{
coefficients: probability assessment method ……………………….…………...63 Vp}^NNYf
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter @kFu*"
variations ………………………………………………………………………...66 hWo =;#B*
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 '
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1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 wmU0E/{9]
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 x; \wY'
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 S/ [E 8T"
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the %ZP+zh n}
central wavelength ………………………………………………………………80 /mM2M-
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 4~ z?"
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 &<pKx!
1.6.1 Common expressions for spectral coefficients of filter-type systems near central q<#>HjC
wavelength ………………………………………………………………………88 ^Q +i=y{W
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 Avlz=k1*
Chapter 2 <spZ! #o
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 lb*8G
2.1 Synthesis methods based on merit function optimization …………………………...98 "xRBE\B
2.1.1 Merit function selection …………………………………………………………98 F^k .is
2.1.2 Merit function optimization ……………………………………………………101 sJ
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2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 $2~\eG=u H
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 ]aryV?!6
2.2.1 Needle-like variations of the refractive index ………………………………….115 sZ<9A Xk-E
2.2.2 The principal idea of the method ………………………………………………119 M$Zo.Bl$(
2.2.3 Description of the method ……………………………………………………...124 fV:4 #j
Bibliography …...………………………………………….……………….………..……130
