Basics of OPTICS OF MULTILAYER SYSTEMS o>l/*i0I
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Contents q; ?Kmk
Preface……………………………………………………………………….………..……….4 my}l?S[2d@
Chapter 1 )*`cJ_t
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: P+Q}bTb8
THEORY……………………………………………………………………………………….5 4/N{~
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 +H SKFp
1.1.1 Layered medium electromagnetic field equations………………………………...5 lc(}[Z/|V
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 V |hr 9
1.1.3 The Fresnel formulas ……………………………………………………………18 S\S31pYT
1.1.4 Other ways of determining amplitude transmittance and reflectance of the =M ."^ X
layered medium…………………………………………………………………..19 ra| Ku!
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 BCI[jfd 7
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 4XNdsb
1.2.1 Matrix calculating method ………………………………………………………22 [r0`D^*=
1.2.2 Description of optical coating and presentation of calculation results…………..28 h|{DIG3
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 o:c:hSV
1.2.4 Approximate formulas…………………………………………………………...33 C~X"ZW:d[
1.2.5 Other recurrent methods…………………………………………………………34 ^|lw~F
1.2.6 The admittance phase plane……………………………………………………...38 0..]c-V(G
1.3 Some common properties of multilayer coatings…………………………………….46 x>Gx yVE
1.3.1 The relation between the characteristic matrix and spectral coefficients of a v/GZBy co>
multilayer coating ……………………………………………………………….47 18WJ*q7:
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 DEQ7u`6
1.3.3 Transmittance and reflectance of the combination of two multilayer V$fn$=
subsystems ……………………………………………………………………....54 hkDew0k
1.4 The multilayer coatings optical properties: impact of variations in the layer ?BnX<dbi&
parameters……………………………………………………………………………...58 QIC? `hk1
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… Zq "
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral MW I7u7{
coefficients: probability assessment method ……………………….…………...63 yfZYGhPN(
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter y4N2gBTKu
variations ………………………………………………………………………...66 nU,~*Us
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 !-~sxa280r
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 y7T<Auue`
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 VLcwBdo
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 +GL[uxe "
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the 1'!%$ D
central wavelength ………………………………………………………………80 ^D?{[LBc
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 .c ]@xoC
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 )?<V-,D
1.6.1 Common expressions for spectral coefficients of filter-type systems near central .OZ\ s%h;
wavelength ………………………………………………………………………88 i '3)5
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 <AN5>:k[pM
Chapter 2 ^ pNA_s!S
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 V$g !#V
2.1 Synthesis methods based on merit function optimization …………………………...98 NJmyp!8
2.1.1 Merit function selection …………………………………………………………98 34I;DUdcE
2.1.2 Merit function optimization ……………………………………………………101 N gagzsJ=
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 5 89P$2e1X
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 K6 c[ W%Va
2.2.1 Needle-like variations of the refractive index ………………………………….115 i$6o>V 6
2.2.2 The principal idea of the method ………………………………………………119 [mFgo
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2.2.3 Description of the method ……………………………………………………...124 : U,-v
Bibliography …...………………………………………….……………….………..……130
