Basics of OPTICS OF MULTILAYER SYSTEMS Wjf,AjL\
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Contents 8l< 4O goK
Preface……………………………………………………………………….………..……….4 * |dz.Tr
Chapter 1 >5%;NI5
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SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: /);S?7u .
THEORY……………………………………………………………………………………….5 p]lZ4#3
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 2*[Gm e
1.1.1 Layered medium electromagnetic field equations………………………………...5 ?q lpi(
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 cM|!jnKm
1.1.3 The Fresnel formulas ……………………………………………………………18 39!$x [
1.1.4 Other ways of determining amplitude transmittance and reflectance of the 4Y .o RB
layered medium…………………………………………………………………..19 655OL)|cD6
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 C]- !u Ly
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 45
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1.2.1 Matrix calculating method ………………………………………………………22 ZYMacTeJjg
1.2.2 Description of optical coating and presentation of calculation results…………..28 v-utDQT3
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 wR(>' ?
1.2.4 Approximate formulas…………………………………………………………...33 Q"(*SA+-|
1.2.5 Other recurrent methods…………………………………………………………34 X`s6lV% \
1.2.6 The admittance phase plane……………………………………………………...38 a7~% ( L@r
1.3 Some common properties of multilayer coatings…………………………………….46 s%Y8;D,~+
1.3.1 The relation between the characteristic matrix and spectral coefficients of a $URL7hrh U
multilayer coating ……………………………………………………………….47 awC:{5R8v
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 c04;2gR
1.3.3 Transmittance and reflectance of the combination of two multilayer &;x* u G
subsystems ……………………………………………………………………....54 lL<LJ
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1.4 The multilayer coatings optical properties: impact of variations in the layer +m >)q4 e
parameters……………………………………………………………………………...58 q4xP<b^
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… Dr oa1_FX
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral U)sw
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coefficients: probability assessment method ……………………….…………...63 pRez${f.(s
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter J? 4E Hl
variations ………………………………………………………………………...66 .{8?eze[m
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 ?LAiSg=eq
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 N"zg)MsX
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 fvNj5 Vq:
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 hN"cXz"/
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the r:~ q {
central wavelength ………………………………………………………………80 )?$zY5
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 n@ PXC8}
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 tbm/gOBw
1.6.1 Common expressions for spectral coefficients of filter-type systems near central t`!@E#VK
wavelength ………………………………………………………………………88 "?n;dXYSi
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 ]IM/R@
Chapter 2 G^W'mV$xl
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 v~AD7k2{8
2.1 Synthesis methods based on merit function optimization …………………………...98 9cJ1J7 y
2.1.1 Merit function selection …………………………………………………………98 m2x=Qv][@c
2.1.2 Merit function optimization ……………………………………………………101 a)qlrtCl
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 ' u84d= *l
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 wpK[;
2.2.1 Needle-like variations of the refractive index ………………………………….115 }7+`[g
2.2.2 The principal idea of the method ………………………………………………119 $a.,; :
2.2.3 Description of the method ……………………………………………………...124 3;<Vv*a"Dm
Bibliography …...………………………………………….……………….………..……130
