Basics of OPTICS OF MULTILAYER SYSTEMS <Pio Q >~
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Contents *2=W5LaK.
Preface……………………………………………………………………….………..……….4 [^M|lf
Chapter 1 2A>C+Y[7 \
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: /~*Cp9F"]
THEORY……………………………………………………………………………………….5 7G"7wYc>R
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 n8 $=f'Hgb
1.1.1 Layered medium electromagnetic field equations………………………………...5 x{Sd
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1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 6b<+8w
1.1.3 The Fresnel formulas ……………………………………………………………18 {y b D
1.1.4 Other ways of determining amplitude transmittance and reflectance of the <5I1 DF[
layered medium…………………………………………………………………..19 UWw}!1
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 <BP RV> 0X
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 (f~gEKcB2u
1.2.1 Matrix calculating method ………………………………………………………22
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1.2.2 Description of optical coating and presentation of calculation results…………..28 zP&q7 t;>
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 i b]vX-
1.2.4 Approximate formulas…………………………………………………………...33 (z2Z)_6L*L
1.2.5 Other recurrent methods…………………………………………………………34 {i>Jfl]G}
1.2.6 The admittance phase plane……………………………………………………...38 87<9V.s 2
1.3 Some common properties of multilayer coatings…………………………………….46 b=1%pX_
1.3.1 The relation between the characteristic matrix and spectral coefficients of a Fu% X
multilayer coating ……………………………………………………………….47 *NlpotW,f
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 U(~U!O}
1.3.3 Transmittance and reflectance of the combination of two multilayer /EU ; ?O
subsystems ……………………………………………………………………....54 k2p'G ')H
1.4 The multilayer coatings optical properties: impact of variations in the layer ik5|,#}m&
parameters……………………………………………………………………………...58 #Qd' + M
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… |l 7% l&!
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral 2tf6GX :
coefficients: probability assessment method ……………………….…………...63 s}ADk-7
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter Me/\z^pF
variations ………………………………………………………………………...66 k_?~<vTM
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 ] H&c'
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 hwVAXsF ~
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 9tk" :ld
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 9P.(^SD][z
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the
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central wavelength ………………………………………………………………80 /.$L"u
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 :}9j^}"c3
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 w<t,j~ Pr#
1.6.1 Common expressions for spectral coefficients of filter-type systems near central CCq T tp
wavelength ………………………………………………………………………88 "-
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1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 I60DUuF
Chapter 2 =Ndli>x}1
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 g1 9S
2.1 Synthesis methods based on merit function optimization …………………………...98 }+0z,s~0.
2.1.1 Merit function selection …………………………………………………………98 b/<mRQ{
2.1.2 Merit function optimization ……………………………………………………101 ]1sNmi$T
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 QaQ'OrP
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 OVR?*"N_
2.2.1 Needle-like variations of the refractive index ………………………………….115 5/M ED}9C(
2.2.2 The principal idea of the method ………………………………………………119 YH\j@ ^n
2.2.3 Description of the method ……………………………………………………...124 PZ,z15PG]
Bibliography …...………………………………………….……………….………..……130
