Basics of OPTICS OF MULTILAYER SYSTEMS modem6#x'
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Contents PXl%"O%d
Preface……………………………………………………………………….………..……….4 |BtFT
Chapter 1 %IIFLlD
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: LGtw4'yr
THEORY……………………………………………………………………………………….5 u>] )q7s
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 > B;YYj~f}
1.1.1 Layered medium electromagnetic field equations………………………………...5 ]#S<]v A
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12
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1.1.3 The Fresnel formulas ……………………………………………………………18 lQgavP W!
1.1.4 Other ways of determining amplitude transmittance and reflectance of the .i;?8?
layered medium…………………………………………………………………..19 ]T40VGJ:h
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 kTzO4s?
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 4 F -<j!
1.2.1 Matrix calculating method ………………………………………………………22 r_8;aPL
1.2.2 Description of optical coating and presentation of calculation results…………..28 `Y!8,( 5#
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 =Y^K
1.2.4 Approximate formulas…………………………………………………………...33 M`iE'x
1.2.5 Other recurrent methods…………………………………………………………34 {a2Gb
1.2.6 The admittance phase plane……………………………………………………...38 4"nYxL"<4
1.3 Some common properties of multilayer coatings…………………………………….46 b "Nd8f [
1.3.1 The relation between the characteristic matrix and spectral coefficients of a h* hkl#
multilayer coating ……………………………………………………………….47 CCC9I8rZD
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 %<|<%~l&
1.3.3 Transmittance and reflectance of the combination of two multilayer D#,A_GA{A
subsystems ……………………………………………………………………....54 k8+U0J_ {'
1.4 The multilayer coatings optical properties: impact of variations in the layer vwAhNw2-
parameters……………………………………………………………………………...58 P~&J@8)c
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… =pj3G ?F#
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral IW}Wt{ 'm
coefficients: probability assessment method ……………………….…………...63 [tC=P&<
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter cl{mRt0
variations ………………………………………………………………………...66 Q 4L7{^[X
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 1;,<UHF8N
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 B< .ZW}#v
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 4UPxV"H
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 -) +B!"1
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the _$vbb#QXZG
central wavelength ………………………………………………………………80 Jh4pY#aF
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 xMpgXB!'
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 W Xf[W
1.6.1 Common expressions for spectral coefficients of filter-type systems near central +'w6=qI
wavelength ………………………………………………………………………88 mtLiS3Nk8
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 {XC[Ia6jtL
Chapter 2 %Yg|QBm|
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 0 \k {v
2.1 Synthesis methods based on merit function optimization …………………………...98 +T,0,^ *
2.1.1 Merit function selection …………………………………………………………98 D deKZ)8
2.1.2 Merit function optimization ……………………………………………………101 ^FT S'/Q
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 VTX6_&Hc1g
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 V HLNJnA
2.2.1 Needle-like variations of the refractive index ………………………………….115 n-GoG(s..b
2.2.2 The principal idea of the method ………………………………………………119 I2) 2'j,B
2.2.3 Description of the method ……………………………………………………...124 oe=1 [9T"
Bibliography …...………………………………………….……………….………..……130
