Basics of OPTICS OF MULTILAYER SYSTEMS O5T{e Bo\
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Contents Y\g3h M
Preface……………………………………………………………………….………..……….4 \bvfE P
Chapter 1 t&e{_|i#+
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: ZyFjFHe+
THEORY……………………………………………………………………………………….5 @*KZ}i@._
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 R%[ c; i
1.1.1 Layered medium electromagnetic field equations………………………………...5 O k=hT|}Y
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 A# YrWW
1.1.3 The Fresnel formulas ……………………………………………………………18 ]Gq !`O1
1.1.4 Other ways of determining amplitude transmittance and reflectance of the Em~>9f
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layered medium…………………………………………………………………..19 SSMHo JGm
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 oE]QF.n#
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 p>8D;#Hm L
1.2.1 Matrix calculating method ………………………………………………………22 LyFN.2qw
1.2.2 Description of optical coating and presentation of calculation results…………..28 +A?U{q
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 mxd r,Idx
1.2.4 Approximate formulas…………………………………………………………...33 tf`^v6 m%]
1.2.5 Other recurrent methods…………………………………………………………34 2 8d'7El$
1.2.6 The admittance phase plane……………………………………………………...38 OYn}5RN
1.3 Some common properties of multilayer coatings…………………………………….46 Se =`N
1.3.1 The relation between the characteristic matrix and spectral coefficients of a c(s.5p ^
multilayer coating ……………………………………………………………….47 }b.%Im<3R
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 |Ds1
1.3.3 Transmittance and reflectance of the combination of two multilayer u;2[AQ.
subsystems ……………………………………………………………………....54 >}6%#CAf
1.4 The multilayer coatings optical properties: impact of variations in the layer Qh\60f> 0
parameters……………………………………………………………………………...58 f9{Rb/l!BQ
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… u.xnO cOH!
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral q^<?]8
coefficients: probability assessment method ……………………….…………...63 Q>Yjy!. <^
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter YS"=yye 3e
variations ………………………………………………………………………...66 -PR N:'T
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 {F.[&/A
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 Vs!Nmv`
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 </*6wpN
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 kM N~Y
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the 4@a i6,<
central wavelength ………………………………………………………………80 gc$l^`+M
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 2g! +<YZ~
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 aAUvlb
1.6.1 Common expressions for spectral coefficients of filter-type systems near central DEZve Qr=
wavelength ………………………………………………………………………88 6qnzBA7
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 Z/+#pWBI!
Chapter 2 zIAD9mQex
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 E hMNap}5"
2.1 Synthesis methods based on merit function optimization …………………………...98 $*fMR,~t&
2.1.1 Merit function selection …………………………………………………………98 \
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2.1.2 Merit function optimization ……………………………………………………101 #S" nF@
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 c yz3,3\e
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 [.wYdv35
2.2.1 Needle-like variations of the refractive index ………………………………….115 c5GuM|*7
2.2.2 The principal idea of the method ………………………………………………119 vy I!]p
2.2.3 Description of the method ……………………………………………………...124 $6SW;d+>n
Bibliography …...………………………………………….……………….………..……130
