Basics of OPTICS OF MULTILAYER SYSTEMS ~rN~Ql%S
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Preface……………………………………………………………………….………..……….4 UbE*x2N
Chapter 1 dU+28
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: X3
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THEORY……………………………………………………………………………………….5 )=V0
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 b/5
1.1.1 Layered medium electromagnetic field equations………………………………...5 glbU\K> >
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 +FRXTku(
1.1.3 The Fresnel formulas ……………………………………………………………18 ^P
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1.1.4 Other ways of determining amplitude transmittance and reflectance of the `ySLic`
layered medium…………………………………………………………………..19 pi[:"}m]/P
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 R_eKKi@VH
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 >y#<WB$i
1.2.1 Matrix calculating method ………………………………………………………22 c&z@HEzV7
1.2.2 Description of optical coating and presentation of calculation results…………..28 %|bqL3)a_
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 |f;u5r!^=
1.2.4 Approximate formulas…………………………………………………………...33 7Rqjf6kX`O
1.2.5 Other recurrent methods…………………………………………………………34 jXB<"bw
1.2.6 The admittance phase plane……………………………………………………...38 A6YkoYgC
1.3 Some common properties of multilayer coatings…………………………………….46 )<-\ F%&b
1.3.1 The relation between the characteristic matrix and spectral coefficients of a +K,]#$k
multilayer coating ……………………………………………………………….47 zL $$G,
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 L l\y2oJ
1.3.3 Transmittance and reflectance of the combination of two multilayer G]X72R?g
subsystems ……………………………………………………………………....54 fT9$0:eO
1.4 The multilayer coatings optical properties: impact of variations in the layer vzA)pB~;
parameters……………………………………………………………………………...58 A
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1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… '+LC.l M
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral m~mw1r
coefficients: probability assessment method ……………………….…………...63 JJ[.K*dO
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter E8j >Toz
variations ………………………………………………………………………...66 e$}x;&c Q
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 &[ ejxK"
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 NPF"_[RoeV
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72
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1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 s ki' I
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the 8`l bKV
central wavelength ………………………………………………………………80 u+ "3l@ Y#
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 'M+iw:R__
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 >J,Rx!fq3
1.6.1 Common expressions for spectral coefficients of filter-type systems near central 1Ys6CJ#
wavelength ………………………………………………………………………88 i_8v > F
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 / @- !JF#g
Chapter 2 Q ]wM WV
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 ZT;$aNy
2.1 Synthesis methods based on merit function optimization …………………………...98 +Z99 x#
2.1.1 Merit function selection …………………………………………………………98 # InuN8sI
2.1.2 Merit function optimization ……………………………………………………101 ] }XsP
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 f*U3s N^y
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 ] /&qv6D*d
2.2.1 Needle-like variations of the refractive index ………………………………….115 ~Ry?}5&:
2.2.2 The principal idea of the method ………………………………………………119 Hz39v44
2.2.3 Description of the method ……………………………………………………...124 OOJg%y*H
Bibliography …...………………………………………….……………….………..……130
