Basics of OPTICS OF MULTILAYER SYSTEMS w iq{ Jo#
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Contents s%:fB(
Preface……………………………………………………………………….………..……….4 I*ej_cFQ^
Chapter 1 A/QVotcU
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: <|8 l ;
THEORY……………………………………………………………………………………….5 oaKf{$vg
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 4/jY;YN,2
1.1.1 Layered medium electromagnetic field equations………………………………...5 db LX}>
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 A`r9"([-A
1.1.3 The Fresnel formulas ……………………………………………………………18 =.%ZF]Oe+#
1.1.4 Other ways of determining amplitude transmittance and reflectance of the cC[n~OV
layered medium…………………………………………………………………..19 7HJv4\K
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 3 x'30
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 T/K.'92S
1.2.1 Matrix calculating method ………………………………………………………22 X=hgLK^3<,
1.2.2 Description of optical coating and presentation of calculation results…………..28 2eK\$_b _
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 "VeUOdNA>
1.2.4 Approximate formulas…………………………………………………………...33 <_>6a7ra
1.2.5 Other recurrent methods…………………………………………………………34 :+5afv}
1.2.6 The admittance phase plane……………………………………………………...38 M;9+L&p=
1.3 Some common properties of multilayer coatings…………………………………….46 E, |n'
1.3.1 The relation between the characteristic matrix and spectral coefficients of a EzyIsp> _
multilayer coating ……………………………………………………………….47
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1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 KCF wO'
1.3.3 Transmittance and reflectance of the combination of two multilayer o
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subsystems ……………………………………………………………………....54 %8 tN$8P
1.4 The multilayer coatings optical properties: impact of variations in the layer [E^X=+Jnz
parameters……………………………………………………………………………...58 $O>@ (K
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… I Q L~I13
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral ;Y '\:
coefficients: probability assessment method ……………………….…………...63 nsp K. *?
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter :2My|3H\
variations ………………………………………………………………………...66 hq*JQb;Y}
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68
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1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 B#MW`7c
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 iK]g3ew|
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 8?YW i
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the 9c^EoYpy-
central wavelength ………………………………………………………………80 9vTQ^*b m
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 !VH Il&Mos
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 HH#i.s2
1.6.1 Common expressions for spectral coefficients of filter-type systems near central \k=Qq(=
wavelength ………………………………………………………………………88 GN9_ZlC
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 2P
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Chapter 2 w3N%J>4_E
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 I`TD*D
2.1 Synthesis methods based on merit function optimization …………………………...98 r8%,xA&
2.1.1 Merit function selection …………………………………………………………98 ,m?D\Pru
2.1.2 Merit function optimization ……………………………………………………101 LPn }QzH
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 +E~`H^
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 U q.~3V+u
2.2.1 Needle-like variations of the refractive index ………………………………….115 K Uut C
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2.2.2 The principal idea of the method ………………………………………………119 cv4M[]U~
2.2.3 Description of the method ……………………………………………………...124 \Ji2u GT
Bibliography …...………………………………………….……………….………..……130
