Basics of OPTICS OF MULTILAYER SYSTEMS XcVN{6-z
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Contents
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Preface……………………………………………………………………….………..……….4 a+w2cN'
Chapter 1 6Y9N= \`
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: KGz Nj%
THEORY……………………………………………………………………………………….5 $%y q[$^
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 RY , <*
1.1.1 Layered medium electromagnetic field equations………………………………...5 i\i%Wi Rl
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 J2bvHxb Rd
1.1.3 The Fresnel formulas ……………………………………………………………18 [C'bfX5HB5
1.1.4 Other ways of determining amplitude transmittance and reflectance of the 3U[O :
layered medium…………………………………………………………………..19 nf.Ox.kM)
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 QJ|@Y(KV0
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 8dGsV5" *
1.2.1 Matrix calculating method ………………………………………………………22 -'! J?~
1.2.2 Description of optical coating and presentation of calculation results…………..28 sh<Q2X
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 $D bnPZ2$
1.2.4 Approximate formulas…………………………………………………………...33 J]F&4 O
1.2.5 Other recurrent methods…………………………………………………………34 Npp YUY
1.2.6 The admittance phase plane……………………………………………………...38 xe@1H\ 7:
1.3 Some common properties of multilayer coatings…………………………………….46 ul~ux$a
1.3.1 The relation between the characteristic matrix and spectral coefficients of a n5:uG'L \
multilayer coating ……………………………………………………………….47 yPN '@{ 5#
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 F-_u/C]
1.3.3 Transmittance and reflectance of the combination of two multilayer @N=vmtLP
subsystems ……………………………………………………………………....54 K" #$",}=
1.4 The multilayer coatings optical properties: impact of variations in the layer G Ec6;uz<
parameters……………………………………………………………………………...58 l A ^1}
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… ] ; w 2YR
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral {)[o*+9
coefficients: probability assessment method ……………………….…………...63 v=U<exM6%
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter ]3KeAJ
variations ………………………………………………………………………...66 ]PXM;w
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 Pvxb6\G&d
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 =rjU=3!&(
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 {v ?Q9
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76
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1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the Jj4 HJ9
central wavelength ………………………………………………………………80 FuhmLm'p
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 %yR XOt2(
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 #}`sfaT
1.6.1 Common expressions for spectral coefficients of filter-type systems near central n;g'?z=hy
wavelength ………………………………………………………………………88 c;l!i-
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 Q: }]-lJg
Chapter 2 w,UE0i9I
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 B*,6;lCjX
2.1 Synthesis methods based on merit function optimization …………………………...98 !~ox;I}S
2.1.1 Merit function selection …………………………………………………………98 O bs#2>h
2.1.2 Merit function optimization ……………………………………………………101 ;Qi:j^+P)
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 )U/jD
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 C:QB=?%;
2.2.1 Needle-like variations of the refractive index ………………………………….115 'VDWJTia
2.2.2 The principal idea of the method ………………………………………………119 ?CpVA
2.2.3 Description of the method ……………………………………………………...124 Aoe\\'O|V
Bibliography …...………………………………………….……………….………..……130
