Basics of OPTICS OF MULTILAYER SYSTEMS lEe<! B$d"
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Contents chF@',9t
Preface……………………………………………………………………….………..……….4 .sOEqwO}>
Chapter 1 hPB^|#}
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: t5Oeb<REz
THEORY……………………………………………………………………………………….5 b,Vg3BS
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 F$k^px
1.1.1 Layered medium electromagnetic field equations………………………………...5 s}3`%?,6y
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 Z>si%Npm\
1.1.3 The Fresnel formulas ……………………………………………………………18 jJK`+J,i}X
1.1.4 Other ways of determining amplitude transmittance and reflectance of the uVn"'p-
layered medium…………………………………………………………………..19 ,s9gGCA
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 5m]N%{<jAB
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 C6T?D 5
1.2.1 Matrix calculating method ………………………………………………………22 h vO
1.2.2 Description of optical coating and presentation of calculation results…………..28 ,'f^K!iA
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 9_
1.2.4 Approximate formulas…………………………………………………………...33 RMvq\J}w!
1.2.5 Other recurrent methods…………………………………………………………34 Gjh8>(
1.2.6 The admittance phase plane……………………………………………………...38 e: aa
1.3 Some common properties of multilayer coatings…………………………………….46 t0*,%ge:<
1.3.1 The relation between the characteristic matrix and spectral coefficients of a t)
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multilayer coating ……………………………………………………………….47 ~0 Ifg_G
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 !RD<"
1.3.3 Transmittance and reflectance of the combination of two multilayer y`| 86`
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subsystems ……………………………………………………………………....54 t3//
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1.4 The multilayer coatings optical properties: impact of variations in the layer P ` xQL
parameters……………………………………………………………………………...58 4{ rqGC /
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… ~>"m`Q&[
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral y k{8O.g
coefficients: probability assessment method ……………………….…………...63 CVy\']
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter ?;0w 1
variations ………………………………………………………………………...66 9z$fDs }.q
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 j*' +f~ A
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 ~Bi>T15e
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 G8t9Lx
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 wJ%;\0 6
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the ;[-TsX:
central wavelength ………………………………………………………………80 rd:WF(]
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 N r,Q u8
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 A 6IrA/b
1.6.1 Common expressions for spectral coefficients of filter-type systems near central d^(7\lw|
wavelength ………………………………………………………………………88
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1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 .V
Chapter 2 ) p^ " J|
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 9Gc4mwu
2.1 Synthesis methods based on merit function optimization …………………………...98 X;&Iu{&=
2.1.1 Merit function selection …………………………………………………………98 tSVWO] <
2.1.2 Merit function optimization ……………………………………………………101 6|G&d>G$_
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 Db`SNk=
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 d2a*xDkv
2.2.1 Needle-like variations of the refractive index ………………………………….115 n(h9I'V8)F
2.2.2 The principal idea of the method ………………………………………………119 j"F?^0aR,Q
2.2.3 Description of the method ……………………………………………………...124 !7h jA=0
Bibliography …...………………………………………….……………….………..……130
