Basics of OPTICS OF MULTILAYER SYSTEMS mM-7
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Contents Qd"u$~ qC
Preface……………………………………………………………………….………..……….4 -ZBSkyMGy
Chapter 1 ?CZ*MMV
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: Pc=:j(
THEORY……………………………………………………………………………………….5 l#;o^H i
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 A?Gk8
1.1.1 Layered medium electromagnetic field equations………………………………...5 @po|07
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 &1ss
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1.1.3 The Fresnel formulas ……………………………………………………………18 <R8!fc{`
1.1.4 Other ways of determining amplitude transmittance and reflectance of the cT3 s{k
layered medium…………………………………………………………………..19 9H,Ec,.
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 ~A-VgBbU>_
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 o3> D~9
1.2.1 Matrix calculating method ………………………………………………………22 xI^nA2 g
1.2.2 Description of optical coating and presentation of calculation results…………..28 ,[)f-FmcU
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 znu [i&\=
1.2.4 Approximate formulas…………………………………………………………...33 D8wZC'7
1.2.5 Other recurrent methods…………………………………………………………34 HD9+4~8
1.2.6 The admittance phase plane……………………………………………………...38 't un;Y
1.3 Some common properties of multilayer coatings…………………………………….46 Ar1X
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1.3.1 The relation between the characteristic matrix and spectral coefficients of a ,v>| Ub,
multilayer coating ……………………………………………………………….47 ~VaO,8&+L
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51
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1.3.3 Transmittance and reflectance of the combination of two multilayer VU(#5X%Pn
subsystems ……………………………………………………………………....54 vm`\0VGSW
1.4 The multilayer coatings optical properties: impact of variations in the layer !-Md+I_
parameters……………………………………………………………………………...58 >d#Ks0\&
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… ,P$Crs[
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral $_b^p=
coefficients: probability assessment method ……………………….…………...63 ~Is-^k)y
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter ulxy 4] h
variations ………………………………………………………………………...66 /_CSRi&
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 OQa;EBO
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 e?eX9yA7F
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 .GNl31f0
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 Gt5'-Hyo
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the ICXz(?a
central wavelength ………………………………………………………………80 yZ57uz
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 `=rDB7!$yL
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 ^+q4* X6VB
1.6.1 Common expressions for spectral coefficients of filter-type systems near central e6igx
wavelength ………………………………………………………………………88 zHW}A
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1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 :} 9Lb)Yp
Chapter 2 YztW1GvI
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97
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2.1 Synthesis methods based on merit function optimization …………………………...98 'Z ,T,zW
2.1.1 Merit function selection …………………………………………………………98 Z*Jp?[##
2.1.2 Merit function optimization ……………………………………………………101 R.B3
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 yZDS>7H
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 >)`V $x
2.2.1 Needle-like variations of the refractive index ………………………………….115 o5 |P5h
2.2.2 The principal idea of the method ………………………………………………119 - p2 =?a
2.2.3 Description of the method ……………………………………………………...124 r-k,4Yz
Bibliography …...………………………………………….……………….………..……130
