Basics of OPTICS OF MULTILAYER SYSTEMS ^ kr)U8
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Contents !I[n|r "
Preface……………………………………………………………………….………..……….4 {h"\JI!
Chapter 1 v -3zav
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: >, E $bm2
THEORY……………………………………………………………………………………….5 ymZ/(:3_
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 J31M:<
1.1.1 Layered medium electromagnetic field equations………………………………...5 S=}~I
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 (U F!Zb]{
1.1.3 The Fresnel formulas ……………………………………………………………18 pQ
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1.1.4 Other ways of determining amplitude transmittance and reflectance of the (U_Q7hj a?
layered medium…………………………………………………………………..19 qDM[7q3.
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 ~
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1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 Z0eBx
1.2.1 Matrix calculating method ………………………………………………………22 mi<D
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1.2.2 Description of optical coating and presentation of calculation results…………..28 9|?Lz
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 !B lk=L+p
1.2.4 Approximate formulas…………………………………………………………...33 wYA/<0'yH
1.2.5 Other recurrent methods…………………………………………………………34 5|CiwQg|,p
1.2.6 The admittance phase plane……………………………………………………...38 (AG
1.3 Some common properties of multilayer coatings…………………………………….46 ;_/q>DR>,3
1.3.1 The relation between the characteristic matrix and spectral coefficients of a b 0b9#9x
multilayer coating ……………………………………………………………….47 qb4;l\SfT
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 $Je"z]cy-
1.3.3 Transmittance and reflectance of the combination of two multilayer &H&P)Px*_
subsystems ……………………………………………………………………....54 5%+}rSn7
1.4 The multilayer coatings optical properties: impact of variations in the layer 3Jm'q,T C
parameters……………………………………………………………………………...58 'd^gRH<z
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… aNC,ccm
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral ocqB-C]
coefficients: probability assessment method ……………………….…………...63 L"h@`3o|
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter lK,=`xe
variations ………………………………………………………………………...66 J,G9m4Z7
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 IZ0$=aB 7
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 qW~ R-g]
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 AaYrVf 9!
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 0@K:Tq-mF
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the A dEbyL
central wavelength ………………………………………………………………80 RzRvu]]8
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 )H9*N B8%
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 iM|"H..
1.6.1 Common expressions for spectral coefficients of filter-type systems near central U|7 Qw|I7
wavelength ………………………………………………………………………88 2nU
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1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 :{s%=\k {d
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SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 "QO/Jl s
2.1 Synthesis methods based on merit function optimization …………………………...98 [Z#.]gb
2.1.1 Merit function selection …………………………………………………………98 @zynqh
2.1.2 Merit function optimization ……………………………………………………101 wUCDJY:,1
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 Z4AAg
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 H='9zqYZ<W
2.2.1 Needle-like variations of the refractive index ………………………………….115 };m7FO
2.2.2 The principal idea of the method ………………………………………………119 bp>ps@zFq
2.2.3 Description of the method ……………………………………………………...124 *:T>~ilF
Bibliography …...………………………………………….……………….………..……130
