Basics of OPTICS OF MULTILAYER SYSTEMS g-"G Zi
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Contents P t/]Z<VL
Preface……………………………………………………………………….………..……….4 0(:SEiz6s
Chapter 1 FoH1O+e
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: Q> rr?L`
THEORY……………………………………………………………………………………….5 P?P.QK
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 +8 itP>
1.1.1 Layered medium electromagnetic field equations………………………………...5 p3{Ff5FZ
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 8"ZS|^#
1.1.3 The Fresnel formulas ……………………………………………………………18 \hBzP^*"n
1.1.4 Other ways of determining amplitude transmittance and reflectance of the ; D/6e6
layered medium…………………………………………………………………..19 N2duhI6
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 Vp|?R65S*
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22
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1.2.1 Matrix calculating method ………………………………………………………22 ?h%Jb^#9
1.2.2 Description of optical coating and presentation of calculation results…………..28 Q9xb7)G
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 "d0=uHd5\
1.2.4 Approximate formulas…………………………………………………………...33 ar}-~~h 5
1.2.5 Other recurrent methods…………………………………………………………34 NMf#0Nz-
1.2.6 The admittance phase plane……………………………………………………...38 U ,;796h
1.3 Some common properties of multilayer coatings…………………………………….46 \]5I atli
1.3.1 The relation between the characteristic matrix and spectral coefficients of a $j<KXR
multilayer coating ……………………………………………………………….47 y RXWd*9
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 [Z #Sj=z
1.3.3 Transmittance and reflectance of the combination of two multilayer #9!7-!4pW
subsystems ……………………………………………………………………....54 g<.Is
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1.4 The multilayer coatings optical properties: impact of variations in the layer _6ck@
parameters……………………………………………………………………………...58 Y|Gp\
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… Yv @n$W`:
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral &r4|WM/ec
coefficients: probability assessment method ……………………….…………...63 #u8#<
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1.4.3 Multilayer coating spectral properties: influence of separate layer parameter
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variations ………………………………………………………………………...66 U&V u%+B
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 g3>>gu#0DC
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 {ilz[LM8(
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 <p*k-mfr
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 ,qv\Y]
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the -D'Xx OI
central wavelength ………………………………………………………………80 F4= =a8
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 W0~G`A(:;
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 wL="p) TO.
1.6.1 Common expressions for spectral coefficients of filter-type systems near central AD?XJ3
wavelength ………………………………………………………………………88 p^RX<L/\=_
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 h@G~' \8 t
Chapter 2 , 1N|lyV
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 :W1?t*z:[
2.1 Synthesis methods based on merit function optimization …………………………...98 7H< IO`
2.1.1 Merit function selection …………………………………………………………98 .O5V;&,
2.1.2 Merit function optimization ……………………………………………………101 -9,~b9$
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 s_VcC_A
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 AguE)I&m
2.2.1 Needle-like variations of the refractive index ………………………………….115 vJ^~J2#5
2.2.2 The principal idea of the method ………………………………………………119 }P.Z}n;Uj
2.2.3 Description of the method ……………………………………………………...124 A`Y^qXFb`
Bibliography …...………………………………………….……………….………..……130
