Basics of OPTICS OF MULTILAYER SYSTEMS ]A3
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Contents 0 6 S
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Preface……………………………………………………………………….………..……….4 f_jhQ..g<g
Chapter 1 cl%+m
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: HYfGu1j?X
THEORY……………………………………………………………………………………….5 2]5{Xmmo9
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 h= sNj
1.1.1 Layered medium electromagnetic field equations………………………………...5 E&P2E3P
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 v4n< G -
1.1.3 The Fresnel formulas ……………………………………………………………18 "r-P[EKpL
1.1.4 Other ways of determining amplitude transmittance and reflectance of the XVN`J]XHk
layered medium…………………………………………………………………..19 !5o j~H
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 @x}"aJgl
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22
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1.2.1 Matrix calculating method ………………………………………………………22 9D3{[
1.2.2 Description of optical coating and presentation of calculation results…………..28 T+<.KvO-
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 `5IrV&a
1.2.4 Approximate formulas…………………………………………………………...33 vQljxRtW
1.2.5 Other recurrent methods…………………………………………………………34 ?;ok 9Y
1.2.6 The admittance phase plane……………………………………………………...38 T- en|.
1.3 Some common properties of multilayer coatings…………………………………….46 N ,Eap KG
1.3.1 The relation between the characteristic matrix and spectral coefficients of a l;lrf3
multilayer coating ……………………………………………………………….47 \wK &wRn)
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 {]T?) !V m
1.3.3 Transmittance and reflectance of the combination of two multilayer = & bI-
subsystems ……………………………………………………………………....54 ;Bs ~E
1.4 The multilayer coatings optical properties: impact of variations in the layer s<s} 6 |Z
parameters……………………………………………………………………………...58 fST.p|b7
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… m4mE7Wn.3
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral ><<>4(eF p
coefficients: probability assessment method ……………………….…………...63 X4
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1.4.3 Multilayer coating spectral properties: influence of separate layer parameter q!$s<n
variations ………………………………………………………………………...66 m\6/:~qWW
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 IfK~~XYG
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 7Y5 r3a}%
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 VeYT [Us"
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 g+ c*VmY
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the nkW})LyB\
central wavelength ………………………………………………………………80 : ky`) F`
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 >h\y1IrAaG
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 k]~o=MLmj
1.6.1 Common expressions for spectral coefficients of filter-type systems near central t6 DSZ^Zq
wavelength ………………………………………………………………………88 q oO`)<
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 &k:xr,N=
Chapter 2 DB/~Z
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 $w0TEO!
2.1 Synthesis methods based on merit function optimization …………………………...98 EeW
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2.1.1 Merit function selection …………………………………………………………98 X1Yw=t~a
2.1.2 Merit function optimization ……………………………………………………101 DrK]U}3fh"
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 Z0,jg)s A4
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 x-BU$bx5
2.2.1 Needle-like variations of the refractive index ………………………………….115 w% %q/
