Basics of OPTICS OF MULTILAYER SYSTEMS tI tX y
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Contents i
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Preface……………………………………………………………………….………..……….4 g7}Gip}.>
Chapter 1 U `R5 'Tf;
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: wvO|UP H\
THEORY……………………………………………………………………………………….5 ciBP7>'::
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 Dv| #u|iw
1.1.1 Layered medium electromagnetic field equations………………………………...5 b LlKe50
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 K0- ypU*P
1.1.3 The Fresnel formulas ……………………………………………………………18 "?]{ %-u
1.1.4 Other ways of determining amplitude transmittance and reflectance of the PDJr<E?
layered medium…………………………………………………………………..19 B~ ]k#Ot)
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 <sWprR
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 4 !i$4
1.2.1 Matrix calculating method ………………………………………………………22 O@u?h9?cf>
1.2.2 Description of optical coating and presentation of calculation results…………..28 |L%Z,:yO
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 z.7cy@N6
1.2.4 Approximate formulas…………………………………………………………...33 QS%%^+E2
1.2.5 Other recurrent methods…………………………………………………………34 :[wsKFaV+
1.2.6 The admittance phase plane……………………………………………………...38 ?I6fye 7
1.3 Some common properties of multilayer coatings…………………………………….46 CJ1 7 n
1.3.1 The relation between the characteristic matrix and spectral coefficients of a JJP08 oP
multilayer coating ……………………………………………………………….47 K{&mI/ ;
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 10)jsA
1.3.3 Transmittance and reflectance of the combination of two multilayer 7&t-pv92*
subsystems ……………………………………………………………………....54 1C< uz29
1.4 The multilayer coatings optical properties: impact of variations in the layer _,p/l&<
parameters……………………………………………………………………………...58 ^ V ?<K.F
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… k.5 u
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral OV m \
coefficients: probability assessment method ……………………….…………...63 Li!Vx1p;u.
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter p`b"-[93
variations ………………………………………………………………………...66 l= =``
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 n!YKz"$
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 -=%@ L&y1
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 XG}C+;4Aw
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 RHmgD;7`
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the {_7 i8c<s=
central wavelength ………………………………………………………………80 a][f
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 ,5i ` -OI
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 JSkLEa~<
1.6.1 Common expressions for spectral coefficients of filter-type systems near central _7H7
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wavelength ………………………………………………………………………88 < vL,*.zd
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 `P@T$bC
Chapter 2 iIMd!Q.)@
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 n,jKmA
2.1 Synthesis methods based on merit function optimization …………………………...98 p2ogn}`
2.1.1 Merit function selection …………………………………………………………98 T ? $:'XJ
2.1.2 Merit function optimization ……………………………………………………101 s %qF/70'
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 t z5e"+T z
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 fmQ_P.c
2.2.1 Needle-like variations of the refractive index ………………………………….115 q1z"-~i )E
2.2.2 The principal idea of the method ………………………………………………119 k jg~n9#T
2.2.3 Description of the method ……………………………………………………...124 OBMTgZHxv
Bibliography …...………………………………………….……………….………..……130
