Basics of OPTICS OF MULTILAYER SYSTEMS ~u& O
toZI.cSg4
Contents Q+ M3Pqy
Preface……………………………………………………………………….………..……….4 ~:b~f]lO
Chapter 1 TB [2!ZW
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: sO-R+G/^7
THEORY……………………………………………………………………………………….5 uvM8 8#
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 rbS= Ewk
1.1.1 Layered medium electromagnetic field equations………………………………...5 IL"#T KKv
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 o% 4+I>
1.1.3 The Fresnel formulas ……………………………………………………………18 +! Ag n)
1.1.4 Other ways of determining amplitude transmittance and reflectance of the R~(.uV`#j
layered medium…………………………………………………………………..19 HON[{Oq
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 SLB iQd.
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 Vta;ibdeqW
1.2.1 Matrix calculating method ………………………………………………………22 s'=]a-l~
1.2.2 Description of optical coating and presentation of calculation results…………..28 >c>ar>4xF
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 M 8L j*JN
1.2.4 Approximate formulas…………………………………………………………...33 bu5)~|?{t
1.2.5 Other recurrent methods…………………………………………………………34 e(5R8u d
1.2.6 The admittance phase plane……………………………………………………...38 PS] X Lz
1.3 Some common properties of multilayer coatings…………………………………….46 F
RUt}*
1.3.1 The relation between the characteristic matrix and spectral coefficients of a raZRa*C;
multilayer coating ……………………………………………………………….47 %6 :2cR
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 V$D
d 7
1.3.3 Transmittance and reflectance of the combination of two multilayer O]!DNN
subsystems ……………………………………………………………………....54 qz2d'OhmtH
1.4 The multilayer coatings optical properties: impact of variations in the layer ;BvWU\!
parameters……………………………………………………………………………...58 4rdrl
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… @h8 ~xs~DG
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral /bk} J:QRg
coefficients: probability assessment method ……………………….…………...63 3Ab$
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter ;< rJ,X#
variations ………………………………………………………………………...66 Wm_-T]#_
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 (o=iX,@'2
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 3 =I Q
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 P=z':4,M}
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 [0@i,7{ZqE
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the YI+|6s [
central wavelength ………………………………………………………………80 ~epkRO="
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 @L7rE)AU.
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 @gk[sQ\O
1.6.1 Common expressions for spectral coefficients of filter-type systems near central A
76yz`D
wavelength ………………………………………………………………………88 2 ARh-zLb
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 5?" ZM'4
Chapter 2 z05pVe/5
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 i:To8kdO
2.1 Synthesis methods based on merit function optimization …………………………...98 M-t9zT
2.1.1 Merit function selection …………………………………………………………98 Jt][b
2.1.2 Merit function optimization ……………………………………………………101 9r}} m0
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 K~G^jAk+
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 ~C+T|
2.2.1 Needle-like variations of the refractive index ………………………………….115 ,)8Hl[ y
2.2.2 The principal idea of the method ………………………………………………119 ;kA2"c] m
2.2.3 Description of the method ……………………………………………………...124 v\u+=}r l
Bibliography …...………………………………………….……………….………..……130
