Basics of OPTICS OF MULTILAYER SYSTEMS qd\5S*Z1
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Contents l`D^)~o8
Preface……………………………………………………………………….………..……….4 l1BbL5#1Q>
Chapter 1 $@k[X h
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: VbR /k,Co
THEORY……………………………………………………………………………………….5 .R5[bXxe7
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 pM ZKF =
1.1.1 Layered medium electromagnetic field equations………………………………...5 Khd "
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 d3D w[4
1.1.3 The Fresnel formulas ……………………………………………………………18 Itn7Kl
1.1.4 Other ways of determining amplitude transmittance and reflectance of the + <A D
layered medium…………………………………………………………………..19 8`Wj 1 , q
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 M JJ]8:%
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 *K#7,*Oz
1.2.1 Matrix calculating method ………………………………………………………22 t<S]YA~N'
1.2.2 Description of optical coating and presentation of calculation results…………..28 u%n6!Zx
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 + c&n7
1.2.4 Approximate formulas…………………………………………………………...33 LB*qL
1.2.5 Other recurrent methods…………………………………………………………34 .Y B}w
1.2.6 The admittance phase plane……………………………………………………...38 g3[Zh=+]E
1.3 Some common properties of multilayer coatings…………………………………….46 ).aQ}G wx^
1.3.1 The relation between the characteristic matrix and spectral coefficients of a Q|40
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multilayer coating ……………………………………………………………….47 )X*?M ?~\
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 R F gy
1.3.3 Transmittance and reflectance of the combination of two multilayer WmU5YZ(mAq
subsystems ……………………………………………………………………....54 -< rQOPH %
1.4 The multilayer coatings optical properties: impact of variations in the layer >s#[dr\ww
parameters……………………………………………………………………………...58 h%'4V<V
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… eZDqW)x
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral =@%;6`AVcp
coefficients: probability assessment method ……………………….…………...63 N[e QT
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter &' ,A2iG
variations ………………………………………………………………………...66 9 [qEJ $--
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 jwsl"z L
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 ,> " rcd
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 +B^(,qKMN
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 !e~Yp0gX#
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the ~" \qX+
central wavelength ………………………………………………………………80 ?v-Y1j
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 /M k85C79
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 HSq.0 vYl6
1.6.1 Common expressions for spectral coefficients of filter-type systems near central 8#% Sq=/+M
wavelength ………………………………………………………………………88 >~O36q^w
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 VayU
Chapter 2 >7@kwj-f)
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 rMDo5Z2
2.1 Synthesis methods based on merit function optimization …………………………...98 w)x`zVwO
2.1.1 Merit function selection …………………………………………………………98 ENu`@S='I3
2.1.2 Merit function optimization ……………………………………………………101 en\shc{R]`
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 Fv!zS.)`
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 gH87 e
2.2.1 Needle-like variations of the refractive index ………………………………….115 X4<!E#
2.2.2 The principal idea of the method ………………………………………………119 =)Z!qjf1U
2.2.3 Description of the method ……………………………………………………...124 & P8 Run
Bibliography …...………………………………………….……………….………..……130
