Basics of OPTICS OF MULTILAYER SYSTEMS \,jrug<C$^
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Contents ')_Gm{A#p
Preface……………………………………………………………………….………..……….4 6kH47Yc?
Chapter 1 .r uGS.nS4
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: -kY7~yS7
THEORY……………………………………………………………………………………….5 (3YqM7cqt
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 o3*IfD
1.1.1 Layered medium electromagnetic field equations………………………………...5 x
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1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 yIC.Jm D*
1.1.3 The Fresnel formulas ……………………………………………………………18 JJJlgr]#
1.1.4 Other ways of determining amplitude transmittance and reflectance of the u,<I%
layered medium…………………………………………………………………..19 Fhw:@@=
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 r:.5O F}
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 * yp}#\rk
1.2.1 Matrix calculating method ………………………………………………………22 AD$k`Cj
1.2.2 Description of optical coating and presentation of calculation results…………..28 Iw(2D(se
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 h*2Q0GRX
1.2.4 Approximate formulas…………………………………………………………...33 K%9PIqK?4
1.2.5 Other recurrent methods…………………………………………………………34 Pnq[r2#]:
1.2.6 The admittance phase plane……………………………………………………...38 w$ Lpuu n{
1.3 Some common properties of multilayer coatings…………………………………….46 @=ABO"CQ
1.3.1 The relation between the characteristic matrix and spectral coefficients of a L12m ;
multilayer coating ……………………………………………………………….47 J0xOB;rd
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 Isv@V .
1.3.3 Transmittance and reflectance of the combination of two multilayer xzF@v> 2S+
subsystems ……………………………………………………………………....54 b%> vhj&F
1.4 The multilayer coatings optical properties: impact of variations in the layer hY=#_r8
parameters……………………………………………………………………………...58 -D DH)VO
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… {'dpRq{c|
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral NyU~8?bp
coefficients: probability assessment method ……………………….…………...63 /zZ$<mVG
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter .um]1_= \
variations ………………………………………………………………………...66 lO},fM2j
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 CU)'x
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1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 vU Bk oC2Q
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 <(x[Qp/5P
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 zp[Uh]-dMK
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the xEtzqP<]
central wavelength ………………………………………………………………80 .Q
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1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 B6~a `~"
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 vH_QSx;C#
1.6.1 Common expressions for spectral coefficients of filter-type systems near central ~6!{\un
wavelength ………………………………………………………………………88 PY7j uS[+
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 !J
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Chapter 2 \ YO1 ;\W
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 eaP,M kK&
2.1 Synthesis methods based on merit function optimization …………………………...98 lC&U9=7W
2.1.1 Merit function selection …………………………………………………………98 u
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2.1.2 Merit function optimization ……………………………………………………101 <; \T
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2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 ? _36uJo}
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 'J~{8w,.
2.2.1 Needle-like variations of the refractive index ………………………………….115 INrl ^P*
2.2.2 The principal idea of the method ………………………………………………119 ,lSt}Lml
2.2.3 Description of the method ……………………………………………………...124 5]c mDk
Bibliography …...………………………………………….……………….………..……130
