Basics of OPTICS OF MULTILAYER SYSTEMS o . _^
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Contents DxD0iJ=W
Preface……………………………………………………………………….………..……….4 }9k q?
Chapter 1 l00D|W_ 9
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: L7b{H2 2
THEORY……………………………………………………………………………………….5 x SUR<
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 />oU}m" k
1.1.1 Layered medium electromagnetic field equations………………………………...5 Af%?WZlOq
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 eyG.XAP
1.1.3 The Fresnel formulas ……………………………………………………………18 $k?L?R1
1.1.4 Other ways of determining amplitude transmittance and reflectance of the V:+bq`
layered medium…………………………………………………………………..19 S`^W#,rj
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 iUKj:q:
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 (M=Br
1.2.1 Matrix calculating method ………………………………………………………22 2u:j6ic
1.2.2 Description of optical coating and presentation of calculation results…………..28 M#p,Z F
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 RAxz+1JT
1.2.4 Approximate formulas…………………………………………………………...33 g:)v thOs
1.2.5 Other recurrent methods…………………………………………………………34 sDC RL%0QK
1.2.6 The admittance phase plane……………………………………………………...38 WI9.?(5q
1.3 Some common properties of multilayer coatings…………………………………….46 %qHT!aP
1.3.1 The relation between the characteristic matrix and spectral coefficients of a n"
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multilayer coating ……………………………………………………………….47 a]k&$
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 %!S
1.3.3 Transmittance and reflectance of the combination of two multilayer w\ :b(I
subsystems ……………………………………………………………………....54 mc=*wr$
1.4 The multilayer coatings optical properties: impact of variations in the layer _7<U[63
parameters……………………………………………………………………………...58 P:TpB6.=q
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… `3Kpr pE8v
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral ?uN(" I
coefficients: probability assessment method ……………………….…………...63 w;(gi
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter :&%;s*-9
variations ………………………………………………………………………...66 9|`@cz w
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 yM2&cMHH~
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 E~P 0}'
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 l1[IXw?
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 ?X1#b2 s
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the .g~@e_;):
central wavelength ………………………………………………………………80 t;]egk
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 (?!0__NN;
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 57>ne)51
1.6.1 Common expressions for spectral coefficients of filter-type systems near central #V 6
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wavelength ………………………………………………………………………88 #77UKYj2L-
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 < &2,G5XA
Chapter 2 ;`B35K
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 "Z k6B"o)
2.1 Synthesis methods based on merit function optimization …………………………...98 c5R{Sl
2.1.1 Merit function selection …………………………………………………………98 G= cx c_9
2.1.2 Merit function optimization ……………………………………………………101 Anv8)J!9u
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 bEKLameKv
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 zTB9GrU
2.2.1 Needle-like variations of the refractive index ………………………………….115 E'8Bw7 Tz
2.2.2 The principal idea of the method ………………………………………………119 q1Sm#_7
2.2.3 Description of the method ……………………………………………………...124 ;%<4U^2
Bibliography …...………………………………………….……………….………..……130
