Basics of OPTICS OF MULTILAYER SYSTEMS 1%1-j
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Contents VaQ}XM
Preface……………………………………………………………………….………..……….4 &,e @pv c3
Chapter 1 ~hM4({/QN
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: F~*
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THEORY……………………………………………………………………………………….5 :+[q `
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 \f
1.1.1 Layered medium electromagnetic field equations………………………………...5 u_:"
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1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 @8/-^Rh*
1.1.3 The Fresnel formulas ……………………………………………………………18 )0UQy#r
1.1.4 Other ways of determining amplitude transmittance and reflectance of the $9hOWti
layered medium…………………………………………………………………..19 Cu/w><h)
1.1.5 Transmittance, reflectance and absorptance …………………………………….20
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1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 Gc
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1.2.1 Matrix calculating method ………………………………………………………22 "I+wU`AIek
1.2.2 Description of optical coating and presentation of calculation results…………..28 <Pf W
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 :L\@+}{( c
1.2.4 Approximate formulas…………………………………………………………...33 x>Q#B v y
1.2.5 Other recurrent methods…………………………………………………………34 {},G xrQm
1.2.6 The admittance phase plane……………………………………………………...38 ! JrV h$K
1.3 Some common properties of multilayer coatings…………………………………….46 2abWIw4
1.3.1 The relation between the characteristic matrix and spectral coefficients of a y;Dw%m
multilayer coating ……………………………………………………………….47 q$H'u[KQ06
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 zeR!Y yt!
1.3.3 Transmittance and reflectance of the combination of two multilayer ( c[|k
subsystems ……………………………………………………………………....54 nwV\ [E
1.4 The multilayer coatings optical properties: impact of variations in the layer N^`F_R1Z
parameters……………………………………………………………………………...58 L4Kkbt<x
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… E5 Y92vu
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral AZtZa'hbkQ
coefficients: probability assessment method ……………………….…………...63 NCl={O9<j
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter pT[C[h:
variations ………………………………………………………………………...66 3 YRhqp"E
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 KeXQ'.x5O
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 GS)l{bS#[O
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 Y{2\== ~
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 N Fc< %#H
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the 'MsxZqW"~
central wavelength ………………………………………………………………80 <\yM{
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1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 [nflQW6
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 w"A'uFXLc
1.6.1 Common expressions for spectral coefficients of filter-type systems near central k*lrE4::a
wavelength ………………………………………………………………………88 (u$Q
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 >Wy@J]Y#
Chapter 2 qFvtqv2
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 "4L' 2w+
2.1 Synthesis methods based on merit function optimization …………………………...98 4$vya+mAk5
2.1.1 Merit function selection …………………………………………………………98 #PtV=Ee1
2.1.2 Merit function optimization ……………………………………………………101 .eJ4F-V
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 rEZa%)XJ
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 l} h<2
2.2.1 Needle-like variations of the refractive index ………………………………….115 6K* 7%8Y/G
2.2.2 The principal idea of the method ………………………………………………119 #msk'MVt
2.2.3 Description of the method ……………………………………………………...124 ^V> sNR
Bibliography …...………………………………………….……………….………..……130
