Basics of OPTICS OF MULTILAYER SYSTEMS yC
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Preface……………………………………………………………………….………..……….4 w`gyE
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Chapter 1 IU!H t>
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: fbC~WV#
THEORY……………………………………………………………………………………….5 q*8lnk
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 f=aIXhiYU
1.1.1 Layered medium electromagnetic field equations………………………………...5 6)[< )?A.[
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 n &} s-`D
1.1.3 The Fresnel formulas ……………………………………………………………18 'Kz9ygZy
1.1.4 Other ways of determining amplitude transmittance and reflectance of the r]LCv sVa
layered medium…………………………………………………………………..19 Hk;-5A|9
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 8Xn!Kpa
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 )q3"t2-
1.2.1 Matrix calculating method ………………………………………………………22 3z[ $4L'.
1.2.2 Description of optical coating and presentation of calculation results…………..28 'UfeluMd
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 k+1gQru{d
1.2.4 Approximate formulas…………………………………………………………...33 u Z(? >
1.2.5 Other recurrent methods…………………………………………………………34 (V?@?2 5
1.2.6 The admittance phase plane……………………………………………………...38 u) *Kws
1.3 Some common properties of multilayer coatings…………………………………….46 uLV BM]Qj
1.3.1 The relation between the characteristic matrix and spectral coefficients of a *Y vRNHP
multilayer coating ……………………………………………………………….47 x(~< t X~
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 JNo8>aFOb
1.3.3 Transmittance and reflectance of the combination of two multilayer lTz6"/
subsystems ……………………………………………………………………....54 SUE
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1.4 The multilayer coatings optical properties: impact of variations in the layer !LIlt`ag9
parameters……………………………………………………………………………...58 g`?:=G:a*
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… KQmZ#W%2m
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral tcL2J .
coefficients: probability assessment method ……………………….…………...63 (E!!pz
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter .zC*Z&e,.[
variations ………………………………………………………………………...66 O4Dr ]Xc]
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 C2/}d? bki
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 A3+6 #?:;
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 x-_vl
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1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 o "" ~jc~
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the G]*|H0j
central wavelength ………………………………………………………………80 6 bO; &
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 qO()w
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 J ?Iq 9f
1.6.1 Common expressions for spectral coefficients of filter-type systems near central urZ8j?}c
wavelength ………………………………………………………………………88 (|u 31[
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 :&yDqoQKJ
Chapter 2 g.C5r]=+&
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 "JT;gaEm
2.1 Synthesis methods based on merit function optimization …………………………...98 JwP:2-o
2.1.1 Merit function selection …………………………………………………………98 w *~Tm >U
2.1.2 Merit function optimization ……………………………………………………101 ]~jN^"o_B
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 `s /?b|,
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 9l
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2.2.1 Needle-like variations of the refractive index ………………………………….115 ][:rLs
2.2.2 The principal idea of the method ………………………………………………119 GdA.g
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2.2.3 Description of the method ……………………………………………………...124 $0qMQ%P
Bibliography …...………………………………………….……………….………..……130
