Basics of OPTICS OF MULTILAYER SYSTEMS ` Nn^
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Contents SR 9 Cl
Preface……………………………………………………………………….………..……….4 w ' E
Chapter 1 or_x0Q
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: {Gnji] v
THEORY……………………………………………………………………………………….5 |kvom 4 T
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 EDR;" G(N
1.1.1 Layered medium electromagnetic field equations………………………………...5 7$(>Z^ Em
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 $73j*@EQA
1.1.3 The Fresnel formulas ……………………………………………………………18 8>Xyz`$kH
1.1.4 Other ways of determining amplitude transmittance and reflectance of the Do7&OBI~
layered medium…………………………………………………………………..19 Z!TLWX "
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 s(Of
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1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 5oQy
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1.2.1 Matrix calculating method ………………………………………………………22 c9\jELO
1.2.2 Description of optical coating and presentation of calculation results…………..28 J4qFU^
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 *rO#UE2
1.2.4 Approximate formulas…………………………………………………………...33 n*6 b*fl
1.2.5 Other recurrent methods…………………………………………………………34 +/60$60[z
1.2.6 The admittance phase plane……………………………………………………...38 n'D1s:W^B
1.3 Some common properties of multilayer coatings…………………………………….46 ]HP
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1.3.1 The relation between the characteristic matrix and spectral coefficients of a qp*C%U
multilayer coating ……………………………………………………………….47 8LP L4l
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 uBLI!N-G
1.3.3 Transmittance and reflectance of the combination of two multilayer :\x)`lu
subsystems ……………………………………………………………………....54 ^Bw2y&nN
1.4 The multilayer coatings optical properties: impact of variations in the layer BN&^$1F((
parameters……………………………………………………………………………...58 (W3~ r
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… _94|^
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral 6P=6E
coefficients: probability assessment method ……………………….…………...63 k%V#{t.
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter 75 ~>[JM
variations ………………………………………………………………………...66 )s6pOxWx
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 \2#>@6Sqrl
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 +0mU) 4n/
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 j )6A
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 XVjs0/5b
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the [*U6L <J I
central wavelength ………………………………………………………………80 4l+"J:,
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 Bk&ry)`gD
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 Z@fMU2e=Z
1.6.1 Common expressions for spectral coefficients of filter-type systems near central 53d8AJ_@X
wavelength ………………………………………………………………………88 V3WHp'1
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 z=>U>
Chapter 2 Hc1S:RW
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 mG2*s ^$
2.1 Synthesis methods based on merit function optimization …………………………...98 z{ U2K '
2.1.1 Merit function selection …………………………………………………………98 GU'/-6-T
2.1.2 Merit function optimization ……………………………………………………101 won;tO]\;@
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 e&zZr]vs]l
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 V|3}~(5=
2.2.1 Needle-like variations of the refractive index ………………………………….115 M=hxOta
2.2.2 The principal idea of the method ………………………………………………119 F@Qz h
2.2.3 Description of the method ……………………………………………………...124 L.XGD|m
Bibliography …...………………………………………….……………….………..……130
