Basics of OPTICS OF MULTILAYER SYSTEMS mSl.mi(JiZ
]K,Tn yp
Contents }*pi<s
Preface……………………………………………………………………….………..……….4 9N 3o-=
Chapter 1 Uf;^%* P4
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: K: # I
THEORY……………………………………………………………………………………….5 fN1-d&T
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 S k\K 4
1.1.1 Layered medium electromagnetic field equations………………………………...5 -Cc^d!::
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 o9yJ f#-En
1.1.3 The Fresnel formulas ……………………………………………………………18 nazZ*lC
1.1.4 Other ways of determining amplitude transmittance and reflectance of the 5 IjGm
layered medium…………………………………………………………………..19 '$]97b7G
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 0rs"o-s<
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 ]Wlco
1.2.1 Matrix calculating method ………………………………………………………22 y(yHt= r
1.2.2 Description of optical coating and presentation of calculation results…………..28 v\%HPMlh
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 . ~~T\rmI
1.2.4 Approximate formulas…………………………………………………………...33 1JG'%8}#8
1.2.5 Other recurrent methods…………………………………………………………34 x@;m8z0
1.2.6 The admittance phase plane……………………………………………………...38 4*cEag
1.3 Some common properties of multilayer coatings…………………………………….46 =|y9U lsD
1.3.1 The relation between the characteristic matrix and spectral coefficients of a
=ncVnW{
multilayer coating ……………………………………………………………….47 t pQ (g%
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 q\4Xs$APq
1.3.3 Transmittance and reflectance of the combination of two multilayer
B Qxs~
subsystems ……………………………………………………………………....54 Zaf:fsj>
1.4 The multilayer coatings optical properties: impact of variations in the layer ~[nSXnPO
parameters……………………………………………………………………………...58 yEoF 4bt
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… Lx SpctiNx
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral q01wbO3-"
coefficients: probability assessment method ……………………….…………...63 w4{<n /"
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter x}I+Iggi
variations ………………………………………………………………………...66 ~1AgD-:Jz
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 \aUC(K~o\;
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 By",rD- r
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 $AjHbU.I{
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 :g=qz~2Xk
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the .|>3k'< l
central wavelength ………………………………………………………………80
goOCu
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 Y0dEH^I
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 cj|80$cSA
1.6.1 Common expressions for spectral coefficients of filter-type systems near central Ma']?Rb`
wavelength ………………………………………………………………………88 g63(E,;;J
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 s.QwSbw-g
Chapter 2 =M [bn q*\
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 +YKi,
2.1 Synthesis methods based on merit function optimization …………………………...98 1POmP&fI(
2.1.1 Merit function selection …………………………………………………………98 b;W3 j
2.1.2 Merit function optimization ……………………………………………………101 &P}_bx
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108
}Gm>`cw-
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 x$.^"l-vX
2.2.1 Needle-like variations of the refractive index ………………………………….115 )9' K($
2.2.2 The principal idea of the method ………………………………………………119 :tB1D@Cb6
2.2.3 Description of the method ……………………………………………………...124 w 3ob IJm
Bibliography …...………………………………………….……………….………..……130
