Basics of OPTICS OF MULTILAYER SYSTEMS 2f s9JP{^0
v4X_v!CQ
Contents 1 VPg`+o
Preface……………………………………………………………………….………..……….4 #}nBS- +
Chapter 1 7 _X&5ni
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: x|&[ hFXD
THEORY……………………………………………………………………………………….5 oM/B.U2a
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 W^-hMT]uD
1.1.1 Layered medium electromagnetic field equations………………………………...5 2pVVoZV.<
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 R:SIs\%o
1.1.3 The Fresnel formulas ……………………………………………………………18 oiIt3<BX
1.1.4 Other ways of determining amplitude transmittance and reflectance of the C!CaGf=
layered medium…………………………………………………………………..19 2l]C55p)s
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 ^xBb$
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 yz54:q?
1.2.1 Matrix calculating method ………………………………………………………22 _Y} ^%eFw
1.2.2 Description of optical coating and presentation of calculation results…………..28 @^w!% ?J
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 B3ohHxHu
1.2.4 Approximate formulas…………………………………………………………...33 }xpe
1.2.5 Other recurrent methods…………………………………………………………34 Yb,G^+;
1.2.6 The admittance phase plane……………………………………………………...38 Y/QK+UMW*
1.3 Some common properties of multilayer coatings…………………………………….46 U "jUMOMZ;
1.3.1 The relation between the characteristic matrix and spectral coefficients of a XRX7qo(0g
multilayer coating ……………………………………………………………….47 h8D tq5t4
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 ]~4}(\u
1.3.3 Transmittance and reflectance of the combination of two multilayer 7` j|tb-
subsystems ……………………………………………………………………....54 x`j_d:C~G
1.4 The multilayer coatings optical properties: impact of variations in the layer L%=BCmMx
parameters……………………………………………………………………………...58 fb;hf:B:
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… # UP ,;W
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral ]lG_rGw
coefficients: probability assessment method ……………………….…………...63 {d {WMq $
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter DVeF (Y3&
variations ………………………………………………………………………...66 }b\ipA,~
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 8k*k
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 Jf8'N
ot
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 `s|\" @2
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 $[L)f|
l
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the /Wta$!X{-
central wavelength ………………………………………………………………80 PT= 2LZ
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 rkER`
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 +eVpMD(
l
1.6.1 Common expressions for spectral coefficients of filter-type systems near central ,m_& eF
wavelength ………………………………………………………………………88 +&@l{x(,
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 .x9nWa
Chapter 2 p-ii($~ }
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 vb4G_ X0S
2.1 Synthesis methods based on merit function optimization …………………………...98 9Y*Vz QE
2.1.1 Merit function selection …………………………………………………………98 o: :ymAj
2.1.2 Merit function optimization ……………………………………………………101 TBLk+AR
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 'e8d["N
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 [pyXX>:M
2.2.1 Needle-like variations of the refractive index ………………………………….115 5w -G]b
2.2.2 The principal idea of the method ………………………………………………119 p>hCh5
2.2.3 Description of the method ……………………………………………………...124 [&k& $04_
Bibliography …...………………………………………….……………….………..……130
