Basics of OPTICS OF MULTILAYER SYSTEMS wKh4|Ka
LG0;#3YwH
Contents %jJG >T
Preface……………………………………………………………………….………..……….4 Xxj-
6i
Chapter 1 l M`2sy
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: /A\8 mL8
THEORY……………………………………………………………………………………….5 Ha#= (9.
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 + /G2fhE
1.1.1 Layered medium electromagnetic field equations………………………………...5 AD> e?u
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 TvoyZW\?w
1.1.3 The Fresnel formulas ……………………………………………………………18 &$BjV{,/zc
1.1.4 Other ways of determining amplitude transmittance and reflectance of the !vi> U|rh
layered medium…………………………………………………………………..19 _~m5^Q&
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 -]Bq|qTH[(
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 _rMg}F"
1.2.1 Matrix calculating method ………………………………………………………22 W ~<^L\Lu
1.2.2 Description of optical coating and presentation of calculation results…………..28 $GV7o{"&
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 zC:AS t
1.2.4 Approximate formulas…………………………………………………………...33 [|wZ77\
1.2.5 Other recurrent methods…………………………………………………………34 ho{*Cjv
1.2.6 The admittance phase plane……………………………………………………...38 YpHg&|Fr
1.3 Some common properties of multilayer coatings…………………………………….46 wVXS%4|v
1.3.1 The relation between the characteristic matrix and spectral coefficients of a },?kk1vIT{
multilayer coating ……………………………………………………………….47 <\ y @*fg+
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 *t FHM &a
1.3.3 Transmittance and reflectance of the combination of two multilayer Fgn TGY}
subsystems ……………………………………………………………………....54
x^qVw5{n
1.4 The multilayer coatings optical properties: impact of variations in the layer ~%F9%=
parameters……………………………………………………………………………...58 &3>)q ul
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… hF?1y `20
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral w_c"@CjkE
coefficients: probability assessment method ……………………….…………...63 'c&Ed
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter \& :nFb%=
variations ………………………………………………………………………...66 g9pZ\$J&
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 .<?GS{6
N
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 ? V1*cVD6i
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 T~?Ff|qFC
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 P{`C^W$J^
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the E`JI>7
central wavelength ………………………………………………………………80 g'f@H-KCD
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 D8Ic?:iX[
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 `RT>}_j
1.6.1 Common expressions for spectral coefficients of filter-type systems near central 4KAZ ':
wavelength ………………………………………………………………………88 iU918!!N
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 ]EbM9Fo-U
Chapter 2 A Q U+mo
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 )}R0Y=e
2.1 Synthesis methods based on merit function optimization …………………………...98 je-!4r,
2.1.1 Merit function selection …………………………………………………………98 %Xd[(Q)
2.1.2 Merit function optimization ……………………………………………………101 Y Uc+0
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 JG. y,<xW
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 M^Yh|%M
2.2.1 Needle-like variations of the refractive index ………………………………….115 bP#:Oi0v`
2.2.2 The principal idea of the method ………………………………………………119 9=M$AB
2.2.3 Description of the method ……………………………………………………...124 g /_5unI}u
Bibliography …...………………………………………….……………….………..……130
