Basics of OPTICS OF MULTILAYER SYSTEMS )@_ 5}8
] p*Fq^
Contents @a}\]REn
Preface……………………………………………………………………….………..……….4 \t
^ 9UN
Chapter 1 ]6].l$%z#
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS: l pnPd{kE
THEORY……………………………………………………………………………………….5 Z$y~:b z
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5 }8dS[-.
1.1.1 Layered medium electromagnetic field equations………………………………...5 rLE5fl5W
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12 >JHQA1mX
1.1.3 The Fresnel formulas ……………………………………………………………18 J3y4 D}
1.1.4 Other ways of determining amplitude transmittance and reflectance of the !"SuE)WM
layered medium…………………………………………………………………..19 #@:GL mD%
1.1.5 Transmittance, reflectance and absorptance …………………………………….20 /TScYE:$HE
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22 -"5r-q q*
1.2.1 Matrix calculating method ………………………………………………………22 LLPbZ9q
1.2.2 Description of optical coating and presentation of calculation results…………..28 8F/JOtkGMt
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30 h@+( VQ
1.2.4 Approximate formulas…………………………………………………………...33 ^q\9HBHT
1.2.5 Other recurrent methods…………………………………………………………34 vt(cC) )
1.2.6 The admittance phase plane……………………………………………………...38 g_e_L39
1.3 Some common properties of multilayer coatings…………………………………….46 kqZ+e/o>O9
1.3.1 The relation between the characteristic matrix and spectral coefficients of a s!?T$@a=
multilayer coating ……………………………………………………………….47 /{!?e<N>
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51 u&r+ylbs I
1.3.3 Transmittance and reflectance of the combination of two multilayer }TG=ZV i
subsystems ……………………………………………………………………....54 'a=' (,%
1.4 The multilayer coatings optical properties: impact of variations in the layer ]dL#k>$0q
parameters……………………………………………………………………………...58 ] ] 50c
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...………… kz^?!l)X0
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral UgD&tD0fp
coefficients: probability assessment method ……………………….…………...63 u .,l_D_
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter c52S2f7
variations ………………………………………………………………………...66 :ywm 4)
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68 : \KJw
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69 lO=~&_
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72 o,_R;'\E[a
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76 }o7"2 h ht
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the t{Z:N']H
central wavelength ………………………………………………………………80 4_d'Uh&]
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84 .NT9dX
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88 wg=-&-
1.6.1 Common expressions for spectral coefficients of filter-type systems near central V]P %@<C
wavelength ………………………………………………………………………88 CYZ0F5+t
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92 et}%E9
Chapter 2 !1xX)XD4y
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97 8}{W.np_
2.1 Synthesis methods based on merit function optimization …………………………...98 aS&,$sR
2.1.1 Merit function selection …………………………………………………………98 |WsB 0R
2.1.2 Merit function optimization ……………………………………………………101 6HRr 4NDcj
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108 x"{WLZ
2.2 Synthesis method based on the needle-like variations of the refractive index ……114 $m;DwlM
2.2.1 Needle-like variations of the refractive index ………………………………….115 :7)lg iM2
2.2.2 The principal idea of the method ………………………………………………119 b9 TsuY
2.2.3 Description of the method ……………………………………………………...124 YxWA]
yL
Bibliography …...………………………………………….……………….………..……130
