Basics of OPTICS OF MULTILAYER SYSTEMS
Contents
Preface……………………………………………………………………….………..……….4
Chapter 1
SPECTRAL CHARACTERISTICS OF MULTILAYER COATINGS:
THEORY……………………………………………………………………………………….5
1.1 Electromagnetic field in layered media; spectral characteristics of layered media…5
1.1.1 Layered medium electromagnetic field equations………………………………...5
1.1.2 Amplitude transmittance and reflectance of the layered medium……………….12
1.1.3 The Fresnel formulas ……………………………………………………………18
1.1.4 Other ways of determining amplitude transmittance and reflectance of the
layered medium…………………………………………………………………..19
1.1.5 Transmittance, reflectance and absorptance …………………………………….20
1.2 Principal recurrent methods for calculating layered media spectral coefficients…22
1.2.1 Matrix calculating method ………………………………………………………22
1.2.2 Description of optical coating and presentation of calculation results…………..28
1.2.3 Recurrent formulas for the amplitude transmittance and reflectance……………30
1.2.4 Approximate formulas…………………………………………………………...33
1.2.5 Other recurrent methods…………………………………………………………34
1.2.6 The admittance phase plane……………………………………………………...38
1.3 Some common properties of multilayer coatings…………………………………….46
1.3.1 The relation between the characteristic matrix and spectral coefficients of a
multilayer coating ……………………………………………………………….47
1.3.2 Relations between spectral characteristics for the direct and reverse waves ……51
1.3.3 Transmittance and reflectance of the combination of two multilayer
subsystems ……………………………………………………………………....54
1.4 The multilayer coatings optical properties: impact of variations in the layer
parameters……………………………………………………………………………...58
1.4.1 Spectral coefficients derivatives with respect to layer parameters …...…………
1.4.2 Impact of the layer parameter errors on the multilayer coatings spectral
coefficients: probability assessment method ……………………….…………...63
1.4.3 Multilayer coating spectral properties: influence of separate layer parameter
variations ………………………………………………………………………...66
1.5 Multilayer periodic systems. Quarter-wave dielectric mirrors……………………..68
1.5.1 Characteristic matrix of a periodic multilayer system …………………………..69
1.5.2 Quarter-wave mirror properties at the central wavelength ……………………...72
1.5.3 Width of the quarter-wave mirror high-reflectance zones ………………………76
1.5.4 Principal properties of a quarter-wave dielectric mirror in the proximity to the
central wavelength ………………………………………………………………80
1.5.5 Dielectric mirrors on a metal substrate ………………………………………….84
1.6 Approximate formulas for dielectric narrow bandpass filters ……………………..88
1.6.1 Common expressions for spectral coefficients of filter-type systems near central
wavelength ………………………………………………………………………88
1.6.2 Research of narrow bandpass filters with a half-wave central layer ……………92
Chapter 2
SYNTHESIS OF MULTILAYER OPTICAL COATINGS ……………………...97
2.1 Synthesis methods based on merit function optimization …………………………...98
2.1.1 Merit function selection …………………………………………………………98
2.1.2 Merit function optimization ……………………………………………………101
2.1.3 General pattern of the synthesis and the problem of the starting design choice .108
2.2 Synthesis method based on the needle-like variations of the refractive