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Approximate Boundary Conditions for the Problem of Calculating Optical Coefficients of Ultrathin Metallic Films in the Microwave and Terahertz Ranges

Authors
  • Glazunov, P. S.1, 2
  • Vdovin, V. A.1
  • Andreev, V. G.1, 2
  • 1 Kotel’nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, 125009, Russia , Moscow (Russia)
  • 2 Moscow State University, Moscow, 119991, Russia , Moscow (Russia)
Type
Published Article
Journal
Optics and Spectroscopy
Publisher
Pleiades Publishing
Publication Date
Sep 01, 2020
Volume
128
Issue
9
Pages
1439–1448
Identifiers
DOI: 10.1134/S0030400X2009009X
Source
Springer Nature
Keywords
License
Yellow

Abstract

AbstractWe report on the approximate boundary conditions obtained for the problem of calculating the optical coefficients of a system consisting of a dielectric substrate and an inhomogeneous ultrathin metallic film with an arbitrary thickness dependence of the conductivity deposited onto this substrate. The boundary conditions have been derived on the basis of the Picard’s method of successive approximations. Analytical expressions for estimating the error of the calculation of the optical coefficients obtained using the proposed approximate boundary conditions are presented. It is shown that the error increases with frequency and film thickness. The maximum error for 10-nm-thick films is no larger than 10.7% at a frequency of 1 THz. As an example, the complex optical coefficients of a system like the Fabry‒Perót etalon and a metallic film without a substrate with the model thickness dependence of the conductivity have been calculated. The coincidence of the results of the calculations performed by the numerical simulation and using the approximate boundary conditions is shown. The possibility of direct calculation of the average conductivity of a film using the experimental reflectance and transmittance is demonstrated.

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