Applied mathematics

Comparison transfer matrix methods and scattering matrix method for investigation the optical properties of multilayer structures

N. V. Egorov^a, A. G. Fedorov^b, V. V. Trofimov<sup>a

a</sup> St. Petersburg State University, 7–9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation
^b M. K. Ammosov North-Eastern Federal University, 58, ul. Belinskogo, Yakutsk, 677027, Russian Federation

Abstract: This article presents an analysis of transfer matrix method (TMM) and scattering matrix method (SMM) for determining reflection and transmission coefficients of thin films. Investigated single layer structures of semiconductor materials (Si, Ge, GaAs), noble metals (Ag, Au, Cu) and multilayer structure of Si. Numeric results were getting in two diapason wavelengths: $\lambda=0.2067$–$0.8267$ $\mu$m and $\lambda=0.2$–$20$ $\mu$m. In this work obtained with TMM and SMM the reflection and transmission coefficient of layer structures. Numerical results of reflection coefficients of all investigation structures were exactly match with literature data. But results we got for the transmission coefficients did not match of literature data for the both of method. This mismatch is investigated, as we assume from some of normalization coefficient, corresponding a refractive index of right side of medium which we didn't take into account.

Keywords: transfer matrix methods, scattering matrix method, reflection coefficient, transmission coefficient, layer structures.

UDC: 53.05, 519.688, 004.942

MSC: 05C85

Received: May 2, 2024
Accepted: October 4, 2024

DOI: 10.21638/spbu10.2024.401