Effective characteristic matrix of ultrathin multilayer structures

• Autorzy: Haija A.J. , Freeman W.L. , Roarty T.
• Języki publikacji: EN

Abstrakty

EN

This paper presents the calculation of the reflectivity, transmissivity and optical constants of ultrathin Cu-Ni multilayer stacks using the characteristic effective medium approximation (CEMA) introduced in an earlier communication. Each of the Cu-Ni multilayer stacks has an identity period of 100 A, Cu - 45 A and Ni - 55 A. Calculations of the reflectivity and transmissivity are executed via the characteristic matrix technique employed in three ways. In the first the characteristic matrix of the Cu-Ni bilayer is calculated and then raised to a power equal to the number of layers in the stack following the characteristic matrix technique. The second is based on the calculation of the characteristic matrix of the bilayer identity period using the effective complex index of refraction of the identity period as derived according to the CEMA. The third is based on the equivalent characteristic matrix of the whole stack represented by one characteristic matrix, also using the CEMA; in this method the equivalent optical constants of the layered structure are also calculated. All calculations are in the visible and for normal incidence. A comparison between results of the first two methods of calculations shows that they are almost identical. However, displaying values using the equivalent effective matrix of the whole structure shows definite quantitative differences throughout the whole studied spectral range. The difference becomes rather noticeable when the number of layers is greater than or equal to six amounting to a minimum total thickness of 600 A for the layered stack as a whole. This establishes a quantitative criterion to the limit beyond which the CEMA cannot be applied.

Słowa kluczowe

EN

multilayers; superlattices; bilayer stacks

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Optica Applicata
• Rocznik: 2006
• Tom: Vol. 36, nr 1
• Strony: 39--50
• Opis fizyczny: Bibliogr. 9 poz.,

Twórcy

autor

Haija A.J.

autor

Freeman W.L.

autor

Roarty T.

• Departament of Physics, Indiana University of Pensylvania, Indiana PA 15705 - 1087, USA

Bibliografia

• [1] ABU EL-HAIJA A.J., Effective medium approximation for the effective optical constants of a bilayer and a multilayer structure based on the characteristic matrix technique, Journal of Applied Physics 93(6), 2003, pp. 1–5.
• [2] ABU EL-HAIJA A.J., FREEMAN W.L., Derivation of the characteristic transfer matrix of the interfacial layer in superlattices using the characteristic effective medium approximation, Physica B: Condensed Matter 339(4), 2003, pp. 221–7.
• [3] ABU EL-HAIJA, A.J., FREEMAN, W.L., MUSTO, A., PAIRAM, E., CEMA corrections of the optical properties of ultra thin Ag-SiO superlattices – in press.
• [4] SHKLYAREVSKII I.N., KORNEEVA T.I., ZOZULYA K.N., Effective optical constants of thin granular silver films, Optics and Spectroscopy 27(2), 1969, pp. 174–6.
• [5] PALIK E.D., Handbook of Optical Constants of Solids, Academic Press, New York 1985.
• [6] ABU EL-HAIJA A.J., MCMARR P.J., MADJID A.H., Computation of the optical properties of nonideal multilayer structures, Applied Optics 18(18), 1979, pp. 3123–6.
• [7] MADJID A.H., ABU EL-HAIJA A.J., Optical properties of very thin, nonideal multilayer superlattice stacks, Applied Optics 19(15), 1980, pp. 2612–22.
• [8] ABU EL-HAIJA A.J., MADJID A.H., WISHAH K.A., Basic optical properties: effective optical constants, skin depth, absorption coefficients and optical conductivity of an ultrathin Ag-SiO superlattice identity period, Optica Applicata 31(4), 2001, pp. 739–49.
• [9] BORN M., WOLF E., Principles of Optics, 6th edition, Pergamon Press, New York 1980.Received July 28, 2005