Nanoplasmonics and surface enhanced spectroscopy

The behaviour of the surface plasmon spectrum in heterogeneous structures depending on the thickness of the metal layer
Kostrobii P.P.1, Polovyi V.Y.1
1 Applied Mathematics Department, Institute of Applied Mathematics and Fundamental Sciences of the LPNU of Ukraine. 5 Mytropolyt Andrei str., Building -79007, Ukraine. 
E-mail: email.of. vitalii.y.polovyi@lpnu.ua

Investigated the behaviour of the spectrum of plasmon-polariton waves in the heterogeneous structure “dielectric-metal-dielectric”. The propagation of the plasmon-polariton waves in the area of surfaces contact (“dielectric-metal”) is described using Maxwell’s equations [1]. In the considered mathematical model, the relation between the electric flux density and the electric strength is nonlocal.
The dielectric permittivity tensor is calculated using a model of the metal layer as a non-interacting electron system in an asymmetric rectangular well of a finite depth.
From the Maxwell equations system obtained dispersion relation in which the dielectric permittivity function of a metal depends on its thickness. Conducted numerical analysis of the dispersion relation. The obtained results prove the feasibility of applying the proposed model, since they qualitatively coincide with the Drude model [1] and the results of the experiment [3].

1.	Maier S Plasmonics. Fundamentals and Application // Springer - Verlag.-2007.-229.
2.	Kurbatsky V. P. Dielectric tensor of low-dimensional metal systems // J. Exp. Theor. Phys.- 2017, P. 148–158.
3.	M. Abd El-Fattah, Zakaria & Mkhitaryan, et al.. Plasmonics in Atomically-Thin Crystalline Silver Films // 2019.-17, N 3.-P. 417-429.