Influence of Specularity Coefficients on the Interaction of Electromagnetic H-Wave with the Thin Metal Film is Disposed on the Dielectric Substrate

Alexey Utkin Igorevich^{*}, Alexander Yushkanov Alexeevich

Theoretical Physics Department, Moscow State Regional University, Moscow, Russia

Abstract

Interaction of electromagnetic H-wave with thin metal film is located between two dielectric environments *ε _{1}*,

Keywords

The Thin Metal Film, Electromagnetic H-Wave, Dielectric Environments, Reflection Coefficient, Transmission Coefficient, Absorption Coefficient

Received: March 1, 2015

Accepted: March 11, 2015

Published online: March 20, 2015

@ 2015 The Authors. Published by American Institute of Science. This Open Access article is under the CC BY-NC license. http://creativecommons.org/licenses/by-nc/4.0/

1. Introduction

Currently microelectronics, optoelectronics and thin-film technology are actively developing. In particular the greatest interest represents researching of interaction electromagnetic radiation with thin conductive films in the different frequency range [1-6]. This interest is related not only with extensive practical importance of thin conductive films, but with some unresolved theoretical tasks.

In our case thickness of the thin metal film *a* is not more, than thickness of skin-layer δ and this thickness comparable with the average free path of electrons Λ. For this reason skin-effect is not considered. Skin-effect was researched in [8] in the case of the thin metal cylindrical wire. Quantum effects are not taken into account. This effects were researched in [9] in the case of quantum film in the dielectric environment.

2. Problem Definition and Methods

Consider the thin metal layer thickness of *a* is located between two dielectric (non-magnetic) environments, with dielectric permeability ε_{1 }(the first environment) and ε_{2} (the second environment) with reflection coefficients *q _{1 }*and

Then behavior of electromagnetic field inside the thin metal layer is described by the equation system [10]:

(1)

*k* = *ω/c* – wave number, *с* – speed of light, *j* – electric current density.

We have reflections coefficient *R*, transmission coefficient *T* and absorption coefficient *A *of thin metal film, when H-wave falling on this film [11]:

(2)

Expression (2) contains *P*^{(1)} and *P*^{(2)} [12] :

(3)

*Z*^{(1)} and *Z*^{(2)}correspond to the impedance of lower surface the layer. In particular *Z*^{(1)}corresponds antisymmetric, in electric field, configuration of the external field:* E _{y}*(0) = -

Expression for surface impedance in the case of interaction H-wave with the thin metal film, were obtained in [11] in the case when wavelength much more thickness of the thin layer:

(4)

For σ_{a} expression (this is electrical conductivity of the thin metal layer, with average thickness of this layer) we used results [13]. In this article we compared our results with experiment data [14]. Our σ_{a }expression have look:

(5)

*x = a/*(*v _{F}*τ) – the dimensionless frequency of bulk electron collision,

Finally, reflection coefficient *R*, transmission coefficient *T* and absorption coefficient *A *(expression (2)) will have look [12]:

(6)

*ε*_{1,2}_{ }=*ε*_{2}/*ε*_{1}, .

Now we will begin to analyze behavior of this coefficients (expression (6)).

3. Results and Discussion

Let us consider behavior of coefficients *R*, *T* and *A* in the case of their frequency dependence with variation dielectric permeability value of the second environment *ε*_{2} and in the case of different reflection coefficients *q*_{1 }and *q*_{2}. Clarify some parameters of potassium for further calculations: ω_{p} = 6.5 10^{15}1/s, *v*_{F }= 8.52 ∙ 10^{5} m/s, τ = 1.54 ∙ 10^{-13} s, *a* = 10 nm.

4. Conclusions

In figure 1 we can see that the descending velocity of the curve increases with increasing values of the dielectric permittivity of the second environment ε_{2}.

In figure 2 we can see that the increase velocity of the curve increases with increasing values of the dielectric permittivity of the second environment ε_{2}.

In figure 3, in the case of not large value of the dielectric permittivity (ε_{2 }< 30) we can see, that coefficient *A *increases, reaches maximum and descents. Cleary visible absorption maxima. In the case of large value of the dielectric permittivity (ε_{2 }> 30) coefficient *A *begin immediately descents.

In figure 4, 5, 6 we can see, that variation of the thin metal layer reflection coefficients q_{1} and q_{2} (from diffuse q_{1} = q_{2} = 0 to reflection q_{1} = q_{2} = 1 cases) affects to *R*, *T*, *A* coefficients. It is obvious that reflection coefficients will change, when the thin metal film borders with different environments. In particular, in figure 6, in the reflection case, coefficient *A* immediately descent. In all other cases coefficient *A* increases reaches its maximum and descents.

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