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
Interaction of electromagnetic H-wave with thin metal film is located between two dielectric environments ε1, ε2 in the case of different incident angles of H-wave θ and in the case of different reflection coefficients q1 и q2 is calculated in this article. Behavior analysis of reflection coefficient R, transmission coefficient T and absorption coefficient A in the case of its frequency dependence y and variation dielectric permeability of its environments is done.
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/
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  in the case of the thin metal cylindrical wire. Quantum effects are not taken into account. This effects were researched in  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 ε1 (the first environment) and ε2 (the second environment) with reflection coefficients q1 and q2 in the case of falling electromagnetic H-wave (from the first environment) at the θ angle. Reflection coefficients q1 and q2 are associated with reflection of electrons from top and lower surfaces layer. Clarify, if electric field vector is parallel the surface of the thin layer, then this wave is called H-wave. Electric field of electromagnetic wave is parallel the thin metal layer and directed along Y-axis, while X-axis is directed into the layer.
Then behavior of electromagnetic field inside the thin metal layer is described by the equation system :
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 :
Expression (2) contains P(1) and P(2)  :
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: Ey(0) = -Ey(a), Hz(0) = Hz(a), and Z(2) – corresponds symmetric configuration: Ey(0) = Ey(a), Hz(0) = -Hz(a) .
Expression for surface impedance in the case of interaction H-wave with the thin metal film, were obtained in  in the case when wavelength much more thickness of the thin layer:
For σa expression (this is electrical conductivity of the thin metal layer, with average thickness of this layer) we used results . In this article we compared our results with experiment data . Our σa expression have look:
x = a/(vFτ) – the dimensionless frequency of bulk electron collision, y = aω/vF – the dimensionless frequency of the electric field, λ = x/(x-iy), σ0 =ω2pτ/4π – the static electrical conductivity, vF – Fermi speed, τ – electron relaxation time, ωp – plasma frequency, q1 и q2 – reflection coefficients.
Finally, reflection coefficient R, transmission coefficient T and absorption coefficient A (expression (2)) will have look :
ε1,2 =ε2/ε1, .
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 ε2 and in the case of different reflection coefficients q1 and q2. Clarify some parameters of potassium for further calculations: ωp = 6.5 10151/s, vF = 8.52 ∙ 105 m/s, τ = 1.54 ∙ 10-13 s, a = 10 nm.
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 ε2.
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 ε2.
In figure 3, in the case of not large value of the dielectric permittivity (ε2 < 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 (ε2 > 30) coefficient A begin immediately descents.
In figure 4, 5, 6 we can see, that variation of the thin metal layer reflection coefficients q1 and q2 (from diffuse q1 = q2 = 0 to reflection q1 = q2 = 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.