6
O. R. Bediukh et al.
Relative dielectric constant of the foam was about 1.1 and of polymer used for the
substrate was about 2. The dielectric loss tangents of both of these materials were
less than 10-3.
In view of the fact that the thickness of the polymer substrate was 0.1 mm, which
was about 1/100 of EMR wavelength in all measuring range, in calculation, we
neglected reflections associated with the presence of the foam and the polymer
substrate.
Therefore, the calculations were carried out in the approximation that the gold
film was in an empty waveguide.
Skin layer thickness in the selected frequency band for gold was more than an
order greater than the gold film thickness. In this case when EMR penetrated the entire
thickness of the film, the reflection coefficient G 1 for the film having a thickness d
and a conductivity σ can be written as [3]
G 1 = −β/(1 + β),
(3)
where β = σ d/(ε 0 c), ε 0 —the permittivity of vacuum, and c—the speed of light in
vacuum.
Accordingly, the transmission coefficient is equal to
T 1 = 1 + G 1 = 1/(1 + β).
(4)
For the 10-nm-thick gold film, the conductivity σ depends both on the thickness
and on the method of preparation of the film.
On the other hand in the case of matched load, G
2
1 corresponds to the power
reflection coefficient that is given by the formula (1).
Therefore, to determine β value, we had the opportunity to use experimental
measurements of the power reflection coefficient for the matched load case.
Power reflection coefficient is equal to square of modulus of complex reflection
coefficient of the field
R = |G|
2
.
(5)
So, in view of the experimental results, we got inequality
0.32 ≤ β
2
/(1 + β)
2
≤ 0.42.
(6)
From here, it was easy to have
1.3 ≤ β ≤ 1.8.
(7)
The reflection coefficient of the field G for the case of shorting connection, taking
into account the multiple reflections between the gold film and the reflecting surface
of shorting can be written as
O. R. Bediukh et al.
Relative dielectric constant of the foam was about 1.1 and of polymer used for the
substrate was about 2. The dielectric loss tangents of both of these materials were
less than 10-3.
In view of the fact that the thickness of the polymer substrate was 0.1 mm, which
was about 1/100 of EMR wavelength in all measuring range, in calculation, we
neglected reflections associated with the presence of the foam and the polymer
substrate.
Therefore, the calculations were carried out in the approximation that the gold
film was in an empty waveguide.
Skin layer thickness in the selected frequency band for gold was more than an
order greater than the gold film thickness. In this case when EMR penetrated the entire
thickness of the film, the reflection coefficient G 1 for the film having a thickness d
and a conductivity σ can be written as [3]
G 1 = −β/(1 + β),
(3)
where β = σ d/(ε 0 c), ε 0 —the permittivity of vacuum, and c—the speed of light in
vacuum.
Accordingly, the transmission coefficient is equal to
T 1 = 1 + G 1 = 1/(1 + β).
(4)
For the 10-nm-thick gold film, the conductivity σ depends both on the thickness
and on the method of preparation of the film.
On the other hand in the case of matched load, G
2
1 corresponds to the power
reflection coefficient that is given by the formula (1).
Therefore, to determine β value, we had the opportunity to use experimental
measurements of the power reflection coefficient for the matched load case.
Power reflection coefficient is equal to square of modulus of complex reflection
coefficient of the field
R = |G|
2
.
(5)
So, in view of the experimental results, we got inequality
0.32 ≤ β
2
/(1 + β)
2
≤ 0.42.
(6)
From here, it was easy to have
1.3 ≤ β ≤ 1.8.
(7)
The reflection coefficient of the field G for the case of shorting connection, taking
into account the multiple reflections between the gold film and the reflecting surface
of shorting can be written as