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[Devices and Methods of Measurements].
2017, vol. 8, no. 1, рр. 55–60
DOI: 10.21122/222095062017815560
56
Introduction
The problem of refractive index measurement
for various dielectric materials and substances is
of great importance for all fields of science and
industry, which use and study the phenomenon
of electromagnetic waves propagation through
matter
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[1–3]
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. For its solving, one applies various
techniques. There are refractometric ones (using
also the phenomenon of total internal reflection) [1,
2–4], interferometric methods (utilizing the phase
relationships between various coherent fields after
transmission and reflection from the testing material)
[1, 2, 5, 6] and others [7–9].
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7671
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measurement
for various dielectric materials and substances is
of great importance for all fields of science and
industry, which use and study the phenomenon
of electromagnetic waves propagation through
matter [1–3]. For its solving, one applies various
techniques. There are refractometric ones (using
also the phenomenon of total internal reflection)
 Exact

[1,
2–4]
 Suffix

, interferometric methods (utilizing the phase
relationships between various coherent fields after
transmission and reflection from the testing material)
[1, 2, 5, 6] and others [7–9]. This topic acquires new
importance last years due to development of study
of heterogeneous disperse systems, i.e. materials
produced by macro and microparticles of different
phases having de
 (check this in PDF content)

 Start

7844
 Prefix

There are refractometric ones (using
also the phenomenon of total internal reflection) [1,
2–4], interferometric methods (utilizing the phase
relationships between various coherent fields after
transmission and reflection from the testing material)
 Exact

[1, 2, 5, 6]
 Suffix

and others [7–9]. This topic acquires new
importance last years due to development of study
of heterogeneous disperse systems, i.e. materials
produced by macro and microparticles of different
phases having developed interfaces (soils, clouds,
foodstuffs, cosmetic products, building, wood, paper
materials and so on) [10, 11].
 (check this in PDF content)

 Start

7867
 Prefix

There are refractometric ones (using
also the phenomenon of total internal reflection) [1,
2–4], interferometric methods (utilizing the phase
relationships between various coherent fields after
transmission and reflection from the testing material)
[1, 2, 5, 6] and others
 Exact

[7–9]
 Suffix

. This topic acquires new
importance last years due to development of study
of heterogeneous disperse systems, i.e. materials
produced by macro and microparticles of different
phases having developed interfaces (soils, clouds,
foodstuffs, cosmetic products, building, wood, paper
materials and so on) [10, 11].
 (check this in PDF content)

 Start

8185
 Prefix

This topic acquires new
importance last years due to development of study
of heterogeneous disperse systems, i.e. materials
produced by macro and microparticles of different
phases having developed interfaces (soils, clouds,
foodstuffs, cosmetic products, building, wood, paper
materials and so on)
 Exact

[10, 11]
 Suffix

. Using measurements
of averaged dielectric permittivity for such materials
under various conditions and over various regions of
electromagnetic radiation, one can investigate their
physical properties, for instance, concentration and
relative position of compounding phases, physical
state and etc (see, for example, [11]).
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 Start

8516
 Prefix

Using measurements
of averaged dielectric permittivity for such materials
under various conditions and over various regions of
electromagnetic radiation, one can investigate their
physical properties, for instance, concentration and
relative position of compounding phases, physical
state and etc (see, for example,
 Exact

[11]
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).
Among the collection of refractive index
determination techniques one can highlights the
ellipsometric ones [8], which allows for solving the
problem of refractive index determination for various
homogeneous and layered media in the wide region
of electromagnetic spectrum at unknown thickness of
different layers.
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 Start

8641
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for such materials
under various conditions and over various regions of
electromagnetic radiation, one can investigate their
physical properties, for instance, concentration and
relative position of compounding phases, physical
state and etc (see, for example, [11]).
Among the collection of refractive index
determination techniques one can highlights the
ellipsometric ones
 Exact

[8]
 Suffix

, which allows for solving the
problem of refractive index determination for various
homogeneous and layered media in the wide region
of electromagnetic spectrum at unknown thickness of
different layers.
 (check this in PDF content)

 Start

9130
 Prefix

The name of the technique reveals its
essence, when sought parameters of tested medium
are determined by measurements of polarization
ellipse parameters for reflected or transmitted beam.
However, the ellipsometric technique produces low
accuracy at very small absorption
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[12]
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, besides,
it uses complicated algorithm of refractive index
computation. In the present work, we present an
additional method of this index determination for
transparent and low absorbing plane materials, based
on field intensity measurements without taken into
account phase relationships, but distinguished by
simplicity of realization.
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Description of the method
Let a beam of electromagnetic radiation of the
frequency ω be incident on a plane dielectric layer
of the thickness h. As it is known, for two orthogonal
polarizations of a plane wave, the amplitude
transmission coefficient for a dielectric layer is
determined by the expression
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[13–15]
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:
(1)
where i = (–1)1/2 is the imaginary unite; k = ω/c is the
wavenumber;
Rvd, Tvd and Tdv are the amplitude coefficients
of plane wave reflection and refraction on the
plane boundaries «air (vacuum) – dielectric» and
«dielectric – air»:
(the Fresnel formulae), written in terms of the
norma
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1)
where i = (–1)1/2 is the imaginary unite; k = ω/c is the
wavenumber;
Rvd, Tvd and Tdv are the amplitude coefficients
of plane wave reflection and refraction on the
plane boundaries «air (vacuum) – dielectric» and
«dielectric – air»:
(the Fresnel formulae), written in terms of the
normal propagation parameters
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[12–15]
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. Here,
ε is the dielectric permittivity of layer material at
the frequency of incident radiation, β = cosφ and
γ = (ε –1 + β2)1/2 are the parameters of normal
propagation for a plane wave in air and in a dielectric,
respectively, φ is the angle of wave incidence on
the surface of a dielectric layer, θ = 0 for the H (or
TE) polarization of incident wave, when its electric
vector i
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Usually, the Fresnel formulae are derived
theoretically for incident field presented by a plane
electromagnetic wave, i.e. for monochromatic
radiation with determined direction of propagation in
space
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[12–15]
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. However, scientific experience show,
that as these formulae, as the formula (1) are valid
for more general case, when radiation is presented
by a spatially bounded beam or by superposition
of waves with various frequencies from narrow
bounded frequency region.
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Then, for the temporal
ω and spatial β frequencies of propagation, one
takes averaged values of these parameters over the
temporal and spatial (angular) spectrum of incident
field (see, for example,
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[16]
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).
The expression (1) can be transformed to the
form:
TDTTikhHEvddv,=
−1
exp(),γ
DRikhvd=−12
2
exp(),γ
Rvd=
−
+
εβγ
εβγ
θ
θ;
Tvd=
+
2β
εβγθ
;Tdv=
+
2εγ
εβγ
θ
θ;
57
where:
(5)
The obtained simple equation allows for calculation
of the refractive index for a dielectric layer using
numerical value of
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However, using of
data on measuring of such coefficients for two
different polarizations, provides the opportunity
to solve this problem independently on the layer
thickness, like it made in
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[17, 18]
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for determining
of the absorption coefficient using the amplitude
coefficients of reflection and refraction. Note that
in the values TH2 and TE2 (3), one can construct the
function, which is not dependent on the thickness:
(4)
Figure 2 – Dependence of functions g(TH ) (curve 1), g(TE)
(curve 2), f(TH ,TE)
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