The 13 reference contexts in paper V. Serdyuk M., J. Titovitsky A., В. Сердюк М., И. Титовицкий А. (2017) “ОПРЕДЕЛЕНИЕ ПОКАЗАТЕЛЯ ПРЕЛОМЛЕНИЯ ПЛОСКОГО ДИЭЛЕКТРИЧЕСКОГО СЛОЯ МЕТОДОМ ИЗМЕРЕНИЯ ИНТЕНСИВНОСТЕЙ ПРОХОДЯЩИХ ПУЧКОВ // REFRACTIVE INDEX DETERMINATION FOR A PLANE DIELECTRIC LAYER USING THE MEASUREMENTS OF TRANSMITTED BEAM INTENSITY” / spz:neicon:pimi:y:2017:i:1:p:55-60

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    DOI: 10.21122/2220-9506-2017-8-1-55-60 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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    . 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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    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)
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    , 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
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    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)
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    [1, 2, 5, 6]
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    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, food-stuffs, cosmetic products, building, wood, paper materials and so on) [10, 11].
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    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
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    [7–9]
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    . 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, food-stuffs, cosmetic products, building, wood, paper materials and so on) [10, 11].
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    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, food-stuffs, cosmetic products, building, wood, paper materials and so on)
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    . 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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    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,
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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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    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
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    [8]
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    , 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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    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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    , 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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    : (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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    . 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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    . 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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    ). The expression (1) can be transformed to the form: 57 TDTTikhHEvddv,= −1 exp(),γ DRikhvd=−12 2 exp(),γ Rvd= − + εβγ εβγ θ θ; Tvd= + 2β εβγθ ;Tdv= + 2εγ εβγ θ θ; 58 (2) Assume that a layer is transparent, i.e. the permittivity ε is real number.
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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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    for determining of the absorption coefficient using the amplitude coefficients of reflection and refraction. Note that in the values |TH|2 and |TE|2 (3), one can construct the function, which is not dependent on the thickness: (4) where:
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