Abstract. Formulas for the
reflection and transmission coefficients of a plane-parallel plate with a
normal incidence of plane electromagnetic waves are derived in experimentally
observed real variables. Formulas of dielectric loss tangents are given.
The Fresnel and Airy formulas are used. To simplify the analysis of
formulas, we derive the relations between the Fresnel coefficients. The
consideration of ensembles of Fresnel-Airi models allows us to get a numerical
model for the reflection and transmission coefficients of a plane-parallel
plate in the microwave range to the case of nonmonochromatic electromagnetic
waves. The equivalence of frequency and plate thickness, which takes place in
the Fresnel-Airy model, is analyzed. Dependences of the reflection and
transmission coefficients on the plate thickness are considered. The decrease
in the amplitudes of the resonance oscillations on these dependences due to the
nonmonochromaticity of electromagnetic waves is analyzed. With a small
absorption of electromagnetic waves, the term "smoothing the
dependences" is inadequate. Despite the decrease in amplitudes, there are
resonant oscillations of a relatively small amplitude and they limit the
accuracy of measurements of the reflection and transmission coefficients. The
possibilities of increasing the accuracy of measurements of the imaginary part
of the complex dielectric permittivity from measurements of the transmission
coefficients for sufficiently thick plates are discussed. The appendix contains
semiempirical formulas for the smoothed dependences of the reflection and
transmission coefficients on the plate thickness.
Key words: reflection, refraction,
Fresnel equations, permittivity, millimeter waves, snow, ice.
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