"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 9, 2017

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The application of Fresnel-Airy model for research of resonance oscillations of plane electromagnetic waves

M. G. Evtikhov

Kotel'nikov Institute of Radio-engineering and Electronics of RAS, Fruazino Branch, Vvedensky Sq.1, Fryazino Moscow region 141120, Russia

 

The paper is received on March 10, 2017, after correction - on September, 18, 2017

 

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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For citation:

M. G. Evtikhov. The application of Fresnel-Airy model for research of resonance oscillations of plane electromagnetic waves. Zhurnal Radioelektroniki - Journal of Radio Electronics, 2017, No. 9. Available at http://jre.cplire.ru/jre/sep17/11/text.pdf. (In Russian)