Abstract-A rigorous solution of the homogeneous Maxwell equations for hybrid modes of a microwave cylindrical cavity with a transverse annular slot in the perfectly conducting walls of arbitrary thickness and a plane infinite anisotropic dielectric passing through the slot is constructed based on eigenfunction expansion. In each of the field existence regions (the cavity itself, the interior of a slot and outer space), the field solution is constructed as a superposition of natural piecewise harmonic and exponential modes that allow for reflection and refraction at the plane boundaries of the dielectric. The dependence of the complex wave number of free oscillations of a resonant system on its geometrical parameters and on complex permittivity of the dielectric is investigated. It is shown that a cylindrical cavity with a transverse annular slot is a stable and high-sensitive system for online measuring of dielectric parameters.
The notion of dielectric order of a multi-component disperse system is introduced and is bounded with the index of the power law of mixing for dielectric permittivities of different components in an electromagnetic field. Using the example of wheat grain under microwave radiation, we phenomenologically describe the effect of continuous modification of dielectric order in a disperse system as a result of its moisture alteration. It is supposed that this effect is conditioned by the known phenomenon of organization and expansion of spatially regulated water structure formations inside grain kernels when they absorb moisture. A new mixing law is established, being in good agreement with this effect. On its basis, a physically correct theory has been developed. It permits calculation of the grain dielectric permittivity over a wide range of moisture content and temperature variation.
An approximate analytic model is presented to describe spatial structure of refracted electromagnetic field arising at oblique incidence of a Gaussian beam on a plane boundary of an absorbing homogeneous medium. The analytic solution is obtained by asymptotic approximation of a Fourier field integral under the condition of great beam width in comparison with a wavelength (the geometrical-optics approximation). This model can be used also for approximate simulation of refracted field in the cases of beam incidence near the critical angle on transparent or absorbing (amplifying) refracting medium, if one artificially introduces the additional absorption (amplification), whose value is proportional to the ratio of the wavelength and the effective beam width. It is shown that the analytic model reflects the general features of refracted field at total internal reflection
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