| Summary: | Background. Dielectric spherical resonators, due to the wide possibilities of their
application, are increasingly becoming a subject for scientific research. Studies of the spectral
characteristics of an open two-layer spherical resonator have shown that when measuring
the dielectric properties of a liquid with losses occupying a small volume, it becomes
necessary to introduce a middle layer. Therefore, the purpose of this work was to analytically
and numerically investigate a dielectric resonator made in the form of a radial threelayer
ball. Materials and methods. First, a review of the theory of natural waves of a dielectric
sphere is given. Special attention is paid to modes with large radial and azimuthal indices.
The system of Maxwell's equations is solved in the case of a space with a dielectric
ball, which is reduced to solving a scalar equation for the so-called Debye potentials. Results.
The initial model problem is reduced to solving a scalar equation for Debye potentials.
The obtained characteristic equation is investigated for the case when the parameters
of the structure of the inner and outer ball coincide. The solutions of this equation allow us
to study the dependence of the complex permittivity of the substance under study on the parameters
of the resonator with its known spectral characteristics. Conclusions. A numerical
method based on finding the root equation using the ranging method is proposed. An algorithm
was developed in the Maple mathematical package and applied to study the structure
of a layer filled with gasoline, air, ethyl alcohol, transformer and fused quartz. The dependences
of the solution of the system on frequencies, as well as the values of the wave number
/ frequency on the radius are illustrated.
|
|---|