Z. E. Eremenko

Whispering-gallery modes in shielded hemispherical dielectric resonators

The results of the numerical and experimental investigations of whispering-gallery (WG) modes in shielded hemispherical dielectric resonators are presented in this paper. It is shown that the Q factor of WG modes in the shielded resonator can be ten times much higher than the Q factor of the similar open hemispherical dielectric-resonator modes. Shielding the resonator can decrease the dimensions of both the dielectric hemisphere and resonator as a whole, saving the high-Q factor of WG modes. The usage of a cylindrical shield and local flat reflectors in the experiment provides the investigation of the high-Q factor of WG modes in the resonator.

Resonant spherical hole in a high loss liquid at millimeter wavelengths

The resonant properties of a quasi-optical spherical hole in a high loss liquid were studied theoretically and experimentally at millimeter wavelengths. The rigorous solutions of Maxwell equations for TE and TM oscillations were obtained as characteristic equations. The numerical solutions of these equations for eigencomplex frequencies and electromagnetic field distribution were found. We were the first who found out that a dielectric spherical hole in a high loss liquid possesses features of a metal cavity resonator. We carried out the experiment to excite TE and TM oscillations in the spherical hole as a resonator into the water. The experimental results agree well with our numerical data for the resonators eigenfrequencies. Noneigen surface oscillations similar to the oscillations in the surface Zennecks wave are excited in such a resonator. The resonant properties of the dielectric quasi-optical spherical hole in a high loss liquid could be used for measuring the permittivity of liquid.

Effect of random surface inhomogeneities on spectral properties of dielectric-disk microresonators: theory and modeling at millimeter wave range.

The influence of random axially homogeneous surface roughness on spectral properties of dielectric resonators of circular disk form is studied both theoretically and experimentally. To solve the equations governing the dynamics of electromagnetic fields, the method of eigenmode separation is applied previously developed with reference to inhomogeneous systems subject to arbitrary external static potential. We prove theoretically that it is the gradient mechanism of wave-surface scattering that is highly responsible for nondissipative loss in the resonator. The influence of side-boundary inhomogeneities on the resonator spectrum is shown to be described in terms of effective renormalization of mode wave numbers jointly with azimuth indices in the characteristic equation. To study experimentally the effect of inhomogeneities on the resonator spectrum, the method of modeling in the millimeter wave range is applied. As a model object, we use a dielectric disk resonator (DDR) fitted with external inhomogeneities randomly arranged at its side boundary. Experimental results show good agreement with theoretical predictions as regards the predominance of the gradient scattering mechanism. It is shown theoretically and confirmed in the experiment that TM oscillations in the DDR are less affected by surface inhomogeneities than TE oscillations with the same azimuth indices. The DDR model chosen for our study as well as characteristic equations obtained thereupon enable one to calculate both the eigenfrequencies and the Q factors of resonance spectral lines to fairly good accuracy. The results of calculations agree well with obtained experimental data.

Permittivity Measurement in a Small Volume of High Lossy Liquid using Microwave Resonator Technique

We propose a new microwave resonator technique of permittivity measurement in a small volume of a high lossy liquid sample. The technique is based on the use of a metal semispherical resonator filled with dielectric. The resonator contains a small semispherical central cavity filled up with a monitored liquid. The characteristic equations for eigen frequencies of electromagnetic oscillations in this resonator has been obtained rigorously and analyzed owing to high symmetry of the resonator with the liquid. On this basis the operating mode of oscillations and optimal sizes of the measuring cavity and the resonator have been found. We discovered the effect of electromagnetic field extrusion out of the small central cavity filled up with the liquid that has big values (much more than one) of the real and imaginary parts of permittivity. The technique has been implemented experimentally in X band. The found theoretically effect of the field extrusion has been confirmed experimentally. The relations for the complex permittivity of liquid using the measured values of the resonator quality factor and resonant frequency has been found

Layered ball resonator for permittivity measurement method of high loss liquids at millimeter wavelength

We propose a new method to measure the complex permittivity (CP) of a high loss liquid at millimeter wavelength. The method is based on the use of an exactly calculated quasi-optical layered ball dielectric resonator. A measured liquid is placed outside of the ball and does not disturb the spherical symmetry of the resonator. The dielectric layer between the ball and liquid is used to dose the losses in the resonator inserted by the measured high loss liquid. We found theoretically and after confirmed experimentally the optimal resonator parameters and an operating frequency mode to provide maximum sensitivity during measurement of the CP of liquid. The CP measurement of a water-alcohol solution was carried out using the proposed method. Quite good agreement between theory and experiment was obtained. The package of original computer software applications was designed to automate experiment and calculate absolute CP values of the high loss liquids using experimental data for resonant frequency and Q-factor.

The Method of Potentials for the Frequency Spectrum of Non-Homogeneous Spherical Cavities

We develop a novel theoretical method for solving the Maxwell equations in cavity resonators with inhomogeneous and asymmetrical filling. The method relies on the transition from vector description of electromagnetic fields in the resonator to a description in terms of two scalar functions (Debye potentials) for which we derive the original control equations. The solution to these equations is carried out with the use of Green functions, for which we obtain the infinite set of coupled equations in the resonance mode representation. The equations, which contain operator-valued potentials, are solved unperturbatively, by applying the original method for resonance mode decoupling. The frequency spectrum of the resonator with central-layered dielectric infill, which is found based on the developed theory, is in good agreement with the spectrum obtained numerically directly from Maxwell equations. The analysis of the inter-frequency intervals in the spectrum reveals its gradual chaotization with breaking the resonator symmetry.

Stochastic scattering by random inhomogeneities in SHF oscillatory systems

Nowadays, theoretical and experimental investigations into spectral properties of disordered oscillatory systems assume ever greater importance. It should be noted that most of the first-principle theories were previously developed for open infinite systems, where very important condition of statistical homogeneity of scattering potential was taken to be met with proper accuracy. Theories for oscillatory systems of finite dimensions were developed to much lesser extent, being essentially based on the random matrix theory (RMT) [1]. Meanwhile, it is well known for a long time [2] that RMT-based analysis is applicable, strictly speaking, to systems which are fully chaotic, whereas resonators with inhomogeneous infill should obey hybrid spectra containing both chaotic and regular components. In our recent papers [3,4], novel theoretical methods for studying spectra of disordered oscillating systems were suggested, which are based on direct solution of Helmholtz equation. Also, experimental studies were performed for the purpose of verification of our theoretical forecasts. The basis of our theoretical methods lies in (a) strict separation of oscillation modes in arbitrary random-inhomogeneous wave systems and (b) in the reduction of wave problems stated initially for systems with surface inhomogeneities to the analogous problems for corresponding systems inhomogeneous in the bulk [5].

Measurement complex permittivity of high loss using resonator with ring cavity

We proposed a new complex permittivity measurement technique for high loss liquids in small volume at millimeter wave band. This technique is based on the use of cavity resonator with radial belt with liquid. Such resonant cell was studied numerically and experimentally. The resonator spectrum was studied depending on permittivity of high loss liquids at deviation of main resonator parameters. A good agreement between numerical study and experimental data has obtained. The optimal resonator proportions corresponding spectral parameters and operating oscillation mode were determined to provide maximal sensitivity during complex liquid permittivity measurement.

Random inhomogeneities in microresonator: Theory and modeling at millimeter wave band

The influence of random inhomogeneities placed on the microresonator face on its spectral properties was studied theoretically and experimentally. The original spectral theory of open dielectric disk resonator with random surface inhomogeneities was elaborated. The mechanisms of the influence of inhomogeneities on eigen resonant frequency and on the spectral lines width were clarified. For that we carried out the modeling of the microresonator with random surface inhomogeneities at millimeter wave band. The qualitative agreement between theory and experiment was obtained.

Differential dielectrometer for the small change measurement of complex permittivity of high loss liquids

The differential dielectrometer (DD) was designed that allows showing surely enough small differences in complex permittivity between two high loss liquids, for instance, dry wines to show up fraud.