High-Q whispering gallery modes in a spherical shell dielectric resonator: Characterization at microwave frequencies

We present a numerical and experimental characterization of high-Q whispering gallery resonant modes excited in a fused quartz spherical shell operated in the 18-26.5 GHz band; easy coupling and selection of modes is a most advantageous feature of the proposed structure with respect to ordinary bulk resonators. The numerical results, based on a finite element algorithm, well match experimental data, which also show the capability of our device to perform gaseous spectroscopy measurements. Received 25 October 2002 Published online 4 February 2003     

Properties of optical resonator with a layered metamaterial

The properties of longitudinal and transverse modes of an open optical resonator containing layers of a metamaterial with negative refractive index are studied. Due to the presence of these layers, the metaresonator acquires unique properties compared to a conventional open resonator. Eigenmodes of the metaresonator are studied in which the properties depend on the average dispersion and the average diffraction, which may be either positive, negative, or zero. The conditions of the existence and profiles of the waveguiding modes are obtained. The resonator with zero average diffraction is of particular interest. It is shown that, in this case, the waveguiding mode may have an arbitrary amplitude profile. Under these conditions, the discrete set of the transverse modes becomes continuous, and the eigenfrequencies become independent of the transverse amplitude profile. The resonator’s stability conditions are derived based on the ray-matrix method and diffraction theory. It is shown that insertion of a metamaterial into the resonator substantially affects the region of stability and existence of the waveguiding modes. In particular, the unstable empty resonator can thus be rendered stable.     

Whispering-gallery modes in a barrel-shaped dielectric resonator

We experimentally study a new type of resonator, namely, a barrel-shaped dielectric resonator with whispering-gallery modes which is formed by the cutting dielectric hemisphere. Compared with a hemispherical dielectric resonator, the E type oscillation spectrum of such a resonator is rarefied with respect to the azimuthal index. Comparative analysis of the electromagnetic characteristics of the barrel-shaped dielectric resonator and half-disk dielectric resonators shows that the radiation losses of the mode energy from the spherical surface are smaller than those from the cylindrical surface. This fact stimulates the high values of the internal Q-factor of modes of the barrel-shaped dielectric resonator. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 12, pp. 1041–1048, December 2005.     

A spherical scatterer inside a circular hollow dielectric waveguide

A theoretical investigation is presented of scattering characteristics of a perfectly conducting spherical object placed inside a quasi-optical transmission line of the millimeter and submillimeter waves in the form of a circular hollow dielectric waveguide (HDW). From the analytical expressions obtained, backscattering and extinction cross sections of this object are derived via the excitation coefficient of the dominantHE ₁₁ mode of the circular HDW and the HDW geometrical parameters. The agreement of the results with the corresponding data for the scattering of a plane homogeneous wave is shown.     

A X-band ESR apparatus using a Whispering Gallery Mode dielectric resonator

The behaviour of a disc-shaped dielectric resonator (DR) working in the Whispering-Gallery Modes (WGM) when used for X-band ESR experiments has been tested. It has been verified that the WGM in the resonator can be excited by using the microwave bridge of a Bruker spectrometer. The microwave field is well confined in the DR also in the absence of metal shieldings as demonstrated by the high Q values of the detected resonances. A large number of such resonances has been detected from eight up to twelve gigahertz making the DR a very broadband device. ESR spectra of various powder and aqueous samples have been obtained and compared with those of the same samples recorded by using a metal cavity. The relative amplitude of the spectra demonstrated that for aqueous samples the sensitivity of DR is similar to that of the metallic cavity. Further investigations are in progress to enhance the overall performance.     

Normal modes and quality factors of spherical dielectric resonators: I — shielded dielectric sphere

Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of μm size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.     

Normal modes and quality factors of shielded composite dielectric spherical resonators

Electromagnetic field analysis of shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials has been made. Characteristic equations for the TE_nmℓ and TM_nmℓ modes have been derived. From these characteristic equations, the resonant frequencies and quality factors have been calculated using numerical method. Computations of the resonant frequencies and quality factors have been made for resonators with parameters suitable for the optical and microware regions. In this paper we have presented the analysis and the results obtained from the numerical computations for shielded composite dielectric spherical resonator in which the dielectric sphere is composed of two concentric spheres with different dielectric materials. Starting from the Maxwell’s equations for such a resonators have been derived and resonant frequencies and quality factor’s have been calculated for the TE_nmℓ and TM_nmℓ modes using numerical method.     

球共振声学法测量普适气体常数

设计和建立了高精度的球共振声学法气体音速测量装置,分析了实际的球共鸣器的结构对共振频率的影响,并给予了相应的修正.测量了温度为29315K,压力在02MPa—08MPa范围内氩气的音速,并根据音速数据确定了普适气体常数.实验温度、压力和普适气体常数的不确定度分别为±14mK,±2kPa和±00036%.最终确定的普适气体常数R为831439±000030J·mol-1·K-1. 关键词： 普适气体常数 音速 球共振器 声学法     

Electromagnetic fluctuations in the dielectric slab resonator

Electromagnetic fluctuations between two parallel (distanceL) infinite extended and perfectly conducting plates are studied. The space between the plates may be homogeneously filled with an isotropic dielectric and magnetic medium. For small values ofLT (T=temperature) the influence of the imaginary part of the dielectric function on the spectral correlations of the radiation field is discussed.The local spectral energy density is calculated. It is shown that the energy density isr-independent for media without dispersion. In this case ther-dependent part of the trace of the electric correlation tensor cancels with the analogous part of the magnetic correlation tensor.For the empty slab the complete spatial and temporal correlation tensors are derived. Two representations suitable for small and large values ofLT are discussed. These representations are expansions arround the 2-dimensional radiation field, i.e. no modes with wave vectors perpendicular to the plates are excited and the half space limit, respectively. Curves of the relative deviation of the electric correlation functions from the infinite isotropic space limit and curves of the degree of anisotropy of the radiation field as functions of the distance to the metallic boundary are displayed.     

Vacuum-field atom trapping in a wide aperture spherical resonator

We consider the situation where a two-level atom is placed in the vicinity of the center of a spherical cavity with a large numerical aperture. The vacuum field at the center of the cavity is actually equivalent to the one obtained in a microcavity, and both the dissipative and the reactive parts of the atoms spontaneous emission are significantly modified. Using an explicit calculation of the spatial dependence of the radiative relaxation rate and of the associated level shift, we show that for a weakly excitating light field, the atom can be attracted to the center of the cavity by vacuum-induced light shifts.     

Synchronization of wakefield modes in the dielectric resonator

Multimode excitation of a wakefield in a planar dielectric resonator by a regular sequence of relativistic electron bunches is studied analytically and numerically. It is shown that, if the wakefield being excited consists of a large number of radial modes, the fields from the regular sequence of the bunches add together. Conditions under which this sequence provides synchronization of the dielectric resonator modes are found. Acceleration of a test bunch in the wakefield of the bunch sequence is studied.     

Computation of the resonant frequency of a dielectric resonator by a differential method

A differential method to compute, with high accuracy, the resonant frequency of a dielectric body with an axis of revolution and placed between two conducting plates is described. The propagation equations, projected on a Fourier basis, are integrated by the Adams-Moulton predictor-corrector algorithm and matched to the modified Bessel expansion of the field. Numerical results obtained for the cylinder shape are compared with those obtained by a modal theory, exhibiting an accuracy better than 10^–4. Results for a dielectric sphere are given as another application.     

The input impedance of the dielectric resonator antenna

Dielectric cylinders of very high permittivity have been used in the past as resonant cavities, but since the structure is not enclosed by metallic walls, electromagnetic fields do exist beyond the geometrical boundaries of the structure and part of the power is radiated. Through the proper choice of geometry and permittivity this radiation can become the dominant feature of the structure and become an efficient antenna for use at millimeter wave frequencies. Both experimental and theoretical investigations of a variety of these dielectric resonator antennas have been undertaken. In particular, the input impedance of a probe-fed cylindrical structure was examined in detail and a comparison of theoretical and experimental results was made.     

非均匀介质球颗粒的等效介电常量

从求解拉普拉斯方程的边值问题出发,讨论了非均匀介质球颗粒的等效介电常量,给出了多种介质组成的多壳层介质球颗粒的等效介电常量的一般递推公式,推导了壳层的介电常量随半径连续变化的梯度介质球的等效介电常量的微分方程．并以壳层的介电常量为幂函数为例,得到了梯度壳层介质球的等效介电常量．     

Experimental determination of spherical resonator diffraction losses

To obtain single transversal mode oscillation of a laser oscillator a pinhole has to be inserted into the resonator. This causes diffraction losses, comparable with the internal losses of the laser system. For a pulsed Nd-YAG-laser, the total losses and the diffraction losses are determined experimentally as a function of the Fresnel number for TEM₀₀ and TEM₀₁ mode. The agreement between the experimental values and numerical data from diffraction theory is satisfying.