Eigenmodes of an anisotropic dielectric spherical body

Prokopenko, Yu.V.; Смирнова, Т. А.; Filippov, Yu. F.

doi:10.1134/1.1736915

Cited by 10 publications

(12 citation statements)

References 5 publications

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“…The electrodynamics of DRs with spherical surfaces was also considered: anisotropic spherical and isotropic spheroid DRs were developed [9, 29, 30]. Here the azimuthally inhomogeneous modes in isotropic spherical and spheroidal DRs were studied for the first time.…”

Section: Types Of Wgm Resonatorsmentioning

confidence: 99%

“…Characteristic equations were obtained, whose solutions determine the resonant frequencies. It was shown that the degeneracy of the mode frequencies, which are inherent for isotropic spheres, is removed under the influence of anisotropy [29] or small ellipticity [9, 30]. In these resonators, the transformations of TE and TM modes result in quasi-TE and quasi-TM modes.…”

Section: Types Of Wgm Resonatorsmentioning

confidence: 99%

“…In these resonators, the transformations of TE and TM modes result in quasi-TE and quasi-TM modes. The eigenfrequencies of the sphere, in which ε −1 /ε +1 <<1, where 2ε ±1 = ε ||1 ± ε ⊥1 , are determined by solving the characteristic equations given in [29]. It was shown that the resonator frequency unambiguously identifies the quasi-TM mns or quasi-TE mns mode, where m, n , and s are the polar, azimuthal, and radial indices, respectively.…”

Section: Types Of Wgm Resonatorsmentioning

confidence: 99%

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Whispering gallery mode resonators in microwave physics and technologies

Barannik

Yakovenko

Cherpak

et al. 2016

Int. J. Microw. Wireless Technol.

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We review the main results of the development of whispering gallery mode (WGM) resonators and their unique applications due to their quasi-optical functionality. Several types of advanced WGM resonators are proposed by the authors. The theoretical results are described for the resonators with an analytical solution of the electromagnetic problems. Special emphasis is given to the interaction of moving charged particles and waves of cylindrical resonators. Important aspects are described concerning the developed sapphire resonators, for which an exact solution can only be found by using specially designed computer program products. A separate section of the paper is devoted to application aspects of the WGM resonators. In particular, it describes advanced solutions for overcoming the problems of measuring the small microwave (MW) surface impedance of unconventional superconductors in the form of large-area thin films and small samples under study. In addition, a demonstration of accurate complex permittivity measurements of small volumes of lossy liquids is provided. Special emphasis is given to highly stable MW signal sources, namely Ka-band transistor-based feedback oscillator and solid-state maser WGM oscillators. Recently obtained results are presented of experimental studies of the auto-oscillatory system developed on the basis of the WGM resonator with relativistic electron beam.

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Section: Types Of Wgm Resonatorsmentioning

confidence: 99%

Section: Types Of Wgm Resonatorsmentioning

confidence: 99%

Section: Types Of Wgm Resonatorsmentioning

confidence: 99%

See 1 more Smart Citation

Whispering gallery mode resonators in microwave physics and technologies

Barannik

Yakovenko

Cherpak

et al. 2016

Int. J. Microw. Wireless Technol.

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show abstract

“…After that, by substituting Eqs. (37) and (38) into Eq (35), the characteristic equation for quasi-TM field gives [41]γ…”

Section: Roots Of Characteristic Equationsmentioning

confidence: 99%

Theory of anisotropic whispering-gallery-mode resonators

Ornigotti

Aiello

2011

Phys. Rev. A

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An analytic solution for a uniaxial spherical resonator is presented using the method of Debye potentials. This serves as a starting point for the calculation of whispering gallery modes (WGMs) in such a resonator. Suitable approximations for the radial functions are discussed in order to best characterize WGMs. The characteristic equation and its asymptotic expansion for the anisotropic case is also discussed, and an analytic formula with a precision of the order O[nu(-1)] is also given. Our careful treatment of both boundary conditions and asymptotic expansions makes the present work a particularly suitable platform for a quantum theory of whispering gallery resonators

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“…The solutions of the electromagnetic wave in anisotropic spheres have been studied analytically and numerically [54][55][56]. The numerical analysis of anisotropic structure is applicable using the compact formalization of the BLF technique from section 5.1.…”

Section: Anisotropic Materialsmentioning

confidence: 99%

Spherical Space Bessel-Legendre-Fourier Mode Solver for Electromagnetic Fields

Alzahrani¹

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Controlling and confining light in three dimensions is of significant interest as it represents devices in their entirety with minimal approximations. Localized modes in resonator structures are commonly modelled using the supercell plane wave expansion method, finite element method, or the finite difference time domain. However, these standard techniques are expensive in terms of computational resources when applied to three-dimensional structures. The technique presented in this thesis is a new method for solving Maxwell's vector wave equations for localized modes in three-dimensional spherically resonator structures as well as its application to sensor configurations. The technique requires minimal implementation, provides normalized results, works for finite size and is computationally efficient. The method is such that the structures under test can be arbitrary shape, isotropic, anisotropic, lossless, or lossy. For the structures examined, a modified basis set composed of spherical Bessel, Legendre and Fourier functions (BLF) are used to expand the electric, magnetic, and inverse relative permittivity. These expansions allow for Maxwell's wave equations to be cast as an eigenvalue problem from which the steady state localized modes (not propagating) can be determined from the eigen-frequencies and eigenvectors. This work applies to a number of spherically symmetric structures. Selections of structures whose resonator properties are reported in the literature are used to compare and verify the accuracy of the use of the BLF functions as an expansion basis.iii Acknowledgement I would like to begin by thanking Prof. Gauthier for the great support he has provided throughout my post-graduate studies. I appreciate everything he has done for me during my stay here as international student, I feel that I have found a good friend as well as a supervisor.

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Eigenmodes of an anisotropic dielectric spherical body

Cited by 10 publications

References 5 publications

Whispering gallery mode resonators in microwave physics and technologies

Whispering gallery mode resonators in microwave physics and technologies

Theory of anisotropic whispering-gallery-mode resonators

Spherical Space Bessel-Legendre-Fourier Mode Solver for Electromagnetic Fields

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