We present an accurate, reliable and versatile method for studying the effect of deformations on the characteristics of the high-Q whispering gallery (WG) modes supported by two-dimensional dielectric resonators (DR). An eigenvalue problem is formulated in terms of contour integral equations and further discretised with the method of analytical regularisation. Such a procedure significantly reduces the number of unknowns whilst providing high and controllable accuracy. Natural frequencies, Q-factors and field patterns of elliptical, flower- and egg-shaped DRs are calculated. Methods to enhance the Q-factors, provide directional light output, and parasitic mode suppression are discussed. The identification of WG modes is simplified by the symmetrical/asymmetrical mode separation included into the formulation of the problem and solution algorithm.

http://www.bio-page.org/boriskina/Boriskina_OQE2003.pdf

Highly efficient design of spectrally engineered whispering-gallery-mode microlaser resonators

High-Q semiconductor microdisk resonators laterally coupled to optical waveguides serve as compact and robust components in wavelength-division-multiplexing systems. We present an efficient algorithm for the two-dimensional design of wavelength-selective filters based on waveguide-coupled whispering-gallery-mode (WGM) microresonators of arbitrary cross-sectional shape. A full-wave integral equation formulation enables us to accurately account for the coupling between the resonator and bus waveguide as well as for radiation and material losses. Furthermore, we apply this approach to the analysis of elliptic-resonator filters. Filter tuning by changing the resonator shape from circular to elliptic reduces the dependence of the coupling efficiency on the width of the air gap. Two alternative coupling designs are suggested for monolithic and hybrid integration technologies. One is based on increasing the coupling length, while the other exploits the field concentration at the increased-curvature portion of the deformed WGM resonator.

http://www.bio-page.org/boriskina/Boriskina_JLT2003.pdf

Tuning of elliptic whispering-gallery-mode microdisk waveguide filters

We report an experimental and theoretical study of whispering-gallery-mode propagation of subpicosecond terahertz pulses in a dielectric cylinder coupled by means of a dielectric slab waveguide. We observed repetitive cavity pulses from this structure for which the output pulse shapes were determined by the multi-whispering-gallery-mode coupling into the cylinder. A coupled-mode theory derived for this cylindrical system and coupling structure gives reasonably good agreement with the experiment in both the frequency and time domains.

Whispering-gallery-mode cavity for terahertz pulses

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Development of a MEMS-based acoustic energy harvester

In this paper, the results of analytical and numerical investigation of whispering gallery modes (WGMs) in parallel-plates-type cylindrical anisotropic and isotropic dielectric resonators are presented. The dependence of the WGMs' resonant frequency, Q-factor, and energy-filling factor upon resonator parameters for the wide range of the azimuthal index has been studied numerically. The optimization of resonator parameters for sensing applications is discussed. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 96–101, 2004; Published online in Wiley Interscience (www.interscience.wiley.com). DOI 10.1002/mop.11296

Resonance characteristics of whispering gallery modes in parallel‐plates‐type cylindrical dielectric resonators

This paper presents a novel calculation method for resonance characteristics of an elliptic dielectric disk resonator. In the elliptic resonator, electromagnetic energy propagates as a whispering gallery (WG) mode along the edge region of the dielectric disk. In the novel analysis, a local propagation constant of the WG mode at each point of the elliptic disk edge is represented by a propagation constant of a WG mode in a circular disk whose radius of curvature, material constants, and thickness are equal to those of the elliptic disk. Therefore, we can easily calculate the resonance characteristics of the elliptic dielectric disk resonator by applying a conventional technique for the circular dielectric disk. The calculated results of the resonant frequencies and field distribution are well confirmed by experiments.

Resonance characteristics of whispering-gallery modes in an elliptic dielectric disk resonator

Resonance and loss characteristics of whispering gallery modes in a dielectric disk resonator are discussed three-dimensionally by using an approximate variable separation method. A radius of the disk is sufficiently large compared to a wavelength. A cylindrical function with a complex order and argument whose absolute values are much larger than unity is included in an eigenvalue equation.



In this paper, the eigenvalue equation is solved analytically by using a newly developed calculation method of the cylindrical function. As a result, resonance and loss characteristics of the dielectric disk resonator in a wide frequency ranging from a microwave to optical wave are understood. The present method can be applied to a whispering gallery mode resonator made of lossy dielectric materials. Therefore, one can obtain a radiation loss separately from a dielectric loss based on a loss tangent of the materials.

Resonance characteristics of whispering gallery modes on a dielectric disk

A new analysis for eigenvalues of Whispering Gallery Modes on a three-dimensional disk resonator with a high dielectric constant is presented. In this analysis, a Generalized Effective Dielectric Constant Method is applied with some modification. The disk resonator is considered to be decomposed into two-dimensional slab waveguides and a cylindrical dielectric rod resonator. A concept of an effective dielectric constant and a caustic radius are newly introduced to obtain the eigenvalues of Whispering Gallery Modes. As a result of comparison with numerical eigenvalues and experimental ones, it is found that this analytical method is useful even so the dielectric disk resonator has a high dielectric constant.

A novel analysis for eigenvalues of a dielectric disk resonator with a high dielectric constant

A coupled mode equation for two nonparallel dielectric waveguides is rigorously derived from the Lorentz reciprocity theorem. the waveguides are located close to each other. Two local coordinate systems are introduced to present an intrinsic mode function. A global coordinator system also is employed to solve the coupled mode equation. As a numerical example, a coupling system consisting of two dielectric disks with different radii is analyzed. the coupled mode equation for whispering gallery modes propagating along a circumference of the disks is solved numerically in the global coordinate system. Eigenvalues of the whispering gallery modes are complex numbers because of radiation and dielectric losses. As a result, electric field distribution and the coupling coefficient around the coupling system are obtained quantitatively.

Coupling characteristics of nonparallel dielectric waveguides

An analysis is presented for a novel coupling configuration in which a circular dielectric disk and ring are arranged eccentrically. Whispering gallery (WG) mode coupling characteristics between the dielectric disk and ring are investigated. In this paper, a coupled-mode equation based on the Lorentz's reciprocity theorem is utilized. Distributed coupling coefficients and electric field distributions around the coupling region are obtained numerically through solving the coupled-mode equation. The theory described in this paper is confirmed by comparing measured electric field distributions with calculated ones. Electromagnetic powers flowed along the disk are also calculated. It is shown that coupling quantity of the eccentric configuration would be easily controlled by changing a radius of the disk or ring. The results obtained here will be used to design a WG mode coupled resonator for millimeter wave integrated circuits.

Yoshiro Tomabechi

Papers

Resonance characteristics of whispering-gallery modes in an elliptic dielectric disk resonator

Resonance characteristics of whispering gallery modes on a dielectric disk

A novel analysis for eigenvalues of a dielectric disk resonator with a high dielectric constant

Coupling characteristics of nonparallel dielectric waveguides

Coupling characteristics of eccentric arranged dielectric disk and ring