Study of whispering gallery modes in double disk sapphireresonators

A mode matching method for determining the resonant frequencies of the whispering gallery modes in a double cylindrical disk dielectric resonator is presented. The method has an improved accuracy in the calculation of the transverse magnetic modes with high axial numbers in a single uniaxial-anisotropic disk resonator. In this paper, frequency tuning and detuning due to the interaction between various whispering gallery modes will also be discussed     

Resonant modes in shielded cylindrical ferrite and single-crystaldielectric resonators

The Galerkin-Rayleigh-Ritz method is applied for computing the first few lowest resonant frequencies of cylindrical anisotropic resonators in a cylindrical cavity. The resonators are allowed to have gyromagnetic and uniaxial dielectric anisotropy with respect to the z-axis of the cylinder. Results of computations of the resonant frequencies are compared to exact solutions for many simple resonant structures and to results of experiments for more complicated structures, with good agreement. A new method of measuring permeability tensor components is presented. The method utilizes two parallel-plate cylindrical resonators operating in the HE⁺-/₁₁₁ and H₀₁₁ modes. A method of measuring the permittivity tensor components of single crystals using one parallel-plate cylindrical resonator operating in two different modes is proposed     

Slot line excitation of whispering gallery oscillations in shielded dielectric resonators

Electrodynamic characteristics of a half-disc shielded dielectric resonator operating in the 8-mm wavelength range have been investigated experimentally. A slot line was proposed for the excitation of whispering gallery modes in such resonator. It has been found out that the proposed excitation technique is effective and allows the high-Q oscillations of higher orders to be excited in a shielded dielectric resonator without additional energy losses. The partial shielding of the resonator in question was proposed for its spectrum rarefaction.     

Modelization of the whispering gallery mode in microgear resonators using the Floquet-Bloch formalism

In this paper, a two-dimensional (2-D) method describing the whispering gallery mode in a microgear resonator is presented. The microgear is a microdisk surrounded by a circular grating. The method, which is based on the Floquet-Bloch formalism, analytically describes the field within the disk and outside the grating. On the other hand, the field within the grating is calculated using a finite-difference scheme in polar coordinates. Matching the boundary conditions, it is possible to work in a forced oscillation regime or in a free oscillation regime (laser mode). The resonant wavelength and quality factor can then be deduced. Compared to the coupled mode theory and to 2-D finite-difference time-domain computations, the method is faster and more accurate. Moreover, a polarization effect of the microgear is demonstrated. The TE polarization experiences a Q-factor improvement contrary to TM polarization. Finally, microgear structures prove to be more efficient than micro flowers.     

Numerical analysis of the whispering gallery modes by thefinite-difference time-domain method

The finite-difference time-domain (FDTD) method is used to analyze the whispering-gallery modes of microdisk lasers. The method takes no a priori assumption. It solves the Maxwell's equations directly while taking into account the actual structure of the microdisk. The numerical results are in agreement with experimentally measured spectrum. Our Q values, however, are higher than previously published theoretical results. By calculating the resonant wavelengths and Q factors for different disk sizes, we demonstrate that the FDTD can be used to optimize the design of microdisk lasers     

New experimental results of millimetre-wave whispering gallery modedielectric resonators excited by microstrip lines

Presents an experimental investigation of planar millimetre-wave dielectric resonators acting on whispering gallery modes and excited by microstrip lines. Experimental results including measured resonant frequencies and loaded quality factors obtained in both Ka bands (26.5-40 GHz and 90-100 GHz) are presented     

Bent planar waveguides and whispering gallery modes: a new methodof analysis

A matrix method for analyzing bent planar optical waveguides is discussed. The method is a modification of an earlier method which yields bend loss directly, inasmuch as a nonuniform refractive index is approximated by a series of linear profiles rather than a series of uniform profiles. The method can be used with absorbing or leaky structures. The effect of whispering gallery modes has also been studied. It appears that a whispering gallery explanation given by H.J. Harris and P.F. Castle (1986) may not be adequate     

On a self-consistent calculation of the self-modulation instability in gyrotrons operating in whispering gallery modes

A self—consistent calculation of the self—modulation instability in gyrotrons operating in whispering gallery modes is carried out in the cold cavity approximation for satellite modes. The approach is illustrated numerically in the case of the planned operation of the KfK gyrotron in the TE_10,4 mode.     

Analysis of curvature losses of whispering gallery modes in anoptical dielectric disk by the finite-element method

The finite-element method is applied to the analysis of curvature losses of whispering gallery modes in an optical dielectric disk. Numerical examples on the dielectric disks with various side shapes are given. We also demonstrate that when the curvature radius of the disk is large enough, the difference between the propagation constants obtained by considering and by ignoring the curvature loss is very small     

Travelling-wave whispering gallery resonance sensor in millimetre-wave range

A high sensitivity sensor with a simple structure is presented for analysis of (bio)chemicals in liquid or solution form. The proposed technique is based on the travelling-wave whispering gallery resonance perturbation method in the millimetre-wave range. The resonance modes are launched inside a dielectric disk through coupling into a dielectric image waveguide. The top surface of the disk is used as the sensing area where the resonancemode interacts with the sample. Theoretical analysis and experimental results for the proposed sensor are discussed.     

Analysis of propagation characteristics of whispering gallery modes in a dielectric disk or a curved rectangular dielectric waveguide

The finite-element method is applied to the analysis of whispering gallery modes in curved optical waveguides. Numerical examples for whispering gallery modes in a dielectric disk with rough boundaries are given. It is demonstrated that the whispering gallery modes and the normal guided modes in a curved rectangular dielectric waveguide are analyzed consistently with this approach, and that the normal guided mode approaches the whispering gallery mode with the increase of waveguide width. The minimum width of the rectangular waveguide needed to support a whispering gallery mode is evaluated.<>     

Thermally induced whispering gallery mode laser in MEH-PPV solutions

We report on thermally activated whispering gallery laser modes of a solution of MEH-PPV conjugated polymer supported by a silica optical fiber. The viscosity of the polymer solution gives place to a thin shell of the gain solution around the fiber driven by capillary action. Whispering gallery modes (WGMs) are thermally induced by a decrease in the refractive index of the polymer solution under intense optical pumping. The laser emission is produced because the evanescent waves of the WGMs couple the surrounding gain medium. These results support the use of conjugated polymers in optofluidic laser systems and highlight the importance of physicochemical properties, such as viscosity and optically induced heating, on the performance of the devices.     

Whispering-gallery-like modes in square resonators

The mode frequencies and field distributions of whispering-gallery (WG)-like modes of square resonators are obtained analytically, which agree very well with the numerical results calculated by the FDTD technique and Pade approximation method. In the analysis, a perfect electric wall for the transverse magnetic mode or perfect magnetic wall for the transverse electric mode is assumed at the diagonals of the square resonators, which not only provides the transverse mode confinement, but also requires the longitudinal mode number to be an even integer. The WG-like modes of square resonators are nondegenerate modes with high-quality factors, which make them suitable for fabricating single-mode low-threshold semiconductor microcavity lasers.     

Fabry-Perot resonators in uniaxially anisotropic media

This paper investigates the resonant modes of Fabry-Perot interferometers with end reflectors embedded in linear, homogeneous, uniaxially anisotropic media. It is shown that for almost all practical cases the resonant modes consist of transverse electric (TE) modes and transverse magnetic (TM) modes relative to the direction of the optic axis in the medium. Two distinct integral equations are derived which together with Maxwell's equations are sufficient to perform a detailed analysis of these modes. However, since the results of the analysis of Fabry-Perot resonators in isotropic regions are available and well understood, the approach of the paper is to reduce a given "anisotropic resonator" to two corresponding equivalent "isotropic resonators": one for determining the TE modes and the other for determining the TM modes. The equivalent isotropic resonator for the TE modes has the same geometry as the actual resonator in the anisotropic medium. The geometry of the equivalent isotropic resonator for the TM modes is derivable in a very simple manner from the geometry of the actual resonator in the anisotropic medium and from the specified orientation of the direction of the optic axis in the medium. The well-known results for resonators embedded in isotropic media may henceforth be applied to determine the resonant modes of the anisotropic resonator.     

Calculation of radiation from a quasi-optical reflector antenna for whispering gallery mode

We propose a method to calculate the radiation characteristics of a quasi-optical reflector antenna for whispering gallery mode called Vlasov's antenna. Correction of the shape of the reflector, which was a parabolic cylinder in the original paper by Vlasov et al. (1975), is performed using wave-normal rays. The radiation field is calculated by means of an image source which is obtained with the geometrical optics. Some numerical results show that the radiated beam is gaussian-like in far zone. A scheme of high-power application (500kW, 106·4GHz, TE_12,2) to a beam transmission system is also presented     

Microstrip resonators on anisotropic substrates

The spectral domain method is applied to study shielded microstrip resonators printed on anisotropic substrates. A Green's function that takes into account the dielectric anisotropy effects is derived through a fourth-order formulation. Galerkin's method is then applied to form the characteristic equation from which the resonant frequency of the microstrip resonator is numerically obtained. Results for a microstrip situated on an isotropic substrate are used to validate the theory     

Generalized multilayer anisotropic dielectric resonators

Modeling of the generalized multilayer cylindrical anisotropic dielectric loaded resonator by a rigorous mode-matching method is presented in this paper. Eigenmodes of the multilayer two parallel-plate waveguides are obtained. By cascading the radial discontinuities of the structure, resonant frequency, field distribution, unloaded Q, and the frequency sensitivity of the resonator are obtained. The method can be used to analyze and design resonators and filters of multilayer structure. The computed results are compared with measured results and with experimental data, and shown to be in good agreement     

Higher order modes in dieletric resonators

Higher order modes excited in oversized dielectric resonators are investigated using an expansion in terms of orthogonal eigenfunctions. Radiation and material losses are taken into account. The calculated results are in excellent agreement with measurements. Different modes are easily identified by plots showing fields and energy distribution. Novel mode charts helpful for resonator design are presented. Tradeoffs between mode separation and quality factor are discussed.<>     

An improved design for quasi-optical mode conversion of whispering gallery mode gyrotron radiation

Results are reported of a theoretical and experimental investigation of a quasi-optical mode converter for the transformation of whispering gallery mode gyrotron output into a linearly polarized Gaussian like beam. The mode converter consists of a helically cut waveguide launcher, similar to that originally proposed by Vlasovet al, followed by a focusing mirror. Theoretical results using aperture field methods indicate that the length of the waveguide launcher is of critical importance in providing a confined radiation pattern. Experimental results on the radiation pattern were obtained for several launcher lengths using a 0.6 MW, 149 GHz pulsed gyrotron operating in the TE_16,2 mode. Radiation pattern results for the optimum launcher length agree well with theoretical calculations using the Stratton-Chu aperture radiation theory for unperturbed waveguide modes. A mirror focusing in the azimuthal direction was designed by a geometrical optics approach to focus the radiation coming from the launcher. Good focusing with 91.4% efficiency (power in the focused beam divided by gyrotron power) was found experimentally using the combined launcher and mirror with the pulsed gyrotron. These results indicate that quasi-optical antennas are useful for transforming high order, high frequency gyrotron modes into directed beams in free space.