Application of the Method of Lines for High-Q Resonant Structures

Abstract

In this paper, we present two applications of electromagnetic software based on the Method of Lines: the rutile-ring method of dielectrically frequency-temperature compensating a high-Q whispering gallery sapphire resonator and a TE 01γ sapphire resonator with distributed Bragg reflector. These studies are based on the Method of Lines in cylindrical coordinates. Because this method use a 2D1/2 resolution, it is possible to take into account layers with very small thickness. The resonant frequencies, field distribution and quality factors can be calculated by this method. Results of Method of Lines are compared with finite element analysis. I IntroductionSapphire is an extremely low loss material. To confine the field within the sapphire and get a high-Q, One of the solutions is to excite Whispering gallery modes. In order to create an oscillator with frequency stability, the resonator must have the frequency-temperature dependence annulled. To compensate the temperature coefficient of permittivity (TCP) for sapphire, thin rutile rings, with opposite TCP, are placed coaxially at the end faces of a sapphire cylindrical resonator operating in WGE 900 mode [1], [2]. Moreover, Bragg reflection occurs between layers of rutile and sapphire and most of the energy is confined into the sapphire.Because WG modes are high order, resonators have large dimensions and consequently a high density of spurious modes.Unlike, fundamental mode TE 01γ , which has good isolation and low spurious mode density, has significant metallic losses due to the cavity. So to solve this problem, we present a second application for the Method of Lines to a sapphire resonator with distributed Bragg reflector which improve the Qfactor decreasing metallic losses.In this paper, Method of Lines (MOL) [3] is used to calculate the dimensions of sapphire and rutile structures to obtained compensation temperature at 72 K. For the second study, MOL is used to get the best Q-factor for a 9 GHz resonant frequency. Then we compare these results with finite element analysis (FE) [5].

High confined Bragg modes for very low phase noise oscillator and narrow band filtering applications

“…While investigating the properties of a conventional Bragg resonator [2], we observed a new type of mode confirmed using rigorous electromagnetic software based on the method of lines (MoL) [3]. This mode is a hybrid Bragg confined mode (HBM).…”

“…MoL software [3] is used to predict the frequency, geometric factor (G) and electric filling factor (Pe) of the fundamental WGH mode family. Simulations are compared with measurements in order to estimate the loss-tangent and the permittivity of the alumina.…”

High-Q Cylindrical Alumina Resonator Based on Bragg Confined Mode of Azimuthal Mode Number Greater Than Zero

“…To characterize the dielectric properties of the alumina we use the whispering gallery mode method [9][10][11]. Modes are simulated using Method of Lines (MoL) software [12] to predict the frequency, geometric factor and filling factor of the fundamental WGH mode family. Simulations are compared with measurements in order to estimate the loss tangent and the permittivity of the alumina sample.…”

“…Density plot (modulus squared) of the dominant electric and magnetic field components for the 13.4 GHz mode of m = 1 as calculated using the Method of Lines[12] (see…”

Low-loss materials for high Q-factor Bragg reflector resonators

“…The simple model is briefly presented and used in this work to calculate the dimensions then a numerical technique based on the Method of Lines (MoL) was used to calculate the resonator properties. The MoL is a semi-analytical method with a rigorous formulation initially developed by mathematicians for the solution of differential equations [7]. To design such structures, many methods of solving the electromagnetic boundary value problems have been developed.…”