Cylindrical distributed Bragg reflector resonators with extremely high Q-factors

A simple non-Maxwellian method is presented that allows the approximate solution of all the dimensions of a multilayered dielectric TE_0qp mode cylindrical resonant cavity that constitutes a distributed Bragg reflection (DBR) resonator. The analysis considers an arbitrary number of alternating dielectric and free space layers of cylindrical geometry enclosed by a metal cylinder. The layers may be arranged axially, radially or both. Given only the aspect ratio of the cavity, the desired frequency and the dielectric constants of the material layers, the relevant dimensions are determined from only a set of simultaneous equations, and iterative techniques are not required. The formulas were verified using rigorous method of lines (MoL) calculations, and previously published experimental work. We show that the simple approximation gives dimensions close to the values of the optimum Bragg reflection condition determined by the rigorous analysis. The resulting solution is more compact with a higher Q-factor when compared to other reported cylindrical DBR structures. This is because, unlike previous analyses, it properly takes into account the effect of the aspect ratio on the Bragg anti-resonance condition along the z-axis of the resonator. By properly taking the aspect ratio into account, we show that the thickness of the Bragg reflectors is equivalent to the thickness of plane wave Bragg reflectors (or quarter wavelength plates). Thus it turns out that the sizes of the reflectors are related to the free space propagation constant, rather than the propagation constant in the z direction.