Simple Design Technique for High Q-factor Bragg Reflector Resonators with Reflectors of Arbitrary Thickness

The Bragg reflection technique improves the Q-factor of a resonator by reducing conductor and dielectric losses by concentrating the field in the inner area of the cavity. In this paper, we present a general way of designing a high Q-factor Bragg resonator, using a simple model of non-Maxwellian equations. The method is a more general method, which allows us to design resonators of cylindrical geometry and arbitrary thicknesses for either the horizontal or cylindrical dielectric reflectors, which is often imposed by the manufacturer. In this work, we only consider cylindrical symmetric resonators operating in transverse electric mode (TE_0,n,p), which only has the E ₀ component made from low-loss single crystal dielectrics. The horizontal plates are of thickness 2.75 mm and radius 24.3 mm, and the rings are 31.8 mm high and of the same radius. The size of the cavity to obtain Bragg reflection may be calculated using the simple model, which is verified with rigorous method of lines analysis. When we fix the number of variation of E₀ in r and z directions to the minimum (fundamental mode) we obtained an unloaded Q-factor of order 2times10⁵ at 9.7 GHz in a single crystal sapphire resonator. Two other cavities were built to investigate Bragg confinement of higher order modes in the sapphire structure at 12.4 GHz with unloaded Q-factors of order 10⁵. We also illustrate the general designing principles of a Bragg reflector with dielectric layers of arbitrary thicknesses using the simple model, with verification using the method of lines