Feasibility study: Ultra-High Q-factor Aperiodic Reflector Resonators

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Resonators with high Q-factor are important components in low-phase noise oscillators for emerging millimetre systems such as automotive radar (72 GHz), point-to-point communications, satellite mobile broadband (20 GHz - 30 GHz) and wireless communications. Temperature stable, high Q resonators are also critical components within frequency standards which can be used to benchmark atomic and optical reference sources. Recent applications of high-Q resonators are in extremely accurate positioning systems for gravitational wave detectors.The term Q is the Quality Factor of the resonator and is a measure of the sharpness of the frequency response. A good analogy is a tuning fork which has a sharp resonance at a fixed frequency - it has a high Q. In a microwave resonance the situation is similar except that we are striking the resonator with microwaves. We would like the resonance to be sharp with a high Q as this enables devices such as oscillators to be constructed. The quality factor Q of a resonator is determined by the loss tangent in the material and the losses in the metallic enclosure which surrounds the resonator. There is a quantity called the geometric factor G and this is related to the ratio of the total magnetic field to the tangential magnetic field at the surface of the enclosure. It turns out that this geometry factor needs to be maximised. There is another quantity called the filling factor and this has a value between near zero and 1. The filling factor is a measure of the amount of electromagnetic energy contained in the dielectric and usually microwave engineers aim to increase the filling factor towards unity. In this proposal however, we take the opposite approach.There are two main strategies for increasing the Q factor. The first and by far the most common is to aim for a high filling factor (as is the case in the usual TE01d or whispering gallery modes). The second approach is to aim for a very low filling factor but maximise the geometry factor. In this proposal we attempt the latter with filling factors approaching zero, but where we still try to maximise G. This will be attempted using a Bragg reflector which can confine the electromagnetic energy. By confining the mode energy within a dielectric Bragg reflecting structure, the filling factor of the dielectric can be reduced due to the fact that air/vacuum contains the mode energy. The geometric factors are still very high due to energy confinement.The Novelty in the proposal: Aperiodic Reflector Resonators.Our initial modelling has revealed a very surprising result. This is a very large enhancement in the Q factor if the layers of the reflector are NOT the same thickness or are aperiodic. The modelled Q of an sapphire 5 shell aperiodic reflector resonator is 1.7 million at 30GHz (Qxf of 50 THz. A periodic Bragg reflector saturates at a Q of 0.46 million and there is no further increase in the Q on adding layers. We intend to use sapphire for this proof of principle.