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

高q因子谐振器是新兴毫米级系统（如汽车雷达（72 GHz）、点对点通信、卫星移动宽带（20 GHz - 30 GHz）和无线通信）中低相位噪声振荡器的重要组成部分。温度稳定，高Q谐振器也是频率标准内的关键组件，可用于基准原子和光学参考源。高q谐振器的最新应用是在引力波探测器的极精确定位系统中。术语Q是谐振器的质量因子，是测量频率响应的清晰度。一个很好的类比是一个音叉，它在一个固定的频率上有一个尖锐的共振，它有一个高q。在微波共振中，情况是类似的，除了我们用微波打击谐振器。我们希望共振尖锐且Q值高，因为这样可以构造振荡器等器件。谐振器的质量因数Q由材料的正切损耗和围绕谐振器的金属外壳的损耗决定。有一个叫做几何因子G的量，它与外壳表面的总磁场与切向磁场之比有关。结果是这个几何因子需要被最大化。还有一个量叫做填充因子，它的值在接近0和1之间。填充系数是对介电介质中所含电磁能量的度量，通常微波工程师的目标是将填充系数提高到统一。然而，在这个提议中，我们采取了相反的方法。增加Q因子有两种主要策略。第一个也是目前为止最常见的目标是高填充系数（就像通常的TE01d或低语画廊模式一样）。第二种方法的目标是一个非常低的填充因子，但最大化的几何因子。在这个提议中，我们尝试用接近零的填充因子来实现后者，但我们仍然试图最大化g，这将尝试使用可以限制电磁能量的布拉格反射器。通过将模式能量限制在电介质布拉格反射结构内，由于空气/真空中包含模式能量，因此可以降低电介质的填充因子。由于能量限制，几何因子仍然很高。提案的新颖之处：非周期反射谐振器。我们最初的模型揭示了一个非常惊人的结果。如果反射器的层厚度不相同或是非周期性的，这是一个非常大的Q因子增强。蓝宝石5壳非周期反射谐振器在30GHz （50thz的Qxf）下的模拟Q值为170万。周期布拉格反射器在Q值为46万时饱和，并且在增加层数时，Q值不会进一步增加。我们打算用蓝宝石来证明这个原理。

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.