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首页> 外文期刊>IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control >Distributed Bragg reflector resonators with cylindrical symmetry and extremely high Q-factors
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Distributed Bragg reflector resonators with cylindrical symmetry and extremely high Q-factors

机译：具有圆柱对称性和极高Q因子的分布式布拉格反射器谐振器

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摘要

A simple non-Maxwellian method is presented that allows the approximate solution of all the dimensions of a multilayered dielectric TE/sub 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 along the axial direction, the radial direction, 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 it properly takes into account the effect of the aspect ratio on the Bragg antiresonance condition along the z-axis of the resonator. Previous analyses assumed the propagation in the z-direction was independent of the aspect ratio, and the layers of the Bragg reflector were a quarter of a wavelength thick along the z-direction. When the aspect ratio is properly taken into account, we show that the thickness of the Bragg reflectors are 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.
机译：提出了一种简单的非麦克斯韦方法，该方法可以近似求解构成分布式布拉格反射（DBR）谐振器的多层电介质TE / sub 0qp /模式圆柱谐振腔的所有尺寸。该分析考虑了由金属圆柱体包围的任意数量的交替交替的圆柱几何形状的电介质层和自由空间层。这些层可以沿轴向，径向或两者布置。仅给出空腔的纵横比，所需频率和材料层的介电常数，仅从一组联立方程确定相关尺寸，并且不需要迭代技术。使用严格的线法（MoL）计算和先前发表的实验工作来验证公式。我们表明，简单逼近给出的尺寸接近通过严格分析确定的最佳布拉格反射条件的值。与其他已报道的圆柱形DBR结构相比，所得解决方案更紧凑，Q因数更高。这是因为其适当地考虑了纵横比对沿着谐振器的z轴的布拉格反谐振条件的影响。先前的分析假设在z方向上的传播与纵横比无关，并且布拉格反射器的层沿z方向的厚度为四分之一波长。当适当考虑纵横比时，我们表明布拉格反射器的厚度等于平面波布拉格反射器（或四分之一波长板）的厚度。因此，事实证明，反射器的尺寸与自由空间传播常数有关，而不是与z方向上的传播常数有关。

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