arXiv quant-ph/06071562006-07quant-ph

任意形状轴对称电磁谐振器回音壁模式的二维有限元模拟

Ex-house 2D finite-element simulation of the whispering-gallery modes of arbitrarily shaped axisymmetric electromagnetic resonators

Mark Oxborrow

备注：: 21 pages, 8 figures, 4 tables; submitted to IEEE Transactions on Microwave Theory and Techniques. Corrected 20th March 2007

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摘要：

它明确地描述了一个流行的，商业上可获得的软件包，用于解决偏微分方程（PDE），基于有限元法（FEM），可以被配置为计算的频率和场的回音壁（WG）模式的轴对称介质谐振器。该方法是可追溯的，它利用偏微分方程求解器的能力，接受定义的解决方案麦克斯韦方程组在所谓的“弱形式”。提供了用于估计WG模式的体积、填充因子以及在闭合（开放）谐振器的情况下其壁（辐射）损耗的相关表达式和方法。由于没有施加横向近似，该方法仍然是准确的，即使是所谓的准TM和TE模式的低，有限的方位角模阶。该方法的通用性和实用性证明了几个非平凡的结构建模：（i）两个不同的光学微腔[一个环形的二氧化硅，其他AlGaAs微盘];（ii）一个三阶微波布拉格腔含有氧化铝层（iii）两个不同的低温蓝宝石X波段微波谐振器。通过拟合后者的一组测量的谐振频率，蓝宝石在液氦温度下的介电常数已被估计。

英文摘要：

It is described, explicitly, how a popular, commercially-available software package for solving partial-differential-equations (PDEs), as based on the finite-element method (FEM), can be configured to calculate the frequencies and fields of the whispering-gallery (WG) modes of axisymmetric dielectric resonators. The approach is traceable; it exploits the PDE-solver's ability to accept the definition of solutions to Maxwell's equations in so-called `weak form'. Associated expressions and methods for estimating a WG mode's volume, filling factor(s) and, in the case of closed(open) resonators, its wall (radiation) loss, are provided. As no transverse approxi-mation is imposed, the approach remains accurate even for so-called quasi-TM and -TE modes of low, finite azimuthal mode order. The approach's generality and utility are demonstrated by modeling several non-trivial structures: (i)two different optical microcavities [one toroidal made of silica, the other an AlGaAs microdisk]; (ii) a 3rd-order microwave Bragg cavity containing alumina layers (iii) two different cryogenic sapphire X-band microwave resonators. By fitting one of the latter to a set of measured resonance frequencies, the dielectric constants of sapphire at liquid-helium temperature have been estimated.

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摘要：

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