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arXiv 1404.4013physics.optics
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回音壁微腔的高效边界元分析

Highly Efficient Boundary Element Analysis of Whispering Gallery Microcavities

Leyuan Pan, Tao Lu

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4 pages, 8 figures, journal
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摘要：

我们表明，边界元回音壁微腔分析的效率可以提高数量级的菲涅尔近似的列入。使用这个公式，模拟的微波盘与波数半径的产品一样大的$kR\approx8,000$被证明在对比以前的记录$kR\approx100$。该方法在计算模场分布和谐振波长时具有较高的精度，但由于采用了直接求根的方法，计算品质因数时的相对误差高达$10%$，这是传统边界元法所不能达到的。最后，四极形腔和直径为$100 μm$的双盘模拟使用尽可能少的$512$边界元，而这样的大腔的模拟使用传统的边界元方法以前没有报道。

英文摘要：

We demonstrate that the efficiency of the boundary element whispering gallery microcavity analysis can be improved by orders of magnitude with the inclusion of Fresnel approximation. Using this formulation, simulation of a microdisk with wave-number-radius product as large as $kR\approx8,000$ was demonstrated in contrast to a previous record of $kR\approx100$. In addition to its high accuracy on computing the modal field distribution and resonance wavelength, this method yields a relative error of $10%$ in calculating the quality factor as high as $10^{11}$ through a direct root searching method where the conventional boundary element method failed to achieve. Finally, quadrupole shaped cavities and double disks as large as $100 μm$ in diameter were modeled by employing as few as $512$ boundary elements whilst the simulation of such large cavities using conventional boundary element method were not reported previously.

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