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arXiv physics/0509226physics.optics
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回音壁模式的几何理论

Geometrical theory of whispering gallery modes

Michael L. Gorodetsky, Aleksey E. Fomin

摘要:

用准经典方法可以得到凸轴对称体中回音壁模本征频率的较精确的解析近似,并以球形介质腔为例,用程函法分析了准经典近似的精度极限。本征频率的计算所获得的系列与已知的系列介质球和数值计算进行了比较。我们展示了如何几何解释允许扩展的方法对任意形状的轴对称体。

英文摘要:

Using quasiclassical approach rather precise analytical approximations for the eigenfrequencies of whispering gallery modes in convex axisymmetric bodies may be found. We use the eikonal method to analyze the limits of precision of quasiclassical approximation using as a practical example spheroidal dielectric cavity. The series obtained for the calculation of eigenfrequencies is compared with the known series for dielectric sphere and with numerical calculations. We show how geometrical interpretation allows expansion of the method on arbitrary shaped axisymmetric bodies.

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