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圆腔回音壁模的自洽场描述
Self-consistent field description of whispering-gallery mode in circular cavity
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摘要: 在引进圆腔特征场及其反射系数的概念基础上,讨论了圆腔回音壁模(WGM)的自洽场描述.基于自洽场要求,得到了同直接求解描述WGM问题的Helmholtz方程一样的本征值方程.基于特征场描述的波一光线对应性,讨论了圆腔WGM自洽形成的几何射线描述.根据特征光线柬自洽的直观图像推导了WGM谐振波数与品质因子Q值,并与直接求解本征值方程所获得的结果符合很好.Abstract: On the base of introduction of circular cavity eigenfield and its reflection coefficient, the self-consistent field description of whispering-gallery mode (WGM) in circular cavity is discussed. Accroding to the self-consistency,the same eigenvalue equation as the one directly deduced from the Helmholtz equation determining WGM is obtained. Also based on the wave-ray correspondence of circular cavity eigenfield,the self-consistent ray description of WGM is discussed. The results of resonance wavenumbers and the Q-factors of WGMs deduced from the intuitive self-consistent picture of eigenray beam are well coincident with the ones obtained by directly solving the eigenvalue equation.
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