无限小半径圆柱体光散射时的多重等离子体共振悖论
Paradox of multiple plasmonic resonances at light scattering by a cylinder of infinitesimal radius
摘要：
本文讨论了在单色电磁波作用下，介电常数为负1且消失半径为R的圆柱体的共振散射截面发散的佯谬。在麦克斯韦方程组的精确解的框架内，在指定条件下的发散是由除了一个多极共振之外的所有多极共振的重叠引起的。结果表明，该悖论是由过于直接的分析的表达式的截面，其中有一个奇异点。为了解决奇异性，首先必须将问题公式化，考虑入射波的最终线宽，然后执行正确的极限跃迁序列。这种方法的应用产生了在消失R处的消失截面。它破坏了采用这样的圆柱体作为超散射体的期望，但同时打开了一扇门，在远场和近场区域中与散射场在小但有限的R处的不寻常的尺寸依赖性相关的违反直觉的效应。
英文摘要：
The paradox of the divergence of the resonant scattering cross section of a cylinder with the permittivity equals minus unity and vanishing radius (R) irradiated by a monochromatic electromagnetic wave is discussed. Within the framework of the exact solution of the Maxwell equations, the divergence at the specified conditions is caused by the overlap of all but one multipolar resonances. It is shown that the paradox is caused by the too straightforward analysis of the expression for the cross section, which has a singularity at this point. To resolve the singularity, one must, first, generalize the problem formulation, taking into account the final linewidth of the incident wave, and then perform the correct sequence of limit transitions. The application of this approach gives rise to the vanishing cross section at the vanishing R. It ruins the expectations to employ such a cylinder as a superscatterer but simultaneously open a door to counterintuitive effects both in far and near field zones related to unusual size dependences of the scattered fields at small but finite R.
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