利用时谐电磁场和波导理论, 推导出锥形空心金属波导中球横电模和球横磁模各电磁场分量的解析表达式, 对输出孔径是亚波长尺寸的锥形空心金属波导内球横电模和球横磁模的传输特性及与锥形空心金属波导内光透射率有关的时间平均能量密度分布进行了详细的分析。运用数值求解获得的精确本征值, 进一步讨论了光波波长、锥形波导的长度、输出孔径以及锥角对锥形空心金属波导内时间平均能量密度分布的影响。研究结果表明, 时间平均能量密度分布在锥形金属波导内呈现准周期性变化, 且周期与传输模式、锥角及光波波长有关。并且, 在传输径向坐标上会出现一个最大值, 最大值的位置随光波波长、锥角发生强烈的变化。

Based on the time-harmonic electromagnetic field and waveguide theory, the analytical expressions for the field components of the spherical transverse-magnetic (TM) and transverse-electric (TE) modes inside a metallic hollow conical waveguide with a sub-wavelength-sized exit hole have been derived. The time-averaged electromagnetic field energy density distribution associated with light transmission and the transmission properties of the spherical TM and TE modal fields inside a sub-wavelength hollow conical waveguide have been studied in detail. Moreover, by using the accurate eigenvalues obtained numerically, the influence of the light wavelength, the taper angle, the aperture diameter as well as the length of the conical waveguide on the time-averaged energy density distribution inside the sub-wavelength metallic hollow conical waveguide has been discussed. The results show that the time-averaged energy density distribution inside the conical waveguide varies quasi-periodically. The quasi-period has relation with the mode, the light wavelength as well as the taper angle. Furthermore, there is a clearly pronounced maximum in the radial dependence. The position of an appreciable maximum for the time-averaged energy density varies rapidly with the light wavelength and the taper angle.