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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干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 theory of time-harmonic electromagnetic field and waveguide, the analytic expressions of the electromagnetic field components in the transverse transverse electromagnetic mode and the transverse magnetic mode in the conical hollow metal waveguide were deduced. For the hollow sphere with the output aperture of sub-wavelength, The transmission characteristics of the electric and transverse magnetic modes and the time-averaged energy density distribution related to the light transmittance in the conical hollow metal waveguide were analyzed in detail. The precise eigenvalues obtained by the numerical solution are used to further discuss the effects of the wavelength of light, the length of the tapered waveguide, the output aperture and the taper angle on the time-averaged energy density distribution in a conical hollow metal waveguide. The results show that the time-averaged energy density distribution changes quasi-periodically in the tapered metal waveguide, and the period is related to the transmission mode, the cone angle and the wavelength of the light wave. And, in the transmission radial coordinates will appear a maximum value, the location of the maximum with the light wavelength, cone angle changes strongly.