Hermite展开应用于介质柱散射的时-频域联合外推

Simultaneous Extrapolation of Electromagnetic Scattering of Dielectric Cylinders in Time-Frequency Domains Based on Hermite Expansions

介质柱在外加平面波照射下其体内会激励产生极化电流时域和频域响应 .利用极化电流的早时响应和低频信息 ,经过联合外推计算 ,获得了时域和频域的完全响应 .本文采用的基本方法是 :根据连带Hermite函数的傅里叶变换的自反性 ,以及散射体在高斯脉冲平面波激励下极化电流的时域响应的持续时间和频域信息的带宽的有限性 ,将时域响应和频域信息均展开为连带Hermite级数的叠加 ,待定系数由早时响应和低频信息联合确定 ,而早时响应和低频信息可分别由时间步进法 (MOT)和矩量法 (MOM)求得 .本文用 4个计算例子验证了这种外推方法 .

The responses of the polarization currents in both time and frequency domains in the cylinder irradiated by the plane wave are produced. The entirety responses of the polarization currents in both time and frequency domains can be obtained at one time by simultaneous extrapolation computation using both the early time response and the low frequency information of the polarization currents. The time domain response of the polarization currents on a scattering object irradiated by a plane wave with a Gaussian pulse in time is expanded as an associate Hermite series. Using the isomorphism of the associate Hermite function and its Fourier transform, the frequency domain information can be obtained similarly to the time domain expansion. According to the corresponding relation between time domain analysis and frequency domain analysis, and using the early time response and the low frequency information of the polarization currents, the unknown coefficients in the expansion series can be decided. Both the early time response and the low frequency information of the polarization currents can be obtained by MOT and MOM respectively. Four examples are presented to illustrate the application of this extrapolation methodology.