Pulsed EM-field diffraction by semi-infinite sheets

Abstract

Electromagnetic (EM) diffraction by a perfectly electrically conducting (PEC) semi-infinite screen is a canonical problem in EM wave theory whose first exact solution is attributed to Sommerfeld [1]. The need for physical insights into EM diffraction problems that would enable the evaluation of antenna performance and EM propagation in a complex environment called for a general solution methodology capable of handling more involved problem configurations. Significant progress in these efforts has been accomplished via integral-equation formulations [2, 3] that are amenable to the Wiener-Hopf (WH) method [4]. Through this methodology, the original Sommerfeld's half-plane problem has been generalized by incorporating finite conductivity of the diffracting screen [5, 6] or by placing the semi-infinite PEC screen on the planar interface of two media [7]. A detailed summary of major achievements in this field of research is given in Ref. [8].Despite a myriad of applications relying entirely on pulsed EM fields, the majority of available analytical solutions have been obtained under the assumption of the sinusoidal time dependence only. In these closed-form frequency-domain (FD) solutions, the (real-valued) frequency parameter generally occurs in intricate functional dependencies, which does not allow achieving their time-domain (TD) counterparts analytically without the use of an inverse (fast) Fourier transform. To provide closed-form analytical solutions directly in the TD, we shall next combine the Cagniard-DeHoop (CdH) technique (see Chapter 1) with the WH method. For truly seminal works pioneering the presented methodology, we refer the reader to [9, 10].