FILT (Fast Inversion of Laplace Transform) method combined with MPMM (Modified Point Matching Method) is used to solve the problem of electromagnetic wave scattering by a circular cylinder with longitudinal slots. Some numerical results for the far field back scattering transient response are presented and discussed by comparing with the response for the perfect cylinder. The physical meaning of the transient wave form is discussed in detail. Also the precision of the analysis is checked carefully.

Superluminal group velocity in dispersive media has long been controversial. A partial source of confusion seems to be the absence of high precision numerical results concerning the waveform of the transmitted signal. This paper gives the precise waveforms of a causal half-sine-modulated pulse and a triangle-modulated pulse propagating in the Lorentz medium. Thus, the effects of analyticity of signal are clarified, which the analysis using Gaussian pulse cannot. Further, to deepen understanding of the mechanism of superluminal group velocity, we give a network theoretic consideration.

Gaussian pulse has no beginning point, so has no Laplace transform and is non-physical. We propose sinnt pulse (referred to as pseudo-Gaussian pulse or PGP) as an approximation of the Gaussian pulse. PGP has the Laplace transform and approaches the Gaussian pulse as n→∞. The propagation of PGP-modulated wave packet in the highly anomalous dispersion band of a Lorentz medium is investigated by numerical inversion of Laplace transform. Our results are greatly different from the conventional results obtained by the saddle point method. Our results show that the velocity of a Gaussian wave packet cannot be explained only by the concept of the group velocity as has been done so far.

The scattering problem of a plane wave by an axially slotted conducting elliptic cylinder in homogeneous medium is investigated. We present an accurate analysis using the modified point matching method, which can reduce the order of the simultaneous equations to be solved at least by a half under the condition of the same accuracy as compared with an usual point matching method. The accuracy of our results is checked by evaluating the relative errors. Numerical results are given for scattered field patterns by a conducting elliptic cylinder with a slot aperture of angle width 120 when the angle of incidence θinO.

The physical meaning of the energy velocity in lossy Lorentz media is clarified. First, two expressions for the energy velocity, one by Brillouin and another by Diener, are examined. We show that, while Diener's is disqualified, Brillouin's is acceptable as energy velocity. Secondly, we show that the signal velocity defined by Brillouin and Baerwald is exactly identical with the Brillouin's energy velocity. Thirdly, by using triangle-modulated harmonic wave, we show that the superluminal group velocity plays its role as a revelator only after the arrival of the signal traveling at the subluminal energy velocity. In short, nothing moves at the group velocity, and every frequency component of a signal propagates at its own energy velocity.