An empirical dispersion formula is proposed and experimentally verified considering higher order modes of the conductor-backed coplanar waveguide with via holes. For this purpose, an effective dielectric constant is extracted up to 100 GHz from measured S-parameters. By fitting the extracted data, an empirical equation is extracted. The simulation of the Gaussian pulse transmission and the comparison results with the modeling data validate the reported expression.

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.