Modeling of dwell time and group delay in dispersive and absorptive media

In this paper, a more general expression that describes the relationship between dwell time and group delay is derived. This expression is valid for all kinds of materials, including negative-index metamaterials (NIMs). An obstacle made of double-negative NIMs (DN-NIMs) and surrounded by a double-positive waveguide was used as a model. In the cases where the obstacle was made of left-handed materials and the surroundings were air, it has been shown that the dwell time and absorption have similar dependences on the incident wave frequency. On the other hand, group delay becomes negative in some cases. Numerical results show that an increase in the length of the obstacle leads to saturation of the dwell time and absorption, which is in accordance with the phenomenon known as the Hartman effect. Similar results were obtained for terahertz range of frequencies and for the dispersive waveguide. In this case, it is shown that there is a certain range of frequencies where group velocity is positive, whereas the phase velocity remains negative, i.e. the peak of the output pulse appears before the peak of the input pulse. Finally, the use of a model that considers an obstacle made of a lossless, non-magnetic metamaterial, with background permittivity equal to 1 and a dispersive waveguide, leads to the appearance of a new delay, called self-interference time.