Time-reversal mirrors (TRMs) refocus an incident acoustic field to the position of the original source regardless of the complexity of the propagation medium. TRMs have now been implemented in a variety of physical scenarios from megahertz ultrasonics with aperture sizes of the order of centimeters to ocean acoustics at hundreds to thousands of hertz with aperture sizes of the order of hundreds of meters. Common to this broad range of scales is a remarkable robustness — exemplified by observations at all scales — that the more complex the medium between the probe source and the TRM, the sharper the focus. The relationship between the medium complexity and the size of the focal spot is studied in this paper. This relationship is certainly the most exciting property of TRM compared to standard focusing devices. A TRM acts as an antenna that uses complex environments to appear wider than it is, resulting in a broadband pulse with a refocusing quality that does not depend on the TRM aperture. In this paper, we investigate both the role of the time-reversal window duration and the bandwidth of the time-reversed signals for various media (waveguide, closed cavity, random medium).