Time evolution of power spectra from two-dimensional passive random media with different shapes

For a set of two-dimensional passive random media that have the same randomness and different shapes, the effects of morphology on the time evolution of the power spectrum of the localized modes supported by the media are investigated. The results demonstrate that the evolving process of the spectrum, the lifetime of short-lived modes and the amount of long-lived modes are morphological-dependent, while the lifetime of long-lived modes is morphological-independent. The denser the medium is, the quicker the evolving process and the shorter the lifetime of the short-lived modes are. Single-mode operation is more possible and occurs more early for a denser medium, which is of practical importance for proposing a mode-selecting technique for random lasers.