  The analysis of wave patterns in a structure which possesses periodicity in
the spatial and temporal dimensions is presented. The topic of imperfect chiral
interfaces is also considered. Although causality is fundamental for physical
processes, natural wave phenomena can be observed when a wave is split at a
temporal interface. A wave split at a spatial interface is a more common
occurrence; however when the coefficients of the governing equations are
time-dependent, the temporal interface becomes important. Here, the associated
edge waves are studied, and regimes are analysed where the growth of the
solution in time is found. Imperfect interfaces, across which the displacements
are discontinuous, are also considered in the vector case of chiral elastic
systems. Analytical study and asymptotic approximations are supplied with
illustrative numerical examples.
