  A time interface (a rapid change of the constitutive parameters of a material
in time), applied within an unbounded medium where a wave travels, can enable
frequency conversion, and is considered the temporal analogue of a spatial
interface between two materials. Here, we study light-matter interactions in
four dimensions, 4D (space, x,y,z, and time, t), by exploring the implications
of applying time interfaces not to the entire space where a wave travels, but
to certain regions of space in order to create spatial interfaces in time.
Different configurations such as induced perpendicular, parallel, and oblique
spatial interfaces via a temporal interface are discussed. It is shown how such
four-dimensional combinations of temporal and spatial interfaces can enable
interesting features such as the 4D generalized Snell law and the temporal
chirp, temporal lensing, and temporal routing of electromagnetic waves. Such
exotic possibilities may provide new ways to manipulate light-matter
interactions via a combination of temporal and spatial interfaces.
