Temporal chirp, temporal lensing, and temporal routing via space-time interfaces

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 analog of a spatial interface between two materials. Here, we study light-matter interactions in four dimensions, 4D (space, and time, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>t</a:mi></a:math>), 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 combination of temporal and spatial interfaces can enable interesting features such as the 4D and and of electromagnetic waves. Such exotic possibilities may provide new ways to manipulate light-matter interactions via a combination of temporal and spatial interfaces.