Fig. 3

A macroscopic time-interface and the associated effect on the wave dispersion of time-scattering. a Field variations at a point in an unbounded homogeneous medium experiencing a time-interface created by a switching refractive index \(n(t)\). The boundary conditions are the continuity of both electric displacement D and magnetic flux density B. An arbitrary wave packet (in yellow) splits into a forward (in blue) and a backward (in red) wave with the same envelope but oscillate at a different frequency. b The arrows in the dispersion diagram show the conservation of the spatial spectrum \(\Delta k\) and the frequency and bandwidth conversion from \(\Delta \omega_{1}\) to \(\Delta \omega_{2}\)