Space-Time Lensing by Accelerated Interfaces in Dispersive Media

We present space-time lensing by synthetic accelerated interfaces in dispersive media.

Frequency-dependent group velocities map spectral components of a pulse onto distinct trajectories in the longitudinal space-time plane, while an accelerated interface reshapes their frequencies through time-dependent Doppler shifts.

We develop an inverse-design procedure for the interface trajectory that focuses a quasi-monochromatic wave packet at a prescribed space-time event for an arbitrary dispersion relation, then extend the construction to polychromatic pulses.

In its time-reversed form, the operation collimates a broadband pulse into a narrow-band wave.

Moreover, cascading the forward and reverse operations enables a broadband pulse to propagate through an otherwise dispersive channel in a spectrally compressed state before being refocused.

Full-wave simulations validate the focusing construction and demonstrate dispersion suppression.