Optical analogy for temporal diffraction in tight-binding lattice

The wave propagating through the temporal boundary has attracted considerable attention in the past few years because of the potential applications of time-varying systems in the optics community. However, temporal diffraction of light remains to be investigated, because free space is non-dispersive. Here, we theoretically provide the analytical expressions for the temporal diffraction contributions of electron waves across the temporal boundary between the free space and a dispersive medium. With the help of coupled waveguide arrays, temporal diffraction is analogously observed by the optical platform. The optical analogy results confirm the theoretical predictions of the temporal diffraction wave at the temporal boundary. By changing the permittivity of the waveguides, implying the coupling coefficient is modified, the temporal diffraction angle is tuned. Our analysis and observations of temporal diffraction of dispersive media have great potential in time-varying physics, signal processing, and photonics communications.