Spatiotemporal coupled-mode equations for arbitrary pulse transformation

Spatiotemporal modulation offers a variety of opportunities for light manipulations. In this paper, we propose a way toward arbitrary transformation for pulses sequentially propagating within one waveguide in space via temporal waveguide coupling. The temporal waveguide coupling operation is achieved by spatiotemporally modulating the refractive index of the spatial waveguide with a traveling wave through segmented electrodes. We derive the temporal coupled-mode equations and discuss how systematic parameters affect the temporal coupling coefficients. We further demonstrated a temporal Mach-Zehnder interferometer and universal multiport interferometer, which enables arbitrary unitary transformation for pulses. We showcase a universal approach for transforming pulses among coupled temporal waveguides, which requires only one spatial waveguide under spatiotemporal modulation, and hence provide a flexible, compact, and highly compatible method for optical signal processing in time domain.