  Spatiotemporal modulation offers a variety of opportunities for light
manipulations. In this paper, we propose a way towards 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.
