  The temporal-mode (TM) basis is a prime candidate to perform high-dimensional
quantum encoding. Quantum frequency conversion has been employed as a tool to
perform tomographic analysis and manipulation of ultrafast states of quantum
light necessary to implement a TM-based encoding protocol. While demultiplexing
of such states of light has been demonstrated in the Quantum Pulse Gate (QPG),
a multiplexing device is needed to complete an experimental framework for TM
encoding. In this work we demonstrate the reverse process of the QPG. A
dispersion-engineered difference frequency generation in non-linear optical
waveguides is employed to imprint the pulse shape of the pump pulse onto the
output. This transformation is unitary and can be more efficient than classical
pulse shaping methods. We experimentally study the process by shaping the first
five orders of Hermite-Gauss modes of various bandwidths. Finally, we establish
and model the limits of practical, reliable shaping operation.
