  Time-of-flight measurements are key to study distributed mode coupling and
differential mode group delay (DMDG) in multimode fibers (MMFs). However,
current approaches using regular photodetectors with limited sensitivity
preclude the detection of weak modal interactions in such fibers masking
interesting physical effects. Here we demonstrate the use of high-sensitivity
superconducting nanowire single-photon detectors (SNSPDs) to measure the mode
transfer matrix of a commercial graded-index multimode fiber. Two high
performance 45-mode multi-plane light conversion (MPLC) devices served as the
mode multiplexer/demultiplexer. Distributed mode coupling and DMDG among
different mode groups are accurately quantified from the impulse response
measurement. We also observed cladding modes of the MMF as a pedestal of the
pulse in the measurement. This work paves way for applications such as quantum
communications using many spatial modes of the fiber.
