Fig. 1.

Time-dependent transmission matrix of an MMF. a Schematics of experimental setup for both transmission matrix measurement and wavefront shaping. A laser beam with tunable frequency is collimated, and its horizontal polarization is selected and split into two arms, with one being the reference and the other propagating through the MMF after reflecting off a spatial light modulator (SLM). The SLM is demagnified and imaged onto the MMF facet. Light transmitted through the MMF is recombined with the reference plane wave, and its horizontal polarization is imaged onto a CCD camera. The path lengths of the two arms are matched by tuning the delay line formed by mirrors M1–M3. L, lens; BS, beam splitter; PBS, polarizing beam splitter. b Temporal shapes of the input pulse (black dotted line, right axis) and the mean eigenvalue of $u^{†}\left(t\right)u\left(t\right)$ (blue solid line, left axis) representing the transmitted intensities of random spatial inputs. The two curves are normalized to have the same area. c–e Magnitudes of the measured time-dependent transmission matrices at three arrival times (marked by red arrows in b), showing strong mode mixing in the fiber. The transmission matrices are measured in k space at input and real space r at output, and subsequently converted to the fiber mode basis