Remote Spatio-Temporal Focusing Over Multimode Fiber Enabled by Single-Ended Channel Estimation

Multimode fiber (MMF) is attractive for a variety of applications requiring a large number of spatially overlapped modes including biophotonics and telecommunications. Superimposing these modes at the input by controlling the amplitude and phase of each individual mode can form arbitrarily structured light at the distal end of the MMF, which provides the possibility for ultra-thin fiber endoscopy, miniature multi-photon microscopy, and remote beam forming. Realistic deployment of this technology for example in a flexible endoscope would require a technique to continuously calculate the proper input modal superpositions over a large bandwidth as the fiber is perturbed without access to the distal end of the fiber. Here, we propose a single-ended channel estimation scheme which can measure broad-band MMF transfer matrix $\mathbf {H}$ at the transmitter employing reflective spatial pilots at the distal end of the MMF. Broadband multiple-input-multiple-output (MIMO) preprocessing is realized through electro-optic modulation for undoing mode scrambling, mitigating modal dispersion and achieving remote coherence control. We demonstrate spatial and temporal mode focusing at the receiver over an MMF guiding six spatial and polarization modes.