Imaging through a square multimode fiber by scanning focused spots with the memory effect

The existence of a shift-shift memory effect, whereby any translation of the input field induces translations in the output field in four symmetrical directions, has been observed in square waveguides by correlation measurements. Here we demonstrate that this memory effect is also observed in real space and can be put to use for imaging purposes. First, a focus is created at the output of a square-core multimode fiber, by wavefront shaping based on feedback from a guide-star. Then, thanks to the memory effect, four symmetrical spots can be scanned at the fiber output by shifting the wavefront at the fiber input. We demonstrate that this property can be exploited to perform fluorescence imaging through the multimode fiber, without requiring the measurement of a transmission matrix.