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

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