Seeing through multimode fibers with hidden memory effects

Multimode fibers provide an attractive platform to perform minimally invasive imaging deep into the human body. However, the presence of mode dispersion and coupling scramble the information carried by light. One way forward is to exploit statistically invariant properties known as memory effects. In multimode fibers with cylindrical symmetry there is a rotational memory effect wherein a rotation of the input field leads to a rotation of the same magnitude at the output. However, a simple rotation is not enough to reconstruct an image, and thus other invariant properties need to be exploited. Here, we demonstrate the existence of a whole family of hidden memory effects that provide us with sufficient information to image through a gradient-index multimode fiber.