Mode control in a multimode fiber through acquiring its transmission matrix from a reference-less optical system

A simple imaging system, together with complex semidefinite programming, is used to generate the transmission matrix (TM) of a multimode fiber. Once the TM is acquired, we can modulate the phase of the input signal to induce strong mode interference at the fiber output. The optical design does not contain a reference arm, no internal reference signal is used, and no interferometric measurements are required. We use a phase-only spatial light modulator to shape the profile of the propagating modes, and the output intensity patterns are collected. The semidefinite program uses a convex optimization algorithm to generate the TM of the optical system using intensity only measurements. This simple, yet powerful, method can be used to compensate for modal dispersion in multimode fiber communication systems. It also yields great promise for the next generation biomedical imaging, quantum communication, and cryptography.