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A simple imaging system together with complex semidefinite programming isused to generate the transmission matrix of a multimode fiber. Once thetransmission matrix is acquired, we can modulate the phase of the input signalto induce strong mode interference at the fiber output. The optical design doesnot contain a reference arm and no interferometric measurements are required.We use a phase-only spatial light modulator to shape the profile of thepropagating modes and the output intensity at an individual pixel is monitored.The semidefinite program uses a convex optimization algorithm to generate thetransmission matrix of the optical system using intensity only measurements.This simple yet powerful method can be used to compensate for modal dispersionin multimode fiber communication systems. It also yields great promises for thenext generation biomedical imaging, quantum communication, and cryptography.

Mode Control in a Multimode Fiber Through Acquiring its Transmission Matrix from a Reference-less Optical System