Polarization Transmission Matrix for Completely Polarization Control of Focal Spots in Speckle Field of Multimode Fiber

The propagation of light transmitting through a scattering medium generates random speckle. Transmission matrix (TM) is introduced to describe this transmission process. In general, only scalar TM is considered. Meanwhile, for a non-polarization maintaining multimode fiber (MMF), depolarization effect is extremely strong. Therefore, the field at the exit end of a MMF is a speckle with random distribution not only in terms of intensity but also polarization. In addition to traditional TM, we propose polarization TM (PTM) to describe the depolarization effect of a MMF. Based on PTM, the speckle pattern formed by a coherent light transmitting through a MMF can be modulated into one focal spot or multiple focal spots with desired polarization.