Coherent measurement of orbital angular momentum (OAM) spectrum of light fields plays a key role in many important applications, such as OAM-based multiplexing in optical communications. The existing methods for measuring the OAM spectrum by spatially separating OAM components or interferometric technique suffer from poor efficiency and interferometric stability requirements. Here, we propose a novel technique to measure the OAM spectrum of light fields in a single shot manner by exploiting a scattering optical element. Our technique enables to directly extract the OAM spectrum from a recorded single-shot speckle pattern using algorithms based on the speckle-correlation scattering matrix and spatial mode decomposition method. As a proof of concept, we built a robust measurement system based on a fast digital micromirror device to demonstrate the feasibility of the proposed technique.
Shaping complex fields with a digital micromirror device (DMD) has attracted much attention recently due to its potential application in optical communication and microscopy. In this paper, we present an optimized Lee method to achieve dynamic shaping of orbital-angular-momentum (OAM) beams using a binary DMD. An error diffusion algorithm is introduced to enhance the accuracy for binary-amplitude hologram design, making it possible to achieve high fidelity wavefront shaping while retaining a high resolution. As a proof of concept, we apply this method to create different classes of OAM beams and experimentally demonstrate the dynamic shaping of different OAM beams including pure modes and mixed modes with a switching rate of up to 17.8 kHz.
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