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Multi-functional diffraction gratings have found broad applications in laser processing, medicine, beam manipulation, etc. However, based on the existing schemes there are still some challenges in fabricating the diffraction gratings with the controllable and arbitrary diffraction intensity of each order, multiple phase distribution, and polarisation of the output. Here, we propose a new phase mixing algorithm based on the random binary matrix and describe the theoretical foundation and experimental realisation of the proposed scheme. Using the new algorithm, several phase-mixing devices were fabricated, and the experiment verified the relationship of the light intensity, polarisation, phase and the algorithm. Our approach is practical to mix the phases of several diffraction gratings to realise the controllable diffraction orders, offering an innovative idea for the research of the liquid crystal phase mixing devices.

Multi-functional liquid crystal devices based on random binary matrix algorithm