Three-dimensional vectorial holography based on machine learning inverse design

The three-dimensional (3D) vectorial nature of electromagnetic waves of light has not only played a fundamental role in science but also driven disruptive applications in optical display, microscopy, and manipulation. However, conventional optical holography can address only the amplitude and phase information of an optical beam, leaving the 3D vectorial feature of light completely inaccessible. We demonstrate 3D vectorial holography where an arbitrary 3D vectorial field distribution on a wavefront can be precisely reconstructed using the machine learning inverse design based on multilayer perceptron artificial neural networks. This 3D vectorial holography allows the lensless reconstruction of a 3D vectorial holographic image with an ultrawide viewing angle of 94° and a high diffraction efficiency of 78%, necessary for floating displays. The results provide an artificial intelligence–enabled holographic paradigm for harnessing the vectorial nature of light, enabling new machine learning strategies for holographic 3D vectorial fields multiplexing in display and encryption.