Three-dimensional vectorial holography based on machine-learning inverse design

Conventional optical holography can address only the amplitude and phase information of an optical beam, leaving the 3D vectorial feature of light 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-perception artificial neural networks. Such 3D vectorial holography allows the lensless reconstruction of a 3D vectorial holographic image with near-unity 3D polarization purity. Holographic information can thus be encoded and encrypted on the wavefront of a 3D vectorial field.