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Three-dimensional vectorial holography based on machine learning inverse design

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Science Advances  17 Apr 2020:
Vol. 6, no. 16, eaaz4261
DOI: 10.1126/sciadv.aaz4261
  • Fig. 1 Principle of 3D vectorial holography based on the machine learning inverse design using the MANN.

    (A) Schematic of floating display of a 3D vectorial holographic image based on a vectorial hologram, which contains a digital phase hologram and a digital 2D vector field derived from the MANN. (B) Schematic illustration of the generation of an arbitrary 3D vectorial field based on the MANN.

  • Fig. 2 Machine learning inverse design of an arbitrary 3D vectorial field using the MANN.

    (A) Schematic illustration of how a 2D vector field in the hologram plane is transformed to a 3D vectorial field in the image plane through a vectorially weighted Ewald sphere. Inset shows the definition of a 3D vectorial field in a spherical coordinate system. (B) The azimuthal spatial components modulated by a π-phase step with an orientation along the horizontal and vertical directions are used to independently manipulate the transverse electric field components Ex and Ey, respectively. A radial spatial component is used for the manipulation of the longitudinal electric field component Ez. The insets show the corresponding intensity distributions of these azimuthal and radial spatial components in the image plane. (C) Schematic of the four 3D vectorial fields derived from the MANN. The insets represent the MANN-derived 2D vector field distributions. (D) Experimental characterization of the three electric field components (Ex, Ey, Ez) of 3D vectorial fields through two-photon fluorescence imaging of the gold nanorods with an orientation along x, y, and z directions, respectively.

  • Fig. 3 Experimental demonstration of 3D vectorial holography.

    (A) Experimental approach of 3D vectorial holography based on a vectorial hologram, which consists of a MANN-derived 2D vector field and a digital phase hologram, respectively. (B) Experimental characterization of a 3D vectorial holographic image captured by a charge-coupled device (CCD). The insets show the two-photon fluorescence images of the three orthogonal components of a single pixel randomly selected from the reconstructed 3D vectorial holographic image. (C) Schematic illustration of the simultaneous generation of four 3D vectorial field distributions on a holographic image. (D) The experimentally reconstructed 3D vectorial field–multiplexed holographic image on a CCD, wherein the pseudocolors consistent with the ones in (C) were used to highlight the four different 3D vectorial fields. The insets of (D) show the experimentally characterized two-photon fluorescence images of the three orthogonal components of four pixels randomly selected from different sections of the multiplexed holographic image.

  • Fig. 4 3D direct laser writing of a vectorial hologram for the lensless reconstruction of 3D vectorial field–carrying and vectorial field–multiplexing holographic images.

    (A) Optical setup for the lensless reconstruction of a 3D vectorial holographic image, wherein a pair of laser-printed phase patterns were used to modulate two orthogonal circular polarization for the generation of the MANN-derived 2D vector fields, which are further directed to a digital phase hologram. The insets present the optical images of the printed high-resolution phase patterns, each of which is with a size of 2 mm by 2 mm. The red arrows label out the laser beam propagation directions. BS, beam splitter; LP, linear polarizer; HWP, half-wave plate; QWP, quarter-wave plate; PBS, polarizing beam splitter. (B) Experimental characterization of the lensless reconstruction of a 3D vectorial holographic image. The insets show the two-photon fluorescence images of the three orthogonal components of a randomly selected pixel in the reconstructed vectorial holographic image. Scale bar, 1 μm (inset). (C) Experimental verification of the divisibility property of a vectorial hologram based on different sections of a laser-printed vectorial hologram. The insets show the optical images of the laser-printed sectional vectorial holograms and their experimentally reconstructed holographic images, respectively. (D) Schematic illustration of the 3D vectorial mapping of eight vector-field distributions in a designed spiral shape as a function of azimuthal angle α. (E) Experimentally reconstructed 3D vectorial field–multiplexed holographic image designed in (D) on a CCD, wherein eight enlarged pixels with pseudocolors were used to highlight the different 3D vectorial fields (insets). Scale bar, 1 μm (inset).

Supplementary Materials

  • Supplementary Materials

    Three-dimensional vectorial holography based on machine learning inverse design

    Haoran Ren, Wei Shao, Yi Li, Flora Salim, Min Gu

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