Hologram design principle

The building block to construct the meta-hologram is a set of nanoslit antennas, which is based on the Pancharatnam-Berry phase tuning (30–35) to modulate the transmitted light. These nanoantennas are made of metallic cells on the quartz substrate, as shown in Fig. 1C. (For different samples, the fabrication processes are different. Details of the fabrication and the dimensions of the nanoslit antenna can be found in section S1.) The slit is designed to be angled with respect to the x axis and to provide different phase shifts. According to the local phase shift associated with the spin-orbit interaction and propagating bounded wave exchange (22), the phase of the cross-polarized light (Φ) depends on the orientation angle (φ) of the nanoslit by the relation Φ = 2φ for circular polarization incident light, which is used to determine the angle of the nanoslit (34, 35). It is worth mentioning that such a nanoslit is efficient for a broadband wavelength covering the visible range (380 to 780 nm). Figure 1D shows the simulation results, demonstrating the phase modulation for the nanoslit antennas at different wavelengths. This achromatic feature is the key feature for our approach to achieve multicolor holography without cross-talk. We use this metasurface with broadband performance to design a single holographic image that contains all the image patterns corresponding to different colors. These images are separated and positioned at different spatial locations. Consequently, these individual image patterns are independent from each other so that the cross-talk among colors is eliminated.

With such nanoslit antennas, the meta-hologram is capable of reconstructing both multicolor 2D and 3D images. We first discuss the process in designing a multicolor 2D meta-hologram based on three primary colors (red, green, and blue). The recording and reconstruction principles are shown in Fig. 2 (A and B, respectively). To design the arrangement of the nanoslit antennas, we first divided a colorful image into its RGB components. The corresponding RGB components are shifted to different locations of the imaging plane to separate themselves from each other. These components then form one new holographic image. The phase distribution of the hologram is calculated by the Gerchberg-Saxton (GS) algorithm based on the image, with the termination condition defined by (36) (2)where SSE is the mean square error between the target image and the holographic image, g(u,v) is the Fourier transform of the incident light wave function, G(u,v) is the Fourier transform of the target image, and ε is the preset tolerance. In our calculation, the local minimum effect of the GS algorithm was not particularly taken care of, and the initialized phase of every pixel of the image is set to be zero.

Fig. 2 Design principle and experimental configuration of meta-holography. (A) Design principle for the holographic imaging. (B) Experimental setup for the reconstruction process. QWP, quarter-wave plate; CCD, charge-coupled device. (C) Phase diagram of the meta-hologram calculated by the GS algorithm corresponding to the flower holographic image. Scale bar, 500 μm. Color bar, phase shift. (D) Scanning electron microscope image of the nanoslit antennas. Scale bar, 1 μm.

The phase distribution of the hologram calculated by the GS algorithm is shown in Fig. 2C. Then, these phased pixels are substituted by the corresponding nanoslits to provide the desired phase shift. The nanoslit antennas are effective for all the wavelengths because of their broadband performance, as shown in Fig. 1D. In the reconstruction process, the individual color component, for example, the red light, obtains not only the red patterns but also the “unwanted” image patterns designed for green and blue light. The selection of the correct image patterns can then be achieved by the off-axis illumination. The GS algorithm relies only on the phase and amplitude of the transmitted light. It is possible to tune the k x and k y components of the transmitted light wave vector using Eq. 3 without affecting the holographic reconstruction (Fig. 3A). For example, the wave vector in the x direction can be calculated as (3)where k 0 is the transmitted light wave vector and θ x is the incident angle with respect to the x axis (see fig. S1). As k x and k y are tuned, the holographic images are shifted on the imaging plane. The correct holographic images can be shifted and superimposed into the final image, whereas the unwanted patterns are moved out of the imaging region. By this reconstruction principle, a single type of the nanoslit antenna is used to control multiple wavelengths.

Fig. 3 k-space modulation. (A) Schematic diagram to demonstrate the modulation of the k space of incident light. (B) Simulation results for the hologram design that shifts all the unwanted images into the k space corresponding to evanescent waves.