Geometric Phase Generated Optical Illusion

An optical illusion, such as “Rubin’s vase”, is caused by the information gathered by the eye, which is processed in the brain to give a perception that does not tally with a physical measurement of the stimulus source. Metasurfaces are metamaterials of reduced dimensionality which have opened up new avenues for flat optics. The recent advancement in spin-controlled metasurface holograms has attracted considerate attention, providing a new method to realize optical illusions. We propose and experimentally demonstrate a metasurface device to generate an optical illusion. The metasurface device is designed to display two asymmetrically distributed off-axis images of “Rubin faces” with high fidelity, high efficiency and broadband operation that are interchangeable by controlling the helicity of the incident light. Upon the illumination of a linearly polarized light beam, the optical illusion of a ‘vase’ is perceived. Our result provides an intuitive demonstration of the figure-ground distinction that our brains make during the visual perception. The alliance between geometric metasurface and the optical illusion opens a pathway for new applications related to encryption, optical patterning, and information processing.


Section 1. 2×2 Dammann grating design to increase the quality of holographic images.
In our experiment, the concept of Dammann grating is adopted in design to increase the fidelity of the hologram images. The difference between 2x2 array and a single period is shown in figure S1. In comparison with a single period, which produces a continuous image with lower image fidelity ( i.e. more laser speckles), the 2x2 periodic hologram generates an image consisting of discrete spots. The design can be further optimized by a N x N (N is an integer) Dammann grating, which can increase the image quality sharply. However, this will in turn require the need for longer fabrication time. Figure S1. The reconstructed image based on phase distribution with single period and 2x2 array, respectively.

Section 2. Detailed fabrication process of nano-pattern using E-beam lithography and lift-off process.
Firstly, the positive poly methyl methacrylate resist film (PMMA 950 A2) is spin coated on the Si substrate with pre-coated gold background layer (150 nm) and the SiO2 spacer (85 nm). The sample is baked at 180℃ on hotplate for five minutes.
Then, the nanostructures are defined on the PMMA film by E-beam lithography (Raith PIONEER) under 30 kV. The exposed sample is subsequently immersed in the developer (MIBK: IPA= 1:3) for 45 s and the stopper (IPA) for 45 s. After that, the sample is raised with DI water and dried by compressed N2 flow. Prior to gold deposition, a titanium layer of ~3 nm is deposited on the silicon dioxide (SiO2) layer for adhesion purpose. A 30 nm gold film is deposited on the sample via electron beam evaporation. Finally, the metasurface structure is achieved by a subsequent lift-off procedure. Figure S2. The target and the reconstructed inverted images versus incident polarization states at 633 nm.

Section 4. The dependence of conversion efficiency and SNR on the wavelength and polarization state of the incident light
To further characterize the metasurface, we measured the efficiency with different polarizations of the incident light at wavelength of 800 nm. The results are shown in Table S1. From the results we can see that the conversion efficiency remains by varying the polarization state of incident light. We also measured the SNR at different wavelengths and polarizations which is given in in Figure S3. The fidelity and the SNR of the reconstructed images get worse at shorter wavelengths. Moreover, the SNR is higher for the circular polarization compared with that for the linear polarization. Figure S3. The measured SNR at different wavelengths and polarizations.

Section 5. The simulated efficiency of single pixel of reflective metasurface
The efficiency of single pixel of metasurface was simulated using CST microwave studio software. The three-layer structure was modelled in CST (see the inset in Fig.   S4). The length, width and thickness of the rod are 220 nm, 80 nm, and 30 nm,  Figure S2 shows the simulated results of the conversion efficiency by plotting rRR 2 and rRL 2 . It should be noted that the Titanium adhesion layer is not added in this simulation. Figure S4. The simulated conversion efficiency of single pixel of reflective metasurface.
Section 6. Experimentally observed reconstructed images at different wavelengths. Figure S5. Experimentally reconstructed images of optical illusion and Moiré fringe at other wavelengths. The wavelengths of the incident beams are 528 nm, 568 nm, 608 nm, and 688 nm, respectively.