Out-of-plane computer-generated multicolor waveguide holography: supplementary material

Multicolor waveguide holography remains a challenge due to its inherent design complexity, compounded by the limited low-loss materials available in the optical range as well as challenges in nanofabrication. In this study, we first propose and experimentally demonstrate a multicolor, computer-generated hologram (CGH) in an all-dielectric waveguide metasurface system. Light beams from three different color laser sources (red, green, and blue) are coupled into the waveguide via a single-period grating without any beam splitters or prisms. A multicolor holographic image can be decoupled in the far field through a binary metasurface CGH without any lenses. This technology enables lens-free, ultraminiature augmented and virtual reality displays.

The multicolor holography waveguide system is designed to couple external light sources to one side of a waveguide through a grating coupler with different incident angles and then decouple the waves out of plane by a computer generated hologram (CGH) on the other side to reconstruct a multicolor holographic image in a range of intended angles in free space.Independent holograms are created for each of the colors and multiplexed into one metasurface binary CGH, for that light from each source propagates within the waveguide with a distinct spatial frequency.
As shown in Figure S1a, the k-space diagram of a grating coupler illustrates how the grating period is determined once the propagation constants of the waves are obtained for the waveguide.Here, the grating equation (mk Λ = k x,inc − k r ) must be satisfied and only the -1st order diffracted waves propagate to the hologram.The k-diagram in Figure S1b shows that if the incident beams accidentally illuminate the hologram directly, only the zero-order reflection of the hologram occurs, but at angles outside of the reconstruction and collection region (gray area).The k-diagram of the hologram decoupler in Figure S1c shows that only the -1st order diffraction participates in forming the holographic images.The generated holographic image are reconstructed over an intended range of angles and collected by an imaging system that consists of a collector lens and a digital camera.
Figure S1d illustrates the multilayer system, showing a grating coupler and a CGH decoupler with waveguide modes propagating in the waveguide region.In a multicolor holographic design, the period is set to be 280 nm, which requires the incident angles are −52.7 • (red), −24.1 • (green) and −5.8 • (blue).The object in the example is taken as a letter combination with a red "R" followed with a green "G" and a blue "B" .Here, the decoupling angle range in the x-direction is set to be from −35 • to −45 • , while it is set to be from −5 • to 5 • in the y-direction.
A theoretical multicolor holographic image of "RGB" is reconstructed in the designed region.Note that the image seems to be a mirror of the object in the 2D profile, while in the actual 3D experiment it is just as the object.As shown, only the letters with the correct color combination locate in the intended range of angles; letters corresponding to other diffracted orders lies outside of the collection region.
To obtain an optimized intensity distribution for the reconstructed holographic image, we follow the design process indicated in the flowchart shown in Figure S2a [1,2].We start with a desired color image that is to serve as the object.For the present work, the images have three colors that are spatially distributed.We then separate the image into three color planes, each resulting in a black and white image corresponding to one of the three color channels.We then map each pixel on each color plane to a decoupling angle located in a certain range.The minimum and maximum of the decoupling angles are chosen such that the Fourier components for each color are disjoint, as shown in Figure S2b and in the example of multicolor RGB letters in Figure S2c.It should be noted that different color planes are combined into a single Fourier space.Then a GS-based hologram generation process is performed [3], as labeled with dashed lines in the Figure S2a.A random phase is superimposed on the desired amplitude to form a complex field and then impose a fast Fourier transform (FFT) to the spectrum domain.Apply a constraint to the generated hologram which requires that the hologram must be a binary hologram due to the limitation of the current fabrication, in which the CGH part metasurface would be either partially etched or not.A reconstruction algorithm is used to check if the holographic image generated by the CGH is acceptable or not when compared to the original object.If not, the modified hologram is converted back to the spatial domain by performing an inverse fast Fourier transform (iFFT).Apply a constraint in the spatial field to enforce the amplitude in the far field connecting to the decoupling angles.The new field is regarded as the initial field for the next iteration.The smallest    feature size designed in the hologram is set to be 100 nm and the periods for the generated holograms for different colors are quite small (less than 300 nm), which makes the reconstructed hologram image only have the -1st diffraction order solution, as shown in Figure S1c.Therefore, no twin images would be generated as happens to other hologram generation methods such as in Gabor holograms [4].

FABRICATION
To validate the designed multicolor waveguide holographic system, different samples have been fabricated utilizing nanofabrication techniques.The main fabrication process of the waveguide holographic samples includes two steps of plasma enhanced chemical vapor deposition (PECVD) and electron-beam lithography (EBL), as shown in Figure S3.First, a 2 µm waveguide cladding layer of SiO 2 is deposited on silicon substrates through PECVD (Advanced Vacuum Vision 310) with a deposition temperature of 250 • C. Then the grating and hologram structures are transferred to the metasurface layer utilizing EBL (Elionix ELS-7500 EX) with an electron beam resist of ZEP-520A, as shown in Figure S3 a and b.The designed thickness of metasurface layer is 300 nm, which is controlled by the dilution ratio with anisole (Sigma-Aldrich, 99.7 %) and the spin-coating speed.The depth of the etched structures is around 60 nm, which is controlled by the EBL dose time and the develop time in O-Xylene (Sigma-Aldrich, > 98%).The metasurface thickness is measured by a film thickness measurement reflectometer (Nanometrics 210).The overall size of the hologram in the metasurface layer is designed to be 300 µm × 300µm (one of the available field sizes for the EBL system) and the smallest feature size is set to be 100 nm.One of the designed grating periods is set to be 280 nm with a fill fraction of 0.5.The structure details of the fabricated holograms and gratings were checked with an SEM (Scanning Electron Microscope, FEI XL30 SEM-FEG) and AFM (Atomic Force Microscope, Digital Instruments Dimension 3100), as shown in Figure S3 c and d.The optical properties of the PECVD grown SiO 2 were characterized by an ellipsometer VASE (Variable Angle Spectroscopic Ellipsometer, J. A. Woollam M-88), and the result could be found in Figure S4 a and b.
A commercial electron-beam resist of ZEP (ZEP520A, ZEON Corporation, Japan) is selected to make the metasurface layer for the following reasons.First, the refractive index of the meta- surface ZEP is larger than that of air and SiO 2 , which makes a perfect waveguide structure.Compared with other potential resist candidates having larger refractive index, such as silicon nitride (SiN x ), the extinction coefficient of ZEP is quite small, which is crucial to efficiently propagate light in the waveguide over a longer distance.The extinction properties have been verified by VASE measurements, as shown in Figure S4 c and d.Furthermore, compared to other commonly used electron-beam resists such as different kinds of PMMA(Polymethyl methacrylate), the resolution and contrast of ZEP is much higher and its etch resistance is better, which makes it a good candidate for structure modeling.Note that both the gratings coupler and the CGH decoupler are formed in the metasurface layer of ZEP.An optical system was built to characterize the performance of fabricated samples and check if the designed holographic images could be reconstructed in the intended range of angles,as shown in Figure S5.The light sources consist of three semiconductor laser modules (Thorlabs, Inc.) with operational wavelengths at 635 (red), 532 (green) and 450 nm (blue).A combination of two lenses (L1 and L2) with the focal lengths of 25 mm and 50 mm are used in each color branch to collimate the beam and adjust the spot size of each light source, while the intensity filters are used to balance the beam power from each source for a better demonstration.The incident angles for three light sources are built to be −52.7 • (red), −24.2 • (green) and −5.8 • (blue), as designed with the grating coupler period of 280 nm.For a singlecolor hologram design, only one light source is needed.For a multicolor design, all the three sources are used to illuminate the grating coupler on a metasurface sample at designed incident angles and a holographic image will be generated at the intended range of angles.The generated holographic images could be observed directly.And it could be collected by an imaging system as well.A collector lens (L3) with the focal length of 200 mm is used to focus the out-coupled holographic image.Then the holographic image is collected with a CCD commercial digital camera (Nikon D90) with a focal length of 130 mm lens.

Fig. S1 .
Fig. S1.A multilayer system for waveguide multicolor holography.(a).Grating coupler k-diagram with red, green and blue light sources incident in specifically designed angles.(b).The k-diagram of a multicolor hologram shows that if the three light sources illuminate the hologram directly only zero-order reflection beams exist in the reflection region.(c).The k-diagram of a multicolor CGH as a decoupler to reconstruct a multicolor holographic image in the intended range of angles which is labeled as the gray region.(d).The multilayer structure of a waveguide multicolor holographic system.

Fig. S2 .
Fig. S2.The process of a multicolor waveguide holographic CGH.(a).Flowchart of the CGH design with the square region labeling the "GS" algorithm-based hologram generation.(b).The constraints in the spectrum domain which requires that the spatial frequencies are separated for the three colors of red, green and blue for the intended range of decoupling angles.(c).The spatial frequencies of RGB three color letters are separated in one single Fourier space.

Fig. S3 .
Fig. S3.Fabrication processes of waveguide holographic samples.(a). the cladding layer of SiO 2 is grown by PECVD.(b). the grating and hologram patterns of metasurface core layer are formed through EBL.(c).SEM image of a part of a fabricated hologram.(d).AFM images of the fabricated grating.