# Mid-Infrared Grayscale Metasurface Holograms
## Materials and Methods  
The configuration schematic of the hologram unit is illustrated in Figure 1a. The Si pillar with radius R and height H was placed on an optically thick, reflecting gold substrate with period P. In our demonstration, the wavelength of incident light emitted from a quantum cascade laser (Daylight Solutions, MIRcat-QT(tm)) was 4.7 \(\upmu\)m. Rough estimation of the position of the first order of Mie resonance gave a resonant wavelength of \(\lambda~{}=~{}2\) nH, where \(n~{}=~{}3.43\) is the refractive index of Si [9; 26]. To be in the parameter range to observe and rely on scattering from the first few resonant modes of the dielectric particles, the height of the nanopillar was chosen as 650 nm. The period of the pillars with square lattice was chosen to be subwavelength in free space but not necessarily subwavelength in the substrate with P \(~{}=~{}2\)\(\upmu\)m. Designing properly the resonant response of our scattering elements, the diffracted modes inside the dielectric can be suppressed. To achieve a good phase sampling of our hologram, a 2\(\pi\) variation at the operation wavelength was needed, which was achieved by considering the scattering of light with nanopillars of different radii. Phase and amplitude characterization of the building blocks was performed using the finite-difference time-domain method, considering a normal incident plane wave and characterizing the transmitted fields after reflecting from the interface [27]. Figure 1b shows the simulation results of the reflection phase delay. From this figure, we see that radii ranging from 320 to 920 nm can achieve the 2\(\pi\) variation. The amplitude of the reflection light was nearly 1 of all types of nanopillars due to low loss in Si and almost perfect mirror reflectivity of Au at mid-IR frequency (blue line shown in Figure 1b). Phase-only holograms, for example, an object \(I(x,y)\) producing a smile logo, were designed using the iterative Fourier transform algorithm, see Figure 2a. The numerical process used to define the phase distribution works as follows. First, it calculates the Fourier transform (FT) of the object to obtain its angular spectrum, which could be read as \(A_{0}\Big{(}f_{x},f_{y}\Big{)}\). The phase profile of \(A_{0}\Big{(}f_{x},f_{y}\Big{)}\) is obtained as \(A_{0}\rho\Big{(}f_{x},f_{y}\Big{)}\). Second, taking the inverse Fourier transform (iFT) of \(A_{0}\rho\Big{(}f_{x},f_{y}\Big{)}\) results in \(I_{0}(x,y)\) with the  
Figure 1: Schematic of the design of the hologram unit. **(a)** Silicon nanopillar with variable radius R and constant period P = 2 \(\upmu\)m and height H = 650 nm is placed on the gold substrate. **(b)** Phase shift (red line) and amplitude (blue line) of the reflection light versus the radii of pillar at wavelength 4.7 \(\upmu\)m.  
phase profile \(I_{0}\prime(x,y)\). Taking \(I_{0}\prime(x,y)\) as a new object and repeating the above iteration process several times until \(A_{n}^{\prime}\Big{(}f_{x},f_{y}\Big{)}=A_{n-1}\Big{(}f_{x},f_{y}\Big{)}\), where the subscript denotes the iteration time, we obtain the final hologram \(B(u,v)=A_{n}^{\prime}\Big{(}f_{x},f_{y}\Big{)}\), where (\(u\),\(v\)) denotes the hologram placed at a different object plane (\(x\),\(y\)). Figure 2b shows the phase-only hologram calculated by the above algorithm composed of 2000 iterations. The iterative Fourier transform algorithm implemented in our manuscript follows the flow chart, see Figure 2c. The optical setup built to characterize our devices is shown in Figure 3a. A laser beam from a mid-infrared quantum-cascade laser (4.7 \(\upmu\)m, 100 mW) was reflected from the beam splitter and directed to the sample at normal incidence. A CaF\({}_{2}\) lens with a focal length of 5 cm was used to FT the reflected light field. The metasurface hologram was placed in the front foci plane of the lens and a mercury cadmium telluride (MCT) detector utilized in two dimensions to scan the back foci plane and collect the spatial field distribution.