# Mid-Infrared Grayscale Metasurface Holograms
## 1 Introduction  
Recently, ultrathin optical metasurfaces have attracted great interest in optics, offering a new avenue to arbitrarily control electromagnetic waves at mid-IR and optical wavelengths [1; 2]. By using subwavelength two-dimensional resonators [3; 4; 5; 6; 7; 8; 9; 10; 11; 12], the phase, amplitude, polarization and dispersion of light can be controlled locally [3]. Although earlier works and many functional metasurfaces are based on plasmonic nanostructures, they usually suffer from low efficiency due to intrinsic loss and limited control on the type of resonances involved in the scattering of light [9]. In contrast, dielectric nanostructures based on Mie resonances possess richer modal response to not only locally controlling the light field but also avoiding absorption loss [10; 11; 12; 13; 14; 15; 16]. Leveraging on low-loss dielectric units and arranging the abrupt phase and amplitude profiles in various patterns, functional optical devices such as flat lenses [17; 18], wave plates [19; 20] and holograms [21; 22; 23; 24] have been demonstrated. The former devices, inspired by the pioneering works in diffraction optics, for example, Fresnel lenses, require relatively simple distribution of elements to impart hyperbolic phase delays. The latter components, however, rely on complex phase distribution, generally obtained from the principle of holography. Holographic methods have generally been developed and used for applications such as virtual imaging, making use of interference and diffraction to record phase information of objects directly onto photographic plates. Three-dimensional images of the recorded object can later be projected in free space by diffracting a reading-coherent beam from the holographic plate. This traditional holographic method requires highly spatially coherent light sources and intensity-sensitive recording media to store the above-mentioned interference pattern with sufficient accuracy. Later, computer-generated holograms have been proposed by coding the information of the object into phase distribution at a specific plane [25]. By storing wavelength-scale phase information onto thephotographic plate, the hologram efficiency is limited by diffraction effect. Dielectric metasurfaces can instead attain deep subwavelength-phase discretization, providing new opportunities in terms of spatial phase resolution, high efficiency and multifunctionals [24]. In this paper, we demonstrate a dielectric polarization-independent metasurface hologram working in reflection mode at mid-infrared wavelengths. Relying on the previous work on dielectric metasurfaces utilizing simultaneous excitation of both electric and magnetic dipole resonances [9], we designed silicon (Si) nanopillars on a gold substrate, varying radii to realize 0-2\(\pi\)-phase modulation. The Gerchberg-Saxton (GS) Fourier transform hologram approach was employed as the algorithm to decide the position of our phase elements. The eight-level discretized phase hologram, which allows us to bypass some nanofabrication difficulties, has been realized and experimentally demonstrated using the mid-infrared optical setup.