# Reconstructing Polarization Multiplexing Terahertz Holographic Images with Transmissive Metasurface
## 1 Introduction  
Holography, an optical technique that can record and reconstruct wavefronts with amplitude and phase information, has attracted tremendous interest [1]. A complicated system for interference and recording is indispensable for conventional optical holography. The development of spatial light modulator (SLM) and computer technology makes holography easier by replacing the recording and reconstruction processes with numerical calculation. However, conventional SLMs, suffering from low resolution, narrow bandwidth, and small field of view, degrade the quality of reconstructed images and restrict their practical applications [1; 2; 3]. Metasurfaces enable the manipulation of amplitude, phase, and polarization of light fields in a subwavelength-scale planar configuration. Through elaborate design and spatial arrangement of meta-atoms, various metasurface devices have been studied with novel functionalities, such as beam splitter [4; 5; 6], metalens [7; 8; 9], optical vortex generator [10; 11; 12], holography [13; 14; 15], and so on. Especially, terahertz (THz) holograms with transmissive metasurfaces have great perspectives for applications in communications, information storage, compared with the reflective metasurface holograms [16; 17; 18]. Many studies of THz metasurface holograms have been reported based on metallic or dielectric metasurfaces [16; 17; 18; 19; 20]. For example, [PERSON] et al. [16] demonstrated a multiplexed THz hologram with simultaneous binary amplitude and binary phase modulation in every pixel by utilizing C-shape bar resonators as the basic unit cells. Different holographic images can be realized at different polarizations and different frequencies. However, the metallic plasmonic metasurfaces suffer from relatively low efficiency resulting from their material nature and weak coupling in the polarization conversion process [21], indicating that ultrathin, compact, and efficient all-dielectric metasurfaces have great prospects. Among the dielectric materials, silicon (Si) is selected as the most constituent material of metasurfaces in the THz range for its merits of low loss, high refractive index, and ease offabrication [22; 23]. It has been reported that Si meta-atoms can be implemented for versatile applications, such as polarization-independent metalenses [24; 25], polarization-dependent THz wavefront manipulation [26], polarization-sensitive modulated optical vortices generation [27; 28], achromatic metalenses [29; 30], and reconfigurable THz metasurface pure phase holograms [31]. In addition, traditional metasurface holograms were achieved based on iterative optimization algorithms (the most commonly used being the Gerchberg-Saxton (GS) algorithms) [31; 32; 33; 34]. For example, [PERSON] et al. demonstrated a high-efficiency transmissive hologram based on GS algorithms and discussed the wave propagation from hologram plane to image plane using the Fresnel diffraction method and Rayleigh-Sommerfeld diffraction method [33]. Sufficient iterations and appropriate modifications are needed to get a convergent map, which makes the design process more complex. Besides, this phase-only modulation method for metasurface holograms brings noise and flaws in image quality stemming from the absence of amplitude information [16; 35; 36; 37]. The simultaneous control of phase and amplitude can achieve better image quality, yet the resolution of the reconstructed holographic images is not at the subwavelength scale [38; 39; 40; 41]. The metalenses utilized to generate holographic images [41; 42; 43] provide inspiration for our work. The focal plane of a metalens can be regarded as a reconstructed image with only a single bright spot, which can be further designed to reconstruct patterned holographic images with subwavelength resolution by optimizing the focal point. Notably, the interleaved meta-atoms for the multiplexing metasurface hologram are well-known concepts in the visible range metasurface.