Phase, polarization, amplitude, and frequency represent the basic dimensions of light, playing crucial roles for both fundamental light-material interactions and all major optical applications. Metasurfaces have emerged as a compact platform to manipulate these knobs, but previous metasurfaces have limited flexibility to simultaneous control them. A multi-freedom metasurface that can simultaneously and independently modulate phase, polarization, and amplitude in an analytical form is introduced, and frequency multiplexing is further realized by a k-space engineering technique. The multi-freedom metasurface seamlessly combines geometric Pancharatnam-Berry phase and detour phase, both of which are frequency independent. As a result, it allows complex-amplitude vectorial hologram at various frequencies based on the same design strategy, without sophisticated nanostructure searching of massive geometric parameters. Based on this principle, full-color complexamplitude vectorial meta-holograms in the visible are experimentally demonstrated with a metal-insulator-metal architecture, unlocking the longsought full potential of advanced light field manipulation through ultrathin metasurfaces.functional layers, emerge as a desirable platform to manipulate the light field at will with large control and flexibility. [3][4][5][6][7] Exciting applications have already been demonstrated on the metasurface platform, including flat diffractive and polarization optical components, much more compact and lightweight than conventional bulky counterparts. By engineering the scattering properties of the individual metaelements constituting the metasurface to mold the geometric phase, resonant phase or propagation phase, we are able to control phase, [8,9] amplitude, [10,11] polarization, [12,13] or frequency [14][15][16] of light, leading to high-efficiency metalenses, [9] high-fidelity holograms, [8] broadband polarization components, [12,17] and highperformance biosensors. [15] However, these ultrathin components tend to focus on single-dimensional light manipulation, controlling either the local phase, or amplitude, or polarization, or frequency, at a time, inherently limiting potential opportunities. For example, metasurface holograms and metalenses based on resonant phase and propagation phase are typically limited to a narrow range of frequencies. [18,19] Geometric Pancharatnam-Berry (P-B) phase metasurfaces operate over broader bandwidths, but they are restricted to circular polarization only. [8] To improve the performance and enrich the functionality of metasurfaces for a broader range of applications, independent

In article number 1910610, Zi‐Lan Deng, Guixin Li, Xiangping Li, and co‐workers show how multi‐dimensional wavefront shaping of light in amplitude, polarization, phase, and frequency can be realized simultaneously through a single layer multi‐freedom metasurface. Consequently, full‐color complex‐amplitude vectorial holographic image can be vividly reconstructed.

In linear optics, the metasurface represents an ideal platform for encoding optical information because of its unprecedented abilities of manipulating the intensity, polarization, and phase of light wave with subwavelength meta-atoms. However, controlling various degrees of freedom of light in nonlinear optics remains elusive. Here, we propose a nonlinear plasmonic metasurface working in the near-infrared regime that can simultaneously encode optical images in the real and Fourier spaces. This is achieved by designing a diatomic meta-molecule, which enables the independent control of the nonlinear geometric phase, polarization, and intensity of second harmonic waves. The proposed nonlinear diatomic metasurface provides an ultracompact platform for implementing multidimensional optical information encoding and may hold great potential in optical information security and optical anticounterfeiting.

Significance Vectorial optical holography, as a scheme to control the polarization distributions of light in the Fourier space, has been experimentally demonstrated in the linear optical regime. However, its nonlinear optical counterpart, which can generate the holographic images at different frequencies to that of the incident light, remains unexplored. Here, we demonstrate nonlinear vectorial holography through the second harmonic generation process on a quad-atom plasmonic metasurface, which consists of gold meta-atoms with threefold rotational symmetry. The proposed metasurface platform may have important applications in vectorial polarization nonlinear optical source, high-capacity optical information storage, and optical encryption.