Nanophotonics 2020; 9(5): 987–1002 Review Qunshuo Wei, Lingling Huang*, Thomas Zentgraf and Yongtian Wang Optical wavefront shaping based on functional metasurfaces https://doi.org/10.1515/nanoph-2019-0478 usually consist of periodic, quasi-periodic, or randomly Received November 25, 2019; revised January 3, 2020; accepted arranged subwavelength antenna arrays, which are made January 7, 2020 of metal or dielectric structures with specific geometries. Their wavefront modulation mechanism does not rely Abstract: Regarded as a kind of smart surfaces, metas- on the accumulation effect during the light propaga- urfaces can arbitrarily tailor the amplitude, phase, and tion process, but by elaborately designing the geometry polarization of light. Metasurfaces usually consist of sub- shapes, structural sizes, and spatial orientation angles of wavelength nanoantenna or nanoresonator arrays, which the nanoantennas, utilizing their strong interaction to the are delicately designed and processed. As an ultrathin, incident light field to realize the abrupt phase, amplitude miniaturized versatile wavefront modulation device, change, and other parameters’ modulation. Compared metasurfaces have great information capacity and can with traditional optical components and bulk metamate- arouse the future development of highly integrated micro- rials, metasurfaces benefit from the reduced absorption nano optoelectronic systems. Exploiting the advantages loss; relatively low fabrication difficulty; ultrathin, ultras- of ultrasmall pixels, flexible design freedom, low loss, mall pixel size; and broadband characteristics. They can and easy processing properties, metasurfaces provide effectively reduce the size of the devices and have signifi- potential feasibility and new perspectives for a plethora cant advantages in the integration with on-chip nanopho- of applications. Here we review the research progress of tonic devices. Due to their great flexibilities, metasurfaces metasurfaces for holographic displays, polarization con- provide a new perspective for the design of various optical version, active modulation, linear and nonlinear wave- systems. Metasurfaces have great potential in plethora front modulation, and prospect the future development of applications such as holography [7–9], generation trend of metasurfaces. of vortex beam [10–12], data storage [13, 14], encryption Keywords: metasurface; holographic display; wavefront and anticounterfeiting [15, 16], metalens and dispersion modulation; polarization conversion; active modulation; control [17–19], asymmetric transmission [20–22] and nonlinear wavefront modulation. nonlinear optics [23–27], and so on, and draw a grand blueprint for the development of optical components to miniaturization, integration, and multifunction. 1 Introduction The wavefront modulation mechanisms of metasur- faces are basically based on three kinds of representative Metasurfaces have attracted extensive attention and design methods: (1) optical resonance from nanoantennas: became a rapidly developing research field due to their by adjusting the geometric parameters such as the size and unique abilities of arbitrarily modulating the phase, orientation angle of each optical antenna, the properties amplitude, and polarization of the electromagnetic wave of the radiation wave can be modulated. Typical struc- with compact footprint and powerful versatility of pro- tures include V-shaped antennas [28], Y-shaped antennas ducing various special optical effects [1–6]. Metasurfaces [29], C-shaped antennas, and so on. (2) Huygens’ metasur- faces: by matching the electric and magnetic polarizabil- *Corresponding author: Lingling Huang, School of Optics and ity within the nanostructure, the transmission can reach Photonics, Beijing Institute of Technology, Beijing 100081, China, unity, and the building block can be viewed as secondary e-mail: [email protected]. https://orcid.org/0000-0002- wave sources. This design method was first experimen- 3647-2128 tally verified in the microwave band [30], and then the Qunshuo Wei and Yongtian Wang: School of Optics and Photonics, dielectric Huygens’ metasurfaces, which are applied in Beijing Institute of Technology, Beijing 100081, China Thomas Zentgraf: Department of Physics, Paderborn University, the holographic field, were also reported [31, 32]. (3) Pan- Warburger Straße 100, 33098 Paderborn, Germany charatnam–Berry (PB) phase (also known as geometric Open Access. © 2020 Lingling Huang et al., published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 Public License. 988 Q. Wei et al.: Optical wavefront shaping based on functional metasurfaces phase), which can be achieved by spatially rotating the holography is considered as the ultimate 3D display nanoantennas: the incident lights of the same polariza- scheme. In recent years, the holographic technology has tion state will produce different phase changes when they made great progress and has been widely used in many reach the same final polarization state through different applications such as stereo display, interferometry, data paths on the Poincaré sphere. The phase change has pure storage, medical imaging, remote sensing imaging, image geometric property, so it is wavelength independent. processing, and recognition. Notably, one of the cut-in- With the advancement of metasurfaces and nanofab- edge research is the combination of holography principle rication technology, the focus and emphasis of research and metasurfaces, that is, encoding the amplitude and have been pushed forward from principles to applica- phase distributions of holograms with two-dimensional tions. Large information capacity and multifunctionality arrays of subwavelength antennas. Compared with the become the research focus for metasurfaces. Except for traditional holographic display technology based on the various multiplexing technologies for static metasur- spatial light modulator, metaholograms not only keep the faces, another intriguing method is to use phase-change ultrathin and compact characteristics of metasurfaces, materials or other ways to modulate the characteristics but also overcome many challenges faced by the tradi- of electromagnetic waves based on metasurfaces through tional holography, such as multiple diffraction orders, external stimuli such as light, heat, electricity, magnet- small field of view, narrow bandwidth, twin image, and ism, and force. These reconfigurable metasurfaces can so on, which greatly improve the reconstruction quality. avoid the obstruction of the material characteristics and In general, the first step of designing a metahologram fixed structures. In addition, the nonlinear effect, which is is to numerically calculate the phase and amplitude distri- aroused by the interaction between the strong laser (such butions on the hologram plane using computer-generated as femtosecond laser pulse) and the metasurfaces, leads holography (CGH) algorithms. The diffraction patterns can to the information modulation at newly generated fre- be expressed by the Fresnel–Kirchhoff integral [33, 34]: quencies. According to the selected optical nanoantennas 1exp()jkr with different shapes, sizes, material components, and Ux(, yz, ) = Ux(,, yd zd) xy (1) h jrλ ∫∫ 00 00 00 different wavefront modulation mechanisms, the phase, amplitude, polarization, angular momentum, frequency, where U (x , y , z ) and U (x, y, z) represent the complex and dispersion can be controlled by metasurfaces; many 0 0 0 0 h amplitude on the object plane (x , y , z ) and the hologram unique optical properties such as designable spectral 0 0 0 plane (x, y, z), respectively; k indicates the wave vector; and responses, dynamic switching characteristics, and nonlin- the distance between two points on the object plane and ear harmonic generation characteristics can be realized. 222 the hologram plane is =−+−+− In this review, we briefly discuss the research progress rx()00xy()yz()0 z . of metasurfaces in the fields of holographic display, wave- According to the above formula, one can simulate the front modulation, and polarization conversion in recent propagation of light and directly calculate the complex years. Next, some novel directions such as active recon- amplitude Uh(x, y, z) of the hologram plane. Note differ- figurable metasurfaces and nonlinear metasurfaces are ent algorithms have been proposed for adapting to differ- introduced. Finally, we also propose the expectations and ent types of metasurfaces [35, 36], including point sources potential development directions of metasurfaces. method, angular spectrum method, and iterative Fourier transform algorithm such as Gerchberg–Saxton algorithm. In order to fully utilizing the excellent wavefront 2 Metasurface holography modulation ability and flexible design freedom of meta- surfaces, various schemes for holographic display based Holography refers to the optical technique for control- on different methods have been proposed in succession ling the wavefront of light as desired by spatially varied [37–39]. Among the wavefront modulation mechanisms, phase and amplitude. Holograms do not record an image PB phase modulation method has broadband disper- directly, but record a series of amplitude and phase dis- sionless characteristics; the phase of each nanoantenna tributions that appear “random distributions.” Because a is related to the combination of the incident and output hologram contains the complete information of the target polarization states and can be modulated