We design reflective resonant metasurfaces that enable highly efficient wavefront shaping with arbitrary scattering pattern, based on the recently introduced metagrating concept . Using finite-sized arrays of suitably tailored optical antennas placed above a reflective ground plane, we create an omnidirectional Lambertian light scattering geometry that can find applications in colorful photovoltaics . Supercells of metagratings with close-to-unity efficiency can be combined in arrays to shape any desired wide-angle scattering pattern, creating a novel way to design light trapping geometries for photovoltaics.
Metagratings, recently introduced in , employ as a starting point the known physics of grating scattering, in which the period determines a discrete set of diffraction orders, and enables additional control over the scattering characteristics by using resonant bianisotropic light scatterers as the elements forming the grating. The carefully engineered scatterers are arranged above a reflecting ground plane with a distance such that interference of scattering and ground plane reflection in the far field causes the incident power to be rerouted towards the desired grating orders. The scattered light can be directed with unitary efficiency into a single diffraction order, or divided at will into multiple diffraction orders.
We apply the metagrating concept to realize a Lambertian angular light scattering distribution, in which light is scattered over a broad angular range according to I(θ)=I_0 cosθ. The surface is composed of supercells, each of which includes a small number of subcells formed by metagrating elements. In this configuration, each supercell is tuned to scatter light with a specific angular dependency and scattering efficiency. Together, the supercells form a metagrating that scatters an incident beam to a Lambertian scattering profile. We find that efficient angular control is already achieved for a small number of scatterers (N~5-12) in each supercell. As a result, the total size of the structure is smaller than 40 micrometers, enabling the creation of a homogenous Lambertian scattering appearance in the far field for photovoltaic applications.
Our initial Lambertian metasurface design is based on analytical antenna theory in which the far-field scattering pattern is calculated using magnetic dipoles as scattering elements. The optimized scattering patterns were found using an analytical optimization procedure. In a more advanced design, we implemented resonant light scattering elements with a magnetic response, which can be experimentally realized using dielectric nanoparticles with a magnetic Mie resonance or plasmonic metallic nanoparticles. These metasurfaces are designed to show Lambertian scattering in a well-defined spectral band, determined by the bandwidth of the Mie/plasmonic resonance.
The resonant Lambertian metasurface design presented here enables the creation of artificial surfaces with a matt colored appearance. This is a major step forward compared to nanopatterned solar cells that we presented earlier that showed colored specular reflection . The new designs will enable many other applications where controlled beam steering in ultrathin optical devices is needed, specifically for light trapping in thin-film solar cells, and spectrum splitting in parallel and series-connected multi-junction architectures. The proposed metagrating designs create full control over the angular distribution of light scattering in ways that cannot be achieved with dielectric or plasmonic scatterers alone. This work therefore is a major step beyond the work on light management using resonant light scatterers performed so far.
 Ra’di Y., Sounas D., and Alù A., Metagratings: Beyond the limits of graded metasurfaces for wavefront control, Phys. Rev. Lett. 119, 067404 (2017).
 Neder V., Luxembourg S.L., and Polman A., Efficient colored silicon solar modules using integrated resonant dielectric nanoscatterers, Appl. Phys. Lett. 111, 073902 (2017).
Verena Neder, Younes Ra'di, Andrea Alù, and Albert Polman, "Lambertian scattering metasurfaces for photovoltaics (Conference Presentation)," Proc. SPIE 10688, Photonics for Solar Energy Systems VII, 106880J (Presented at SPIE Photonics Europe: April 24, 2018; Published: 23 May 2018); https://doi.org/10.1117/12.2317486.5788752782001.
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