Photonic metasurfaces can be used to locally control the phase, polarization, and amplitude of electromagnetic waves by scattering the wave at the sub-wavelength building blocks of the metasurface. By structuring the metasurface in a suitable way, a large variety of applications with ultrathin components become possible. For instance, metasurfaces can be used for imaging, sensing, and microscopy. Phase plates introducing a helical and radial phase profile are of interest for information technologies, as they can extend the information volume of data transfer by, e.g., encoding information in the azimuthal and radial indices of Laguerre-Gaussian modes.
We demonstrate metasurfaces based on off-resonant optical scatterers that generate Laguerre-Gaussian modes from a Gaussian input beam. We show how the geometrical Pancharatnam-Berry phase can be used to design a metasurface with spatially variant phase shifting property. The according phase plates are characterized not only by the continuous phase shift in azimuthal direction around the beam axis, but also by phase discontinuities in radial direction.
The metasurfaces are fabricated using electron beam lithography. We employ gold rods with a length of 220 nm to modify the properties of a circular polarized wave. More specifically, the locally induced phase of light with the opposite helicity can be controlled by rotating each rod by a certain angle relative to a reference axis. This arises from the geometrical Pancharatnam-Berry phase: The phase shift introduced by a rod is proportional to the inclination angle of the antenna with the reference axis. To achieve an azimuthal phase gradient, necessary to generate a helical phase profile, the orientation of the rods placed on a circle around the metasurface center rotates by multiples of π per turn. To design radial discontinuities, neighboring rods are shifted by π/2. Since the rods are not necessarily driven in resonance, this metasurface allows for broadband operation in the visible and near-infrared regime.
Interferometric measurements reveal a spiral phase distribution resulting from the introduced helical phase profile. By the method of digital holography and the use of a holographic microscope, the phase introduced by the metasurface can be reconstructed. An achromatic grating allows the control of coherence in this apparatus . Therefore, high resolution phase maps can be measured.
In addition to the Laguerre-Gaussian metasurfaces, we also present a multifunctional metasurface that coalesces the functionality of two conventional optical elements. In particular, it combines the property of generating a doughnut shaped intensity pattern with the focusing property of a lens. Three dimensional phase measurements of this metasurface were performed. Our experimental results are in good agreement with numerical calculations using Fourier optics and Fresnel approximation.
 Slabý, Tomáš, et al. "Off-axis setup taking full advantage of incoherent illumination in coherence-controlled holographic microscope." Optics Express 21.12 (2013): 14747-14762.
Alexander Faßbender, "Broadband Laguerre-Gaussian metasurfaces and direct phase mapping (Conference Presentation)," Proc. SPIE 10671, Metamaterials XI, 106711A (Presented at SPIE Photonics Europe: April 25, 2018; Published: 23 May 2018); https://doi.org/10.1117/12.2306783.5788799594001.
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