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Acquiring precise information about the mode content of a laser is critical for multiplexed optical communications, optical imaging with active wave-front control, and quantum-limited interferometric measurements. Hologram-based mode decomposition devices, such as spatial light modulators, allow a fast, direct measurement of the mode content, but they have limited precision due to cross-coupling between modes. Here we report the first proof-of-principle demonstration of mode decomposition with a metasurface, resulting in significantly enhanced precision. A mode-weight fluctuation of $6\times 10^{-7}$ was be measured with 1 second of averaging at a Fourier frequency of 80 Hz, an improvement of more than three orders of magnitude compared to the state-of-the-art spatial light modulator decomposition. The improvement is attributable to the reduction in cross-coupling enabled by the exceptional small pixel size of the metasurface. We show a systematic study of the limiting sources of noise, and we show that there is a promising path towards complete mode decomposition with similar precision., Comment: Peer-reviewed version. Accepted for publication in Physical Review A. 6 pages, 8 figures

In recent years, optical vortex beams possessing orbital angular momentum have caught much attention due to their potential for high capacity optical communications. This capability arises from the unbounded topological charges of orbital angular momentum (OAM) that provides infinite freedoms for encoding information. The two most common approaches for generating vortex beams are through fork diffraction gratings and spiral phase plates. While realization of conventional spiral phase plate requires complicated 3D fabrication, the emerging field of metasurfaces has provided a planar and facile solution for generating vortex beams of arbitrary orbit angular momentum. Here we realize a novel type of geometric metasurface fork grating that seamlessly combine the functionality of a metasurface phase plate for vortex beam generation, and that of a linear phase gradient metasurface for controlling the wave propagation direction. The metasurface fork grating is therefore capable of simultaneously controlling both the spin and the orbital angular momentum of light.

We prescribe a novel approach for continuously tailoring the local phase of the nonlinear polarizability which can lead to an arbitrary phase profile for harmonic generations. The introduced phase of the nonlinear polarizability is inherently a geometric Berry phase arising from the spin rotation coupling of light in the nonlinear regime. This approach provides new routes for controlling the optical nonlinear processes., Comment: 5 pages, 1 figure

Nonlinear processes are often governed by selection rules imposed by the symmetries of the molecular configurations. The most well-known examples include the role of mirror symmetry breaking for the generation of even harmonics, and the selection rule related to the rotation symmetry in harmonic generation for fundamental beams with circular polarizations. While the role of mirror symmetry breaking in second harmonic generation has been extensively studied in plasmonic systems, the investigation on selection rules pertaining to circular polarization states of harmonic generation has been limited to crystals, i.e. symmetries at the atomic level. Here we demonstrate the rotational symmetry dependent third harmonic generation from nonlinear plasmonic metacrystals. We show that the selection rule can be imposed by the rotational symmetry of meta-crystals embedded into an isotropic organic nonlinear thin film. The results presented here may open new avenues for designing symmetry-dependent nonlinear optical responses with tailored plasmonic nanostructures., Comment: 13 pages, 3 figures