Metaoptics for the spin-controlled generation of orbital angular momentum vector beams

. Moving from diffractive optics to metalenses, novel tools for structuring light are provided for the integration in compact optical layouts. Here we propose new metaoptics designed for light shaping into structured beams implementing on-demand vectorial configurations. Different optical layouts are achieved in order to generate orbital angular momentum (OAM) vector beams with different shape and peculiarities.


INTRODUCTION
A metamorphosis is occurring in the design and fabrication of nanostructured optical devices.By encompassing two emerging fields, structured optics and structured light, the design of a new generation of metasurface optics is expected to provide the keyelements of future optical architectures based on the manipulation of the spatial degrees of freedom of light.In particular, beams carrying orbital angular momentum (OAM) have gained increasing interest with formidable applications in a wide range of fields, such as particle tweezing, microscopy, high-capacity communications, and security.[1] The ability to generate structured light with arbitrary controlled polarization in a compact optical path is a challenge of the last years in optics and photonics field.In this regard, our work proposes the design, fabrication, and characterization of new dielectric metaoptics able to generate orbital angular momentum beams with on-demand different vectorial behaviors acting only on the input polarization.Furthermore, depending on the azimuthal angle of the linearlypolarized light impinging the metasurface, it is possible to explore different states of the Hybrid Poincaré Sphere (HPS) at a prefixed position in space.

METHODS AND RESULTS
The general state of a first order vector beam can be described in terms of Laguerre-Gaussian (LG) beams and circular polarization basis as: where the two angles  and  refer to the coordinates of the corresponding point on the HPS, represent right-handed and left-handed circular polarization states, respectively.Nevertheless, it must be remembered that by properly combining the control of both the geometric and dynamic phases, acting on the pillar orientation and varying its cross-section, respectively, a dual-functional metalens (DFML) is able to behave in two different ways depending on whether the input beam is right-handed (RCP) or left-handed circularly polarized (LCP).( ) We defined two different phase equations in order to generate vector beams (VB); the first one generates focalized VBs (fVBs) into a desired position in space ( ) where l is the amount of OAM per photon transferred to the impinging beam (or topological charge), in units of ħ, λ is the working wavelength, f is the focal length, and =(x0, y0) are the focus coordinates on the focal plane perpendicular to the propagation axis (z) and placed at a distance f.And the second one to generate perfect vortex vector beams (PVVBs) by adding a term  3) it is possible to generate perfect vortices vector beams with controlled radius and width.Our metaoptics are designed as array of periodic subwavelength metastructures (the so-called meta-atoms) composed by silicon nanofins on a silicon substrate .Each meta-atom acts like a half-wave plate at 1310 nm that exploits both the geometrical and dynamical phases in a different way depending on its position on the entire metalens.[2] We performed a custom Finite-Element Method (FEM) simulation in the wavelength domain (COMSOL® Multiphysics) to extrapolate a set of 13 metaunits, with a trasmission efficiency of 75%, which compose the metalens.The optical elements have been fabricated in the form of phase-only metasurfaces (metaatoms) using high-resolution electron-beam lithography of a resist layer followed by inductively coupled plasma reactive ion etching to transfer the mask to the silicon substrate (Fig. 1).We design two metasurfaces with radius of 250 µm, the first one generates a first order fVB (l=±1) using Eq.3 and a focal length f=1mm, the second one able to structure a first-order PVVB with f=1mm and β=0.01rad.We simulated the optical response with a custom MatLab® code implementing the Fresnel propagator for a squared simulation window with a side of 500 µm and pixel size of 600 nm.The simulations considered metalenses of radius 250 µm, designed at the working wavelength of 1310 nm with a phase discretization over 13 levels and illuminated by a Gaussian beam with a beam waist of 200 µm to cover adequately the metasurface area and avoid boundary effects.The intensity of the simulated electric field has been normalized to unity (Fig. 2).Then, we characterized the generated vector beams using a custom optical bench setup integrating a linear rotating polarizer as analyzer in order to visualize the extected two-petal intensity structure (showing the constituent linearlypolarized Hermite-Gaussian beam), with orientation depending on the type of vector beam (Fig. 3).

CONCLUSIONS AND DISCUSSION
The main objective of the work is the design of tiny highresolution optics generating structured beam and offering a significant improvement in terms of compactness of the optical architecture and ease of integration with other optical elements and devices.We present the design of dual-functional metasurfaces for the generation of OAM beams.By exploiting the spin-dependent generation of light using the dual-functional metasurfaces we designed vector beams able to change their polarization state by varying the impinging input linear polarization angle, showing a higher quality than the previous ones reported in the literature.The design extends significantly the functionality of standard spiral phase plates and q-plates, providing advanced optical elements for applications in microscopy, optical micromanipulation, and classical and quantum information, with unprecedented potential levels of compactness and integration into today's technology.
straightforward to obtain the general formula[3]:

Fig. 1 .
Fig. 1. a) Whole area of a fabricated metasurface (250 µm radius).b) Zoom of the metasurface central area.It is worth noting the different meta-atoms rotated by different angles.