Spin-to-orbital angular momentum conversion in dielectric metasurfaces

Spin-to-orbital angular momentum conversion in dielectric metasurfaces Robert Charles Devlin*, Antonio Ambrosio*, Daniel Wintz, Stefano Luigi Oscurato, Alexander Yutong Zhu, Mohammadreza Khorasaninejad, Jaewon Oh, Pasqualino Maddalena, Federico Capasso Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA CNR-SPIN U.O.S. Napoli, Complesso Universitario di Monte Sant’Angelo, Via Cintia, 80126 – Napoli, Italy Dipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte Sant’Angelo, Via Cintia, 80126 – Napoli, Italy University of Waterloo, Waterloo, ON N2L 3G1, Canada

momentum is a powerful manipulation tool to spin the trapped object [6,7] as well as to control its orientation [8].
The characteristic screw-type dislocation of a helical mode can be imposed on the wave-front of a propagating beam by means of different devices, for example, pitch-fork holograms [9,10] or cylindrical and axicons lenses and reflectors [11,12].
Additionally, helical modes can be also produced by exploiting the geometrical phase (also known as Pancharatnam-Berry (PB) phase) [13,14], to create inhomogeneous gratings for the wavefront reshaping [15,16]. In these spin-orbital angular momentum converters (SOC) the OAM of the vortex beam is entangled with the spin momentum of the illuminating light: switching the handedness of the illuminating beam polarization (spin momentum) flips the handedness of the vortex. Locking the OAM to the spin momentum has unique applications in quantum computing and communications, allowing encoding of quantum units [17] and fast switching related to the modulation of incident polarization of light [18].
More recently, the wavefront manipulation allowed by metasurfaces [19] has been used to produce a variety of PB optical elements, e.g., lenses [20,21] and spin-OAM converters in the near-infrared [15,16,22,23]. Similar approaches have allowed working with visible light although with low transmission efficiency in the bluest part of the spectrum [24,25,26,27,28]. To date, the most versatile spin-orbital momentum converters for visible light are the liquid crystal devices developed by Marrucci et al. in 2006 and known as q-plates [29]. They have found numerous applications in quantum optics although limited by degradation effects, fabrication reproducibility and resolution in defining the extent of the topological singularity region [30,31,32,33,34].
In order to describe some general features of a SOC based on PB phase, it is useful to define the orientation angle α (x, y) of the optical axis (fast or slow) of each element of the device in the transverse plane (x-y plane). Regardless of the constituents, if each element imposes a π phase delay between the field transverse components, an x y α in the transverse plane. Analogously to what reported in the first description of a q-plate [29], if the azimuthal variation of the angle α in the PBdevice follows the relation α = qϕ + α 0 , the incident wave front is then turned into a helical wave front composed of 2 q intertwined helical surfaces which carries an orbital angular momentum ℓ = ±2q , where the sign depends on the handedness of the incident light polarization (α 0 is a constant). For instance, if q = 1 and the incident light is left-circularly polarized (spin momentum of +! ), the out coming light is rightcircularly polarized (spin momentum of −! ) with an OAM per photon of 2! and zero net angular momentum transferred to the device (Fig. 1 a). For q ≠ 1there will be a net angular momentum exchange with the PB-device to preserve the total angular momentum of the system.
Each fin is 250nm long, 90nm wide and 600nm tall. The radial distance between two fins is of 325nm (Fig. 1 b). Figure 2 a and b show the scanning electron microscope (SEM) images of the devices with q = 0.5 and q = 1 ( ℓ = 1 and ℓ = 2 respectively).
The insets of Fig. 2 a and b show the devices as imaged in cross-polarization: the azimuthal variation of the optical field polarization direction after the device is turned into 4q intensity lobes by the second polarizer.
In order to fully characterize the vortex beams that our devices produce, a Mach-Zehnder interferometer was used as shown in Figure 2 c. In this configuration, the source beam (a solid state laser emitting at 532nm with power lower than 2mW) is  interference experiments are widely used to reveal phase singularities [4]. The pitchfork-like interference was obtained when the vortex beam was interfered with a Gaussian beam incident at an angle (the incident angle sets the fringes spacing).
Instead, when the vortex beam was collinear with the reference beam from the lower arm of the interferometer, a spiral was obtained as interference picture, with a number of arms equal to the topological charge of the vortex beam. The handedness of the incident circularly polarized light sets the orientation of the pitchforks and spirals. Figure 3 shows how our approach can be used to produce optical vortices with higher values of topological charge, ℓ = 5 (Fig. 3 a-d) and ℓ = 10 ( Fig. 3 e-h). Each individual device is 500µm in diameter and all devices are on the same glass substrate In our devices we reached absolute efficiencies (the amount of light from the illuminating beam that is actually converted into the helical mode) of 60% (Supplementary Information). This makes them usable for practical applications.
As further demonstration of the versatility of our approach, we designed a SOC that produces a vortex beam with fractional topological charge. This is possible when a non-integer phase discontinuity is introduced in the azimuthal evolution of the helical mode. In this case, Berry described the optical vortex as a combination of integer charge vortices with a singularity line in the transverse plane surrounded by alternating optical single charge vortices [40,41]. From a quantum optics point of view, the average angular momentum per photon has a distribution peaked around the nearest integer value of the topological charge and a spread proportional to the fractional part of the charge [42]. We fabricated a SOC producing a 6.5 topological charge vortex beam. Figure 4 a shows the intensity distribution of the resulting helical mode at about 55µm from the device plane ( Supplementary Information) and Fig. 4 b shows pitchfork-like interference obtained in the Mach-Zehnder configuration of helical modes with same OAM but phase singularities lines with a relative π orientation are orthogonal [42]. This has been used, for instance, to observe highdimensional photon entanglement [43,44].
Our approach to SOC enables a new and unique feature, the generation of collinear beams with different OAM, a functionality that cannot be achieved with liquid crystals. To demonstrate this concept, we designed an interlaced q = 2.5 and  It is important to note that each nanofin in our device has two interfaces, glass-TiO 2 and air-TiO 2 . Illuminating one side or the other, as in Figure 5 f, does not alter the phase delays imposed by the nanofins (Supplementary Information) but only slightly affects light coupling into the latter, due to the different reflectance of the air-TiO 2 and glass-TiO 2 interfaces. We measured a small decrease (< 5%) in the device efficiency when illuminating from the air-side, due to the lower refractive index.
In the setup of Figure 5 f, the beams illuminating the sample from opposite interfaces have opposite handedness (Methods). The double-face characteristic of our devices together with the illumination configuration of Figure 5 f allows one to simultaneously generate similar beams with opposite topological charges. This configuration was also used to obtain the intensity distributions of Figure 5 b and c representing the helical modes at optical ports 3 and 2 respectively.
Although we limited our interlaced design to two collinear beams, it is possible to produce three or more collinear vortices simultaneously as well as + ℓ and -ℓ collinear vortices (Supplementary Information). This can find important applications in entanglement and quantum computing experiments. Moreover, the quantum description of the photon statistics produced by our interlaced device has never been investigated and represents a stimulating direction for future work. Finally, although we did not test our devices at high incident power, we expect good tolerance to heating since TiO 2 has an intensity damage threshold of 0.5 J/cm 2 in the femtosecond regime [45]; thus we envision using such devices for non-linear optics with pulsed lasers. 9 In summary we have demonstrated that the interaction of light with designer metasurfaces can lead to the generation of complex wavefronts characterized by arbitrary integer and fractional topological charges and in particular to co-propagating beams with different orbital angular momenta. Our approach represents a major advance in design with respect to liquid crystals devices and as such has considerable potential in several areas of optics and photonics, ranging from quantum information processing to optical trapping and complex beam shaping.

Device fabrication
All devices used above were fabricated on a fused silica substrate. Resist was spun at 1750 rpm in order to achieve a thickness of 600 nm. The resist was then baked at 180 o C for 5 mins. The patterns were exposed using electrom beam lithography (ELS-

Double-side illumination
The double-side illumination ( figure 5 f) is simply obtained by rotating by 90° the beam-splitter at the exit of the Mach-Zehnder configuration of Figure 2 c. In this case, there are two light beams, whose power can be made equal by suitably balancing the two arms, circularly polarized with opposite handedness that simultaneously illuminate the device from opposite sides at normal incidence. In this configuration, the helical modes propagating towards optical port 2 and 3 have also opposite wavefront handedness. All authors discussed the results and commented on the manuscript.

Additional information
Supplementary information is available in the online version of the paper.   Simulated intensity patterns for collinear 5 and 10 topological charge beams. f, Sketch of the setup that allows illumination of the transparent devices from the glass and air side simultaneously with circularly polarized beams of opposite handedness. This setup was also used to obtain the intensity distributions of Fig. 5 b and c.