Measuring orbital angular momentum (OAM) states of vortex beams is of great importance in diverse applications employing OAM-carrying vortex beams. We present a simple and efficient scheme to measure OAM states (i.e. topological charge values) of vortex beams with annular gratings. The magnitude of the topological charge value is determined by the number of dark fringes after diffraction, and the sign of the topological charge value is distinguished by the orientation of the diffraction pattern. We first theoretically study the diffraction patterns using both annular amplitude and phase gratings. The annular phase grating shows almost 10-dB better diffraction efficiency compared to the annular amplitude grating. We then experimentally demonstrate the OAM states measurement of vortex beams using annular phase grating. The scheme works well even for high-order vortex beams with topological charge value as high as ± 25. We also experimentally show the evolution of diffraction patterns when slightly changing the fractional topological charge value of vortex beam from 0.1 to 1.0. In addition, the proposed scheme shows potential large tolerance of beam alignment during the OAM states measurement of vortex beams.Angular momentum can be divided into spin angular momentum (SAM) and orbital angular momentum (OAM) in paraxial beams, which are related to circular polarization and spatial distribution, respectively. In 1992, Allen and coworkers recognized that helically phased beams comprising an azimuthal phase term exp(ilϕ), have an OAM of lħ per photon, where l is topological charge value, ϕ is azimuthal angle, and ħ is Plank's constant h divided by 2π1 . In recent years, optical beams carrying OAM (i.e. OAM modes), also referred to as vortex beams, have attracted more and more attention owing to their distinct characteristics such as the phase singularity at the beam center and the resultant doughnut shape intensity profiles. OAM modes with different topological charge value l, are theoretically unbounded and orthogonal to each other. Similar to other mode bases in free space or fiber, OAM modes are another basis with which to represent spatial modes. Different mode bases including OAM modes can be employed in mode-division multiplexing (MDM), which a subset of space-division multiplexing (SDM). Very recently, OAM modes have shown great potential for MDM both in free space and fiber-based optical communications [2][3][4][5] . Vortex beams or OAM modes also provide unique opportunities for manipulation of micro-/nano-particles as it asserts torque in addition to forces related to optical intensity gradient, giving rise to orbital and spin movements beyond trapping. Remarkably, for diverse applications of vortex beams in optical communications 2-5 , optical tweezers 6,7 , optical trapping 8 and quantum information technology 9 , an accurate measurement of the topological charge values of vortex beams, which includes the magnitude and the sign, is of great importance.Until now, a wide variety of methods have been proposed t...

Orbital angular momentum (OAM), one fundamental property of light, has been of great interest over the past decades. An ideal OAM generator, fully compatible with existing physical dimensions (wavelength and polarization) of light, would offer the distinct features of broadband, polarization diversity, and ultra-compact footprint. Here, we propose, design, fabricate, and demonstrate an ultra-compact chip-scale broadband polarization diversity OAM generator on a silicon platform with a 3.6 × 3.6 μm2 footprint. The silicon OAM chip is formed by introducing a subwavelength surface structure (superposed holographic fork gratings) on top of a silicon waveguide, coupling the in-plane waveguide mode to the out-plane free-space OAM mode. We demonstrate in theory and experiment the broadband generation of polarization diversity OAM modes (x-/y-polarized OAM+1/OAM−1) from 1500 to 1630 nm with high purity and efficiency. The demonstrations of an ultra-compact broadband polarization diversity OAM generator may open up new perspectives for OAM-assisted N-dimensional optical multiplexing communications/interconnects and high-dimensional quantum communication systems.

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