Optical singularities, particularly phase and polarization singularities, are crucial in modern optics with applications spanning imaging, metrology, nonlinear optics, optical tweezers, sensing, quantum information, and optical communication. Phase singularities, exemplified by optical vortices (OVs), possess unique properties like spiral phase wavefronts, orbital angular momentum (OAM), and donut-shaped intensity distributions, enabling enhanced information transmission in optical communication and manipulation of nanoparticles in optical tweezers. Polarization singularities, often found in cylindrical vector beams (CVBs) such as radially and azimuthally polarized beams, facilitate subwavelength focusing and the creation of optical needles. Cylindrical vortex vector beams (CVVBs), possessing both phase and polarization singularities, offer even greater control in various optical applications. Detecting both singularities simultaneously is challenging, especially in integrated systems. Existing methods, such as holography, metasurfaces, and optical transformation, suffer from drawbacks like precise beam alignment requirements, complex detection processes, and low diffraction efficiencies. This paper introduces a novel on-chip plasmonic spin-Hall nanograting to address these limitations, enabling simultaneous detection of both phase and polarization singularities in CVVBs.

The paper reviews existing methods for detecting the topological charge of OAM beams, including holography, metasurfaces, optical transformation techniques, and photonic circuits. It highlights the limitations of these methods, such as the need for precise alignment, complex detection, and low efficiency, particularly within integrated optical systems. The concept of CVVBs as a superposition of left-circularly polarized (LCP) and right-circularly polarized (RCP) OVs is introduced, providing a theoretical framework for simultaneous detection of phase and polarization singularities. The Jones matrix representation of a CVVB is presented, demonstrating its decomposition into LCP and RCP OVs with different topological charges. This forms the foundation for the proposed method that simultaneously detects both the topological charge and spin of the input beam.

The proposed device consists of a plasmonic spin-Hall nanograting structure. The central component is a double grating with different periods (A₁ and A₂) for the upper and lower parts, creating symmetry breaking. These grating lines are replaced by spin-Hall meta-slits (pairs of nanoslits oriented at ±45°), providing chiral response. The design principle is based on the k-vector matching condition for SPP excitation (KSPP = G + KOAM), where KSPP is the SPP wave vector, G is the reciprocal vector of the grating, and KOAM is the azimuthal component of the incident OAM beam. The symmetry breaking allows distinguishing the sign of the topological charge. The different periods A₁ and A₂ are calculated to ensure unidirectional SPP propagation based on the topological charge. The integration of spin-Hall meta-slits introduces chiral sensitivity, enabling polarization detection. The structure's functionality is explained using both wave vector analysis and finite-difference time-domain (FDTD) simulations. Fabrication was performed using focused ion beam (FIB) lithography. Optical microscopy was used to experimentally verify the structure's ability to detect both the sign of the topological charge and the polarization state by measuring the SPP propagation angle and resulting displacement on an output grating.

FDTD simulations and experimental results confirmed the structure's ability to simultaneously detect both phase and polarization singularities. The nanograting design successfully distinguishes the sign of the topological charge by directing the SPP wave to different directions based on the incident beam's properties. The integration of spin-Hall meta-slits adds chiral sensitivity, allowing the structure to discriminate between LCP and RCP light. The output SPP wave's propagation angle is directly related to the topological charge, which allows for quantitative measurement of this value. Experimental results using FIB-fabricated devices show that the SPP propagation direction accurately reflects the topological charge (l = ±1, ±2, ±3) and polarization (LCP/RCP) of the incident OAM beam. The measured vertical displacement between the excitation spot and output coupling spot accurately correlates with the theoretical predictions, validating the proposed method and its effectiveness in simultaneously identifying both phase and polarization singularities.

The presented on-chip plasmonic spin-Hall nanograting offers a compact and efficient solution for simultaneous detection of phase and polarization singularities. The structure overcomes limitations of previously reported techniques by providing a simple, integrated approach capable of distinguishing both the magnitude and sign of topological charge as well as polarization. The experimental validation strongly supports the theoretical model and demonstrates the practical feasibility of the device. This advancement is significant for applications requiring precise control and manipulation of light fields within integrated photonic systems, such as advanced optical communication and quantum information processing.

This research demonstrates a novel on-chip plasmonic device for simultaneous detection of phase and polarization singularities in CVVBs. The device leverages a symmetry-breaking spin-Hall nanograting to achieve unidirectional SPP excitation depending on both the topological charge and polarization of the incident light. Experimental results validate the design principles and demonstrate the structure's potential for compact, integrated optical systems. Future research could focus on improving the efficiency, expanding the detectable range of topological charges, and exploring applications in advanced optical systems.

The current design exhibits limitations in its efficiency, especially for higher-order OAM beams. Ohmic losses in the SPP propagation limit the overall efficiency. The resolution of the device might also be improved to accurately discern topological charges with absolute values greater than 6. Further research could explore alternative materials and designs to enhance efficiency and expand the range of detectable topological charges.