Spatially variant arbitrary polarization shaping for optical skyrmions generation

Abstract: Polarization is fundamental degree of freedom of light, crucial for applications from imaging to quantum optics. Although numerous methods can spatially manipulate the polarization orientation, e.g., for generating vector beam, achieving simultaneous, spatially resolved control of both the orientation (ψ) and ellipticity (\c{hi}) remains challenging. Here, we present an efficient and compact platform to generate spatially variant arbitrary polarization states, e.g., optical skyrmions, in free space, using cascaded spatially variant waveplates in a single silica glass plate via ultrafast laser direct writing. We propose two configurations: (1) a spatially variant half-waveplate (S-HWP) and followed by a quarter-waveplate (S-HWP); and (2) two cascaded spatially variant quarter-waveplates (S-QWPs). Design rules linking the target polarization parameters (orientation ψ and ellipticity \c{hi}) to the fast-axis distributions enable spatially resolved arbitrary polarization control. Using these devices, we realize Néel-, Bloch-, and anti-skyrmions of different orders (e.g., second and fourth) and n-π textures (2π and 3π), with polarization-resolved measurements in excellent agreement with simulations. We further demonstrate 3 by 3 arrays comprising either identical or hybrid skyrmions. This approach enables the realization of spatially variant arbitrary polarization state and scalable skyrmion lattices.

• The paper presents an analytical and experimental framework using cascaded spatially variant QWPs to achieve arbitrary polarization shaping for creating diverse optical skyrmion textures.
• Utilizing Stokes vector formalism and Müller matrix analysis, the authors derive a mapping between desired polarization states and spatial fast-axis orientation for precise skyrmion generation.
• Experimental validation shows high simulation-experiment agreement, demonstrating helicity-dependent switching and scalable 3×3 skyrmion arrays for advanced photonic applications.

Spatially Variant Arbitrary Polarization Shaping for Optical Skyrmions Generation

Abstract and Motivation

The paper presents an analytical and experimental framework for the spatially resolved arbitrary polarization shaping of light and demonstrates its utility by generating various types of optical skyrmions in free space. The approach employs cascaded spatially variant waveplates (S-WPs), specifically quarter-wave plates (QWPs) and half-wave plates (HWPs), which are fabricated by ultrafast laser direct writing in a single silica glass substrate. This platform is designed to overcome the limitations of conventional spatial light modulators and previously reported spin-orbit waveplates, particularly regarding simultaneous, spatially resolved control of polarization orientation (ψ) and ellipticity (χ).

The motivation is underpinned by the growing role of complex polarization fields in quantum optics, imaging, and information technologies, as well as the intrinsic interest in optical topological textures, such as skyrmions, which are robust against perturbations due to their nontrivial topology.

Analytical Foundation and Device Architecture

The theoretical core of the methodology is the formulation of polarization state engineering as a mapping problem on the Poincaré sphere, parametrized by the orientation angle ψ and the ellipticity angle χ at each spatial position. The generation of optical skyrmions—vector fields characterized by a topological invariant—requires local control over both parameters. The authors derive explicit relationships between the desired polarization state and the spatial fast-axis orientation of two cascaded waveplates, utilizing Stokes vector formalism combined with Müller matrix analysis.

Two device configurations are examined:

• (1) S-HWP + S-QWP with linearly polarized input: This allows arbitrary output polarization but demands the fabrication of both HWPs and QWPs with spatially resolved axes.
• (2) S-QWP + S-QWP with circularly polarized input: A more fabrication-friendly configuration, as HWPs are eschewed in favor of QWPs, reducing process time and eliminating fabrication artifacts, such as horizontal dark lines.

The fast-axis maps for these devices are calculated analytically, enabling the device to output the designed spatial polarization for incident light of defined input polarization.

Fabrication via Ultrafast Laser Direct Writing

The S-WP elements are manufactured in silica glass using ultrafast laser direct writing. The process creates spatially variant birefringence by engraving filamented nanopores, whose orientation and ellipticity can be independently prescribed. The QWPs are written as two superimposed birefringent layers, each introducing approximately 65 nm of retardance, totaling a quarter-wave at 532 nm. SEM imagery confirms the alignment and nanoscale morphology of the induced birefringence regions.

Experimental Generation and Characterization of Optical Skyrmions

The platform enables the direct fabrication and generation of diverse optical skyrmion textures—Néel-type, Bloch-type, anti-skyrmions, and high-order variants with topological charges $\lvert N_{\text{sk}} \rvert > 1$ or arbitrary $n\pi$ winding numbers. Polarization-resolved measurements validate the accuracy of the generated fields, with close agreement to simulations for every targeted skyrmion configuration.

Notably, the system demonstrates helicity-dependent switching of skyrmion number and type: incident right- and left-hand circular polarization directly controls the sign of the skyrmion number, which enables dynamic optical manipulation capabilities.

Skyrmion Lattices and Scalable Arrays

A salient feature is the demonstration of 3×3 skyrmion arrays—termed “optical skyrmion crystals.” Both uniform (identical skyrmion units) and heterogeneous (different skyrmion types/numbers within one array) configurations are realized. The lateral dimensions of individual skyrmion units (300 μm × 300 μm) can be further reduced via demagnification, suggesting scalability toward higher-density arrays. This is instrumental for emerging applications in parallel, multidimensional data storage and multiplexed photonic information processing.

Numerical Performance and Claims

• Simulation-Experiment Agreement: The measured Stokes component distributions are in excellent correlation with theoretical predictions, confirming the analytical design framework and fabrication fidelity.
• Topological Flexibility: Arbitrary topological charges and multiple skyrmion type (Néel, Bloch, anti-skyrmion) fields are generated and confirmed.
• Fabrication Efficiency: Transitioning from HWPs to cascaded QWPs halves the processing time and mitigates artifacts, enabling practical, large-scale fabrication.

Implications and Future Perspectives

This work establishes a compact, robust, and analytically tractable route for free-space generation of arbitrary spatial polarization, positioning cascaded S-QWPs as a general platform for topological light field engineering. The findings have several implications:

• Practical photonics: The device is optically robust, compact, and compatible with high-intensity beams, making it suitable for high-power laser processing and demanding applications such as UV beam generation and laser-driven inertial confinement fusion.
• Data storage and multiplexing: The ability to produce customizable, scalable arrays of optical skyrmions with well-defined topological invariants provides an extra degree of freedom for optical data storage, beyond amplitude, phase, and wavelength multiplexing.
• Quantum and nonlinear optics: The device potentially enables the generation of vector beams that, through high-order harmonic generation, could lead to attosecond skyrmion fields in the XUV domain, as well as serving as spatial polarization shapers in complex quantum photonic experiments.

Moreover, because the formulation is analytical, it is readily transferable to other polarization-manipulating platforms, including metasurfaces and liquid-crystal devices, broadening its impact across photonics.

Conclusion

The presented research achieves analytically prescribed, spatially variant arbitrary polarization shaping using cascaded spatially variant QWPs fabricated via ultrafast laser writing in silica glass. It enables the scalable free-space generation of optical skyrmions of arbitrary type and order, with high fidelity and fabrication efficiency. This methodology not only progresses optical topological field engineering but also catalyzes further developments in multidimensional photonic information technologies and high-field laser applications.