Inverse-Designed Metasurfaces for Compact Optical Skyrmion Generation with High Topological Fidelity

Abstract

Optical skyrmions are structured vector fields with nontrivial polarization topology and subwavelength-scale features. One common approach to generating optical skyrmions is the superposition of a zeroth-order Bessel beam and a higher-order Bessel beam carrying orbital angular momentum, with each beam possessing an orthogonal circular polarization state. However, creating such complex beams typically requires bulky free-space optical setups; therefore, recent efforts have focused on compact optical skyrmion generators based on metasurfaces. Nevertheless, achieving the degrees of freedom required for simultaneous phase and polarization control remains challenging because of the limited design flexibility of conventional meta-atoms. Here, we address this challenge by employing an inverse-design approach and demonstrate a single-layer metasurface that generates high-fidelity optical skyrmions. We employ an adjoint-based topology-optimization method to design a silicon metasurface that converts an incident beam into an optical skyrmion without the need for additional optical components. The optimized metasurface generates an optical skyrmion with skyrmion number $(N_\mathrm{sk}) = 0.970$. This work demonstrates that inverse design can be a promising route to compact skyrmion generators, and our approach provides a basis for near-field particle manipulation and the generation of independent topological bits in dense photonic integration.

Figures (4)

• Figure 1: Inverse-designed metasurface for optical skyrmion generation. (a) Schematic illustration of the inverse-designed silicon metasurface. A single-layer metasurface converts a normally incident $45^{\circ}$-linearly polarized Gaussian beam into an optical skyrmion. From top, the desired polarization-vector field, the normalized out-of-plane Stokes parameter $(S_z)$, and the intensity profile $(I)$. (b) The desired field is composed of two orthogonal vector channels; the zeroth-order Bessel beam $(J_0)$ and the first-order Bessel beam $(J_1)$. Their corresponding amplitudes (top) and phase distributions (bottom) are shown, respectively. Here, both Bessel beams include only the inner ring in their intensity profiles, while the outer concentric rings are neglected; in this work, we refer to this as a truncated Bessel desired beam. (c) The superposition of $J_0$ and $J_1$ components creates the resulting desired skyrmion field. The intensity profile, the polarization-ellipse map, and the skyrmion texture are presented. In the accompanying skyrmion-texture color bar, the vertical axis denotes the normalized out-of-plane Stokes parameter $S_z$, and the horizontal axis denotes the Stokes-space azimuthal angle, written here as $\tan^{-1}(S_y/S_x)$. (d) Radial intensity profiles of the RCP $J_0$ and LCP $J_1$ components, illustrating truncation at their first radial zeros. (e) Mapping of the desired polarization field onto the Poincaré sphere, yielding a theoretical skyrmion number $(N_\mathrm{sk}) = 0.994$.
• Figure 2: Comparison between a conventional forward-design workflow and the inverse-design workflow. (a) Schematic illustration describing a metasurface design strategy for controlling the phase of the incoming beam. A unit-cell library, which consists of various meta-atoms with different structural dimensions, is first constructed, and their phases are calculated. Once the desired phase is set, meta-atoms are distributed over two-dimensional space to impart the phase change to the incoming beam. However, this method misses effects arising from nearby structures and coupling. Therefore, the final phase becomes distorted compared with the intended phase. (b) Schematic illustration describing the gradient-based inverse-design framework. The desired skyrmion field is defined directly on the observation plane as the objective, and the three-dimensional structure is updated via repeated electromagnetic simulations, adjoint sensitivity analysis, and parameter updates so that the emitted field reproduces the desired field itself.
• Figure 3: Inverse design of the optical skyrmion. (a) Figure of merit (FoM) as a function of iteration during the optimization. The projection-function parameter $\beta$ is progressively increased to enforce binarization of the design, and the skyrmion-number score is activated in the later stage of the optimization, as indicated by the red dashed line. (b) Comparison between the desired and optimized observation-plane fields within the ROI $A=\{(x,y):r\le r_1\}$, showing the intensity distribution (top) and the skyrmion-density map (bottom). (c) Representative intermediate states at selected iterations, again cropped to $A$, including the intensity profile (top), skyrmion-density distribution (middle), and corresponding material layout in the design region (bottom). The optimization gradually evolves from the initial structure toward a binary silicon--air pattern that more closely reproduces the desired field. (d) Schematic of the final optimized device, in which a normally incident $45^{\circ}$-linearly polarized Gaussian beam is transformed by the disk-shaped design region into the desired skyrmionic vector field above the metasurface.
• Figure 4: Final optimized metasurface and performance. (a) Binary material layout of the optimized 6.00 $\mu$m-diameter device, together with orthogonal cross-sections through the 0.800 $\mu$m-thick silicon layer on silica. (b) Simulated amplitude (top) and phase (bottom) of the two constituent circular-basis fields at the observation plane, obtained by resolving the simulated transverse field into the same basis used to define the desired right-circularly polarized $J_0$ and left-circularly polarized $J_1e^{i\phi}$ terms; the field maps are shown only within the ROI $A=\{(x,y):r\le r_1\}$. (c) Total skyrmion output within the same ROI, shown as the intensity profile, a polarization-ellipse map plotted on the total-intensity background of the superposed skyrmion field, with ellipse grayscale indicating local handedness, and the skyrmion texture. In the accompanying skyrmion-texture color bar, the vertical axis denotes the normalized out-of-plane Stokes parameter $S_z$, and the horizontal axis denotes the Stokes-space azimuthal angle, written here as $\tan^{-1}(S_y/S_x)$. (d) Cumulative leakage outside the ROI, accumulated from $r=r_1$ outward within the same circular monitor window $\Omega=\{(x,y):r\le 3.00~\mu\mathrm{m}\}$ used in the FoM concentration term, for the inverse-designed confined skyrmion and the corresponding unconfined Bessel-mode skyrmion. (e) Poincaré-sphere mapping of the simulated Stokes vector over $A$, yielding $N_\mathrm{sk} = 0.970$.