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Abstract Transformation optics has formulated a versatile framework to mold the flow of light and tailor its spatial characteristics at will. Despite its huge success in bringing scientific fiction (such as invisibility cloaking) into reality, the coordinate transformation often yields extreme material parameters unfeasible even with metamaterials. Here, we demonstrate a new transformation paradigm based upon the invariance of the eigenspectra of the Hamiltonian of a physical system, enabled by supersymmetry. By creating a gradient-index metamaterial to control the local index variation in a family of isospectral optical potentials, we demonstrate broadband continuous supersymmetric transformation in optics, on a silicon chip, to simultaneously transform the transverse spatial characteristics of multiple optical states for arbitrary steering and switching of light flows. Through a novel synergy of symmetry physics and metamaterials, our work provides an adaptable strategy to conveniently tame the flow of light with full exploitation of its spatial degree of freedom. 

Abstract Structured lights, including beams carrying spin and orbital angular momenta, radially and azimuthally polarized vector beams, as well as spatiotemporal optical vortices, have attracted significant interest due to their unique amplitude, phase front, polarization, and temporal structures, enabling a variety of applications in optical and quantum communications, micromanipulation, and super‐resolution imaging. In parallel, structured optical materials, metamaterials, and metasurfaces consisting of engineered unit cells—meta‐atoms, opened new avenues for manipulating the flow of light and optical sensing. While several studies explored structured light effects on the individual meta‐atoms, their shapes are largely limited to simple spherical geometries. However, the synergy of the structured light and complex‐shaped meta‐atoms has not been fully explored. In this paper, the role of the helical wavefront of Laguerre–Gaussian beams in the excitation and suppression of higher‐order resonant modes inside all‐dielectric meta‐atoms of various shapes, aspect ratios, and orientations, is demonstrated and the excitation of various multipolar moments that are not accessible via unstructured light illumination is predicted. The presented study elucidates the role of the complex phase distribution of the incident light in shape‐dependent resonant scattering, which is of utmost importance in a wide spectrum of applications ranging from remote sensing to spectroscopy.