Broadband continuous supersymmetric transformation: a new paradigm for transformation optics

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.