With supersymmetry, smooth, versatile on-chip light manipulation is now possible

Transformation Optics has formulated a versatile framework to shape the flow of light and adjust its spatial properties at will. The coordinate transformation often provides extreme material parameters that are not realizable even with metamaterials.

In a new article published in eLight, a team of scientists led by University of Pennsylvania professor Liang Feng has developed a new chip that can transmit different optical states to switch luminous fluxes. Their article, titled “Broadband Continuous Supersymmetric Transformation: a new paradigm for transformation optics,” attempts to provide an adaptive strategy for taming the flow of light.

Attempts to bend light as needed and to arbitrarily alter its spatial properties are rooted in the fundamentals of electromagnetics. The form invariance of the Maxwell equations under coordinate transformations led to the formulation of the transformation optics. Their equivalence allows the rearrangement of electromagnetic fields in a given coordinate system. It has opened avenues to a number of fascinating functions such as camouflage and illusion optics.

Metamaterials exhibit excellent design flexibility and allow for a wide range of optical properties. The experimental realization of transform optics has been in a stalemate for a decade, as the optical extremity and singularity often result from the transform. Therefore, new schemes for transform optics with broadband parameter values ​​within achievable limits are essential.

For example, conformal imaging with the spatially varying local refractive index has been demonstrated. This technique can perform the coordinate transformation using inhomogeneous Si nanostructures. It can provide fine phase front control for multicolor carpet coatings. This approach highlighted the possibility of exploiting the gradient index (GRIN) to warp space. However, a paradigm shift beyond traditional coordinate transformation is required to achieve richer functionality than bending the trajectories.

The research team is pursuing a different approach than conventional transformation optics: observing the Hamiltonian of the system to be transformed. The invariance of the Hamiltonian under symmetry operation gives us insights into how a system can be transformed with a conserved quantity. In particular, supersymmetry (SUSY) is characterized by the degenerate eigenenergy spectra between two distinct Hamiltonians, which has facilitated advanced control over the spatial properties of light.

The strategic coupling between the original optical system and its dissipative super partner has sparked intriguing applications such as high radiance single-mode microlaser arrays and mode multiplexing. These earlier experimental studies are based on lattice Hamiltonians that can be factored via a matrix operation. Therefore, they constructed systems consisting of many coupled discrete elements corresponding to coupled waveguides or resonators.

In contrast, the extended method of SUSY, which can generate an infinite number of strictly isospectral potentials, has remained experimentally unexplored because it requires an intrinsically different approach to realize arbitrary potentials. At the same time, its mathematical framework is ideal for the continuous Hamiltonian transform to enable a specific scenario for transform optics.

The research team reported the first experimental demonstration of the continuous SUSY transformation through the development of a novel GRIN metamaterial on a Si platform. The idea is to construct a metamaterial that can emulate arbitrary potentials to achieve advanced light control by transforming the optical media under supersymmetry.

They used the synergy of supersymmetry and metamaterial to design a spatially varying dielectric constant. It presented a two-dimensional map in which arbitrary transforms are simultaneously prescribed to multiple optical states for routing, switching, and spatial mode shaping, while strictly preserving their original propagation constants. Their result was a broadband continuous SUSY transformation optics. The interplay of supersymmetry and a metamaterial demonstrated in this study shed light on a new way to fully utilize the spatial degrees of freedom of a chip for versatile photonic functionalities.

The team’s continuous SUSY transformation approach is scalable to a higher number of eigenstates and free parameters. It applies to more complicated index distributions and creates an ideal platform for on-chip space division multiplexing in information technologies. Furthermore, further extending the SUSY transformation to higher dimensions may provide a design strategy to unlock the full potential of metamaterials in three-dimensional space.