A research team at Xi'an Jiaotong University (XJTU) has found a way to understand and control the topological properties of systems in real space from virtual space using conformal symmetry in transformation optics.

The research team led by Professor Ma Xikui of the XJTU Research Center of Advanced Electromagnetic Regulation and Power Conversion Technology worked on the project with researcher Ding Kun of the Department of Physics at Fudan University, and Professor John Pendry at the Imperial College London.

The research started from a surface plasmon system with conformal symmetry. By constructing a conformal map with multiple singularities, the system in virtual space is projected into a real space system with lower Hilbert space dimensions, pointing out the connection between the eigenmodes of the system in the two spaces related by conformal mapping.

The researchers found that singularities in conformal mapping can be used to control the topology invariants of the system, and based on this, a general design scheme of the adjustable topological boundary state system was given.

This project has revealed for the first time the possibility of cross-application of transformation optics and topological photonics in the design of topological photonic devices.

The relationship between the singularity of conformal mapping and the topological properties of the system

a. The relationship between the coordinates of the singular point of the conformal mapping and the center coordinates of the maximum localized Wannier function of the system;

b. The magnetic field amplitude distribution of the Vanier function of the metasurface generated by different conformal mapping parameters.

Titled Revealing Topology with Transformation Optics, the paper was published in Nature Communications. The XJTU School of Electrical Engineering is the first unit of the paper. Doctoral student Lu Lizhen is the first author. Ding and Pendry are corresponding authors.

The project was financed by the National Natural Science Foundation of China, the Gordon and Betty Moore Foundation, and the Engineering and Physical Sciences Research Council (EPSRC).

After years of theoretical development and technological precipitation, transformation optics has become the core technology of many electromagnetic and optical device designs, and has important application values in electromagnetic stealth and phantoms, wave absorption, and electromagnetic energy concentrators.

Link to the paper: https://www.nature.com/articles/s41467-021-27008-x