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Revealing topology with transformation optics
Lizhen Lu1,2, Kun Ding3,4, Emanuele Galiffi2,5
1State Key Laboratory of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi'an Jiaotong University, 710049, Xi'an, China.
Nature Communications
|November 26, 2021
Summary
Researchers visualize symmetry in a virtual space to understand topological phases in plasmonic systems. This approach enables intuitive engineering of edge states by controlling topological invariants.
Area of Science:
- Physics
- Materials Science
- Optics
Background:
- Symmetry analysis is crucial for understanding physical systems and topological phases.
- Conventional symmetry analysis occurs in physical or reciprocal space.
- Transformation optics offers a novel approach to visualize symmetries.
Purpose of the Study:
- To demonstrate visualization of symmetries in a transformed coordinate space.
- To explore the construction of topologically non-trivial systems using transformation optics.
- To investigate the control of topological invariants and engineering of edge states.
Main Methods:
- Utilizing virtual space from transformation optics.
- Projecting higher-dimensional virtual systems onto lower-dimensional real systems.
- Analyzing modes in virtual space to construct topological systems.
- Controlling topological invariants via conformal mapping singularities.
Main Results:
- Symmetries and topological transitions are visualized in a spectrally related virtual space.
- Transformation optics facilitates the construction of topologically non-trivial plasmonic systems.
- Singularities in conformal mapping allow intuitive engineering of edge states.
Conclusions:
- The interplay of transformation optics and topology provides new insights into physical systems.
- This framework can be generalized to other wave phenomena beyond photonics.
- The method offers intuitive control over topological properties and edge states.
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