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Revealing topology with transformation optics.

Lizhen Lu1,2, Kun Ding3,4, Emanuele Galiffi2,5

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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.

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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.