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Related Experiment Video

Updated: Aug 24, 2025

Fabricating Metamaterials Using the Fiber Drawing Method
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A quantum graph approach to metamaterial design.

Tristan Lawrie1, Gregor Tanner2, Dimitrios Chronopoulos3

  • 1School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK.

Scientific Reports
|October 26, 2022
PubMed
Summary

This study introduces a novel quantum graph model for designing 2D metamaterials. This flexible approach enables precise control over exotic properties like negative refraction and beam steering for advanced wave manipulation.

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Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Quantum Mechanics

Background:

  • Metamaterials offer exotic properties like cloaking and perfect lensing.
  • Reliable mathematical models are crucial for metamaterial design and composition.
  • Existing models often lack the flexibility to engineer specific properties.

Purpose of the Study:

  • To develop a quantum graph approach for designing 2D metamaterials.
  • To demonstrate the engineering of metamaterial properties through band diagram manipulation.
  • To showcase the model's capability in controlling wave phenomena like refraction and beam steering.

Main Methods:

  • Utilizing an infinite square periodic quantum graph as a 2D metamaterial paradigm.
  • Modeling sub-wavelength resonant elements using finite quantum graphs with tunable scattering matrices.

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  • Analyzing metamaterial properties via band diagrams and the Transfer Matrix Method for layered structures.

    • Main Results:

    • Demonstrated control over metamaterial properties by manipulating the band diagram.
    • Successfully modeled wave transport and scattering in the quantum graph structure.
    • Showcased positive and negative refraction, along with beam steering, using Gaussian beam solutions.

    Conclusions:

    • The quantum graph modeling technique is highly flexible and adaptable for metamaterial design.
    • This approach is ideal for creating metamaterials with exotic band structures.
    • The model facilitates testing multi-layer setups and wave steering effects effectively.