A quantum graph approach to metamaterial design
Abstract Since the turn of the century, metamaterials have gained a large amount of attention due to their potential for possessing highly nontrivial and exotic properties—such as cloaking or perfect lensing. There has been a great push to create reliable mathematical models that accurately describe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2022-10-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-022-22265-2 |
| _version_ | 1811335177628024832 |
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| author | Tristan Lawrie Gregor Tanner Dimitrios Chronopoulos |
| author_facet | Tristan Lawrie Gregor Tanner Dimitrios Chronopoulos |
| author_sort | Tristan Lawrie |
| collection | DOAJ |
| description | Abstract Since the turn of the century, metamaterials have gained a large amount of attention due to their potential for possessing highly nontrivial and exotic properties—such as cloaking or perfect lensing. There has been a great push to create reliable mathematical models that accurately describe the required material composition. Here, we consider a quantum graph approach to metamaterial design. An infinite square periodic quantum graph, constructed from vertices and edges, acts as a paradigm for a 2D metamaterial. Wave transport occurs along the edges with vertices acting as scatterers modelling sub-wavelength resonant elements. These resonant elements are constructed with the help of finite quantum graphs attached to each vertex of the lattice with customisable properties controlled by a unitary scattering matrix. The metamaterial properties are understood and engineered by manipulating the band diagram of the periodic structure. The engineered properties are then demonstrated in terms of the reflection and transmission behaviour of Gaussian beam solutions at an interface between two different metamaterials. We extend this treatment to N layered metamaterials using the Transfer Matrix Method. We demonstrate both positive and negative refraction and beam steering. Our proposed quantum graph modelling technique is very flexible and can be easily adjusted making it an ideal design tool for creating metamaterials with exotic band diagram properties or testing promising multi-layer set ups and wave steering effects. |
| first_indexed | 2024-04-13T17:20:18Z |
| format | Article |
| id | doaj.art-457dac3599c24a7d8af0e4a16b959fb6 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-13T17:20:18Z |
| publishDate | 2022-10-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-457dac3599c24a7d8af0e4a16b959fb62022-12-22T02:38:00ZengNature PortfolioScientific Reports2045-23222022-10-0112111410.1038/s41598-022-22265-2A quantum graph approach to metamaterial designTristan Lawrie0Gregor Tanner1Dimitrios Chronopoulos2School of Mathematical Sciences, University of NottinghamSchool of Mathematical Sciences, University of NottinghamDepartment of Mechanical Engineering and Mecha(tro)nic System Dynamics (LMSD), KU LeuvenAbstract Since the turn of the century, metamaterials have gained a large amount of attention due to their potential for possessing highly nontrivial and exotic properties—such as cloaking or perfect lensing. There has been a great push to create reliable mathematical models that accurately describe the required material composition. Here, we consider a quantum graph approach to metamaterial design. An infinite square periodic quantum graph, constructed from vertices and edges, acts as a paradigm for a 2D metamaterial. Wave transport occurs along the edges with vertices acting as scatterers modelling sub-wavelength resonant elements. These resonant elements are constructed with the help of finite quantum graphs attached to each vertex of the lattice with customisable properties controlled by a unitary scattering matrix. The metamaterial properties are understood and engineered by manipulating the band diagram of the periodic structure. The engineered properties are then demonstrated in terms of the reflection and transmission behaviour of Gaussian beam solutions at an interface between two different metamaterials. We extend this treatment to N layered metamaterials using the Transfer Matrix Method. We demonstrate both positive and negative refraction and beam steering. Our proposed quantum graph modelling technique is very flexible and can be easily adjusted making it an ideal design tool for creating metamaterials with exotic band diagram properties or testing promising multi-layer set ups and wave steering effects.https://doi.org/10.1038/s41598-022-22265-2 |
| spellingShingle | Tristan Lawrie Gregor Tanner Dimitrios Chronopoulos A quantum graph approach to metamaterial design Scientific Reports |
| title | A quantum graph approach to metamaterial design |
| title_full | A quantum graph approach to metamaterial design |
| title_fullStr | A quantum graph approach to metamaterial design |
| title_full_unstemmed | A quantum graph approach to metamaterial design |
| title_short | A quantum graph approach to metamaterial design |
| title_sort | quantum graph approach to metamaterial design |
| url | https://doi.org/10.1038/s41598-022-22265-2 |
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