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SUMMARY:Modelling Metamaterials via Quantum Graph Theory - Dr Tristan Lawr
 ie\, University of Nottingham/University of Exeter
DTSTART:20250826T150000Z
DTEND:20250826T170000Z
UID:TALK235261@talks.cam.ac.uk
CONTACT:Dr Matthew Nethercote
DESCRIPTION:Since the turn of the century\, metamaterials have attracted s
 ignificant attention due to their potential to exhibit highly nontrivial a
 nd exotic properties\, such as cloaking and perfect lensing. A key challen
 ge in their development is the creation of reliable mathematical models th
 at accurately describe the required material compositions. In this work\, 
 we adopt a quantum graph approach to metamaterial design\, in which an inf
 inite square periodic quantum graph—constructed from vertices and edges
 —serves as a paradigm for a two-dimensional metamaterial. Wave transport
  occurs along the edges\, while the vertices act as scatterers modelling s
 ubwavelength resonant elements.\n\nThe metamaterial properties are underst
 ood and engineered by manipulating the band diagram of the periodic struct
 ure\, either by varying the vertex scattering properties or by altering th
 e graph topology. These engineered features are demonstrated through the r
 eflection and transmission behaviour of Gaussian beam solutions at an inte
 rface between two distinct metamaterials. The proposed quantum graph model
 ling framework is highly flexible and easily adjustable\, making it an ide
 al design tool for creating metamaterials with exotic band structures and 
 filtering capabilities.\n\nThe reliability of the model is verified throug
 h numerical simulations using COMSOL and confirmed experimentally in both 
 the acoustic and microwave regimes. As an example\, we conceptualise and n
 umerically simulate a resonant metamaterial interface incorporating non-lo
 cal—beyond nearest-neighbour—coupling\, which acts as a discrete angul
 ar filter. This structure can be designed to achieve perfect transmission 
 at customisable angles of incidence\, without diffraction\, enabling tailo
 red transmission in arbitrarily narrow wavenumber windows.
LOCATION:Centre for Mathematical Sciences MR13\, CMS
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