Wave scattering simulation unlocks potential for advanced metamaterials

A new software package developed by researchers at Macquarie University can accurately model the way waves - sound, water or light - are scattered when they meet complex configurations of particles.

This will vastly improve the ability to rapidly design metamaterials – exciting artificial materials used to amplify, block or deflect waves.

The findings, published in the journal Proceedings of the Royal Society A on 19 June 2024, demonstrated the use of TMATSOLVER – a multipole-based tool that models interactions between waves and particles of various shapes and properties.

The TMATSOLVER software makes it very easy to simulate arrangements of up to several hundred scatterers, even when they have complex shapes.

Lead author Dr Stuart Hawkins from Macquarie University's Department of Mathematics and Statistics says the software uses the transition matrix (T-matrix) – a grid of numbers that fully describes how a certain object scatters waves.

“The T-matrix has been used since the 1960s, but we’ve made a big step forward in accurately computing the T-matrix for particles much larger than the wavelength, and with complex shapes,” says Dr Hawkins.

“Using TMATSOLVER, we have been able to model configurations of particles that could previously not be addressed.”

Dr Hawkins worked with other mathematicians from the University of Adelaide, as well as the University of Manchester and Imperial College London, both in the UK, and from the University of Augsburg and University of Bonn, both in Germany.

“It was fantastic to work on this project and incorporate the TMATSOLVER software into my research on metamaterials,” says Dr Luke Bennetts, a researcher at the University of Adelaide and co-author of the article.

“It meant I could avoid the bottleneck of producing numerical computations to test metamaterial theories and allowed me to easily generalise my test cases to far more complicated geometries.”

Applications in metamaterials

The researchers demonstrated the software's capabilities through four example problems in metamaterial design.
These problems included arrays of anisotropic particles, high-contrast square particles, and tuneable [JvE1] periodic structures that slow down waves.

Metamaterials are designed to have unique properties not found in nature, letting them interact with electromagnetic, sound or other waves by controlling the size, shape and arrangement of their nanoscale structures.

Examples include super-lenses to view objects at the molecular scale; invisibility cloaks, which refract all visible light; and perfect wave absorption for energy harvesting or noise reduction.

The findings from this research and development of the TMATSOLVER tool will have wide application in accelerating research and development in the growing global market for metamaterials which can be designed for precise wave control.

“We have shown that our software can compute the T-matrix for a very wide range of particles, using the techniques most appropriate for the type of particle,” Dr Hawkins says.

“This will enable rapid prototyping and validation of new metamaterial designs.”

Professor Lucy Marshall, Executive Dean, Faculty of Science and Engineering at Macquarie University, says the software could accelerate new breakthroughs.  

“This research represents a big leap forward in our ability to design and simulate complex metamaterials, and is a prime example of how innovative computational methods can drive advancements in materials science and engineering,” says Professor.