Invisibility cloaks? 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.

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The wave beneath their wings

It's a common sight: pelicans gliding along the waves, right by the shore. These birds make this kind of surfing look effortless, but actually the physics involved that give them a big boost are not simple.

Researchers at the University of California San Diego have recently developed a theoretical model that describes how the ocean, the wind and the birds in flight interact in a recent paper in Movement Ecology.

UC San Diego mechanical engineering Ph.D. student Ian Stokes and adviser Professor Drew Lucas, of UC San Diego's Department of Mechanical and Aerospace Engineering and Scripps Institution of Oceanography, found that pelicans can completely offset the energy they expend in flight by exploiting wind updrafts generated by waves through what is known as wave-slope soaring. In short, by practicing this behavior, sea-birds take advantage of winds generated by breaking waves to stay aloft.

The model could be used to develop better algorithms to control drones that need to fly over water for long periods of time, the researchers said. Potential uses do not stop there.

"There's a community of biologists and ornithologists that studies the metabolic cost of flight in birds that can use this and see how their research connects to our estimates from theory. Likewise, our model generates a basic prediction for the winds generated by passing swell, which is important to physicists that study how the ocean and atmosphere interact in order to improve weather forecasting," Stokes said.

"This is an interesting project because it shows how the waves are actually moving the air around, making wind. If you're a savvy bird, you can optimize how you move to track waves and to take advantage of these updrafts. Since seabirds travel long distances to find food, the benefits may be significant," Lucas said.

Stokes and Lucas are, of course, not the first scientists to study the physics of the atmosphere that pelicans and other birds are hardwired to intuit so they can conserve energy for other activities. For centuries, humans have been inspired by the sight of birds harnessing the power and patterns of the winds for soaring flight.

That's how it started with Stokes, who is now in the second year of his PhD at UC San Diego. As a UC Santa Barbara undergraduate, Stokes, a surfer and windsurfer in his off hours, needed a project for his senior physics class and thought of the birds that would accompany him on the waves. When he looked closer, he appreciated the connection between their flight dynamics and the study of environmental fluid dynamics, a speciality of scientists at UC San Diego. The project ultimately turned into a master's thesis with Lucas, drawing inspiration from oceanographers at Scripps who seek to understand the interactions between the ocean and atmosphere.

Wave-slope soaring is just one of the many behaviors in sea-birds that take advantage of the energy in their environment. By tapping into these predictable patterns, the birds are able to forage, travel, and find mates more effectively.

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