Material behaviour is traditionally determined by chemistry. Free electrons in metals give rise to conductivity, unfilled orbitals make elements reactive. Metamaterials, on the other hand, have properties that come mainly from its internal design, not just from what it is made of.

These types of materials are characterised by a specifically designed larger-scale repeating pattern that interacts with waves in a chosen way. Invisibility cloaks are one such example. These are designed so that waves bend around an object and then recombine on the other side, making the object scatter much less light, sound or another type of wave.

The challenge is designing metamaterials to give you exactly the properties that you want. Two equations come into play.

1. The Laplace equation. This describes steady-state conditions with no oscillations or waves and has only one free parameter. It is easy to use but the metamaterial properties you can get are often limited.
2. The Helmholtz equation. This describes oscillations – sound waves, light waves etc. To use this equation, the wave medium usually needs two material parameters. For acoustics, these are equivalent to mass density and bulk modulus, which together determine how sound travels. Harder to work with, but more powerful.

The goal of new research from a team of researchers from China and Singapore is to have the best of both worlds. They were able to develop a mathematical correspondence between these two equations and use it to design metamaterials with new properties. Counterintuitively, they found that less complicated designs can achieve more. This less-for-more approach doesn’t try to design every aspect of how a wave behaves, but instead starts with a simpler, more manageable problem to access a wide range of useful effects.

The team used acoustics as testbed to demonstrate the power of their work. They demonstrated a range of novel phenomena such as three-dimensional freeform conformal cloaking, an experimentally validated waveguide cloak and the hyperbolic invisibility mentioned earlier. Because the technique is based on equations shared by several types of waves, their approach could also be applied to water waves and electromagnetic waves. This makes it a broadly transferable strategy for designing metamaterials

Real devices will still face practical limits from losses, dispersion and the need to approximate continuous material properties with fabricated structures. However, this new work does offer a practical method to design new metamaterials with exotic properties, and to manipulate waves beyond conventional constraints.