# Next generation metamaterials: exploiting four dimensions

Lead Research Organisation: Imperial College London
Department Name: Mathematics

### Abstract

The speed of a wave moving through a material is set by the refractive index; something immutable we might look up in a table and perhaps promptly forget. But imagine having the power to change it at will. What could we do? It would allow a single object to have different functions: a chassis that becomes transparent at the flick of a switch, or a room that can be made instantly private, turning thin walls into sound absorbers.

Yet these ideas are just the beginning of the story. If we can rapidly switch the wave speed, then completely new effects emerge. For example, changing the refractive index abruptly causes a wave to "reflect in time" - a paradoxical temporal analogue of the ordinary reflection we see and hear every day (e.g. the echo from a wall), but one that can cause the wave to gain energy. Other new effects arise if we can also change the refractive index differently at each point in space. With this control it becomes possible - for instance - to make a stationary object look like it is moving. Unlike true motion there is no restriction on this speed, and we can even mimic objects moving faster than light!

Our research will develop new materials where the refractive index can be changed in time, exploring switchable functionality and the plethora of new wave effects that emerge when the material properties are varied rapidly. This is not always an easy thing to do and to avoid potential obstacles to our research we take a "wave agnostic" view, where we - in parallel - explore the effects of a time varying wave speed for airborne acoustic waves, mechanical vibrations, radio frequency waves, terahertz waves, and in optics.

To illustrate the huge advantage of this approach, consider the time scales involved: "rapid" means the change must be imposed more quickly than the wave oscillates. For audible sound this is milliseconds, for visible light femtoseconds. We should use very different techniques in these two cases! In optics, special materials are subject to ultra-fast, high-intensity fields, while in acoustics we use electronically controlled transducers. Through considering different wave regimes we can implement a time varying wave speed by the most promising means, avoiding the limitations of any individual technique.

Our program of research is split into four, first developing experiments to demonstrate rapid switching of acoustic, elastic, and electromagnetic wave speeds in time, and the theory required to design them. The second part pushes this work to the next stage, developing materials where the wave speed varies in both space and time, allowing us to e.g. mimic motion. Having developed these experimental and theoretical capabilities, the final two parts of the project explore new wave effects in these materials, specifically wave amplification and unusual materials where the wave can only propagate in one direction.

While our research is a fundamental study into wave physics in time-varying materials, we predict multiple applications of this technology. Future communications (6G) is perhaps the simplest. This will need an enormous number of separately powered antennas to precisely direct beams of electromagnetic waves. But if we can rapidly change the reflective properties of a surface next to a single antenna, we can make it alone perform the function of these many different antennas, reducing energy requirements and complexity!

Wave-based computing is a second example: like every physical process, the scattering of a wave from a material is equivalent to a computation. Although electromagnetic waves perform this computation very quickly - at the speed of light! - to use it as a "computer" we need to program it. The material properties are fixed, so the wave always scatters in the same way. If we can switch the material properties, we can program it and create a new class of high-speed computational devices based on wave-scattering.

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