A vast number of the latest discoveries and advances in technology have been spurred by the creation of artificially crafted materials, and metamaterials appear to be one of the most promising findings at the forefront of this horizon.

What exactly is a metamaterial, you ask? Metamaterials are structures built from smaller artificial components, which are designed to exhibit properties beyond (as indicated by the Greek prefix “meta-”) what is found in nature. For this article, we’ll delve deeper into how metamaterials are currently being used in optics.

When light passes through a material, it is distorted to some extent. The most commonly used example of this effect, known as refraction, is looking at a straw placed in a glass of water – it appears to be bent at a different angle below the surface of the water than above. The light rays we observe bouncing off of the straw reach our eyes at different angles, since some of them pass through the water while others pass through the air. We can even calculate the angle at which a ray leaves a boundary between two different materials using the mathematical relationship provided by Snell’s Law:

$$n_1\sin\theta_1 = n_2\sin\theta_2$$

This relationship states that the sine of the angle of the ray (measured from the vertical normal) is inversely proportional to the index of refraction, n, of the material. Therefore, materials with higher indices bend light towards the normal, and materials with lower indices bend light away from the normal. However, all natural materials maintain the direction of propagation (a ray traveling down and to the right will still travel down and to the right, albeit at a different angle/steepness); they all have positive indices, and the angle of the refracted ray is positive as well. At this point, you might be able to guess what I’m about to say…

Exactly. Metamaterials surpass what we find in nature, because they can exhibit a negative index of refraction! Assuming the first material is natural, the angle of the incident ray is always positive, so the angle of the refracted ray through a metamaterial is negative, or in the opposite direction.

Researchers have found applications for the immense control of light exhibited by metamaterials by creating two-dimensional metamaterials known as metasurfaces. These surfaces can be carefully constructed, “pixel by pixel,” to bend incoming light in a very specific way. A surface is first created, after which we can choose to either etch patterns on each pixel or leave it unaltered. Together, even patches on the scale of a few square nanometers can concentrate lasers, depict hologram-like images, and do so much more!

Until earlier this year, the main obstacle in using larger metasurfaces was determining the appropriate pattern of etching – as the surfaces grew in size, the number of possible patterns grew exponentially. While it is not impossible to try every pattern until the right one is found, it isn’t a very realistic approach either. But mathematicians at MIT have recently discovered an optimization method that tackles the task with significantly more efficiency than brute force.

The new approach begins by breaking larger (note that we’re still referring to relatively small sizes) surfaces into several smaller patches. Each patch is then “optimized” by repeatedly tweaking individual pixels until the effect more closely resembles the intended outcome. By doing this simultaneously for each patch, the final pattern is reached within a matter of hours – whereas the same process would previously have been “virtually intractable.”Metamaterials and metasurfaces are also being studied for use in a variety of other neat devices. For example, can we devise a material that can camouflage objects under it using the concept of negative refraction? Expanding the same ideas to sound, can we devise metamaterials that trap sound waves and vibrations? The questions are endless – but with continued research, so are the possibilities.