A revolution in lens-making

Understanding of optics has changed no end since the world’s oldest known lens was ground nearly 3,000 years ago in modern-day Iraq. Yet its Assyrian maker would instantly recognise today’s lenses, which continue to be made much as they were then: by fashioning a piece of transparent material into a solid with curved surfaces. Just as invariably, the curves introduce optical aberrations whose correction requires tweaking the lens’s geometry in complicated ways. As a consequence, lenses remain bulky, especially by the standards of modern electronics.

Enter Federico Capasso, of Harvard University. He and his colleagues have created a lens that is completely flat and the width of two human hairs. It works because its features, measured in nanometres (billionths of a metre), make it a “metamaterial”, endowed with some weird and useful properties.

According to the laws of quantum mechanics, a particle of light, called a photon, can take literally any possible path between source A and point B. However, those same laws stipulate that the path of least time is the most likely. When a photon is travelling through a uniform medium, like a vacuum, that amounts to a straight line. But although its speed in a vacuum is constant, light travels at different (lower) speeds in different media. For example, it moves more slowly in glass than it does in air. So in a medium composed of both air and glass, light’s most likely path from A to B will depend on the thickness of glass it needs to traverse, as well as the total distance it needs to cover. That means that the light may sometimes prefer to bend. This is the quantum-mechanical basis of refraction.

In order to maximise the probability that photons from A will end up precisely at B, those going in a straight line need to be slowed down relative to those taking a more circuitous route, so that, in effect, all hit B the same time. This can be done by forcing the former to pass through more glass than the latter. The result is a round piece of glass that is thick in the middle, where the straight-line path crosses, and tapers off towards the edge, where the less direct routes do—in other words, a focusing lens, with its focal point at B.

Dr Capasso’s lens, described in Nano Letters, also slows photons down. But instead of using varying thickness of glass to do the job, he and his team created an array of antennae which absorb photons, hold on to them for a short time and then release them. In order for this trick to work, though, the distance between the antennae has to be smaller than the wavelength of the light being focused. In Dr Capasso’s case that means less than 1,550 nanometres, though he thinks that with tweaking it could be made to work with shorter-wavelength visible light, too.

Creating the array involved coating a standard silicon wafer, 250 microns thick, with a 60-nanometre layer of gold. Most of this layer was then stripped away using a technique called electron-beam litography, leaving behind a forest of V-shaped antennae arranged in concentric circles. By fiddling with their precise shape, after much trial and error, antennae lying on different circles could be coaxed into holding on to the photons for slightly different lengths of time, mimicking an ordinary glass lens. The whole fragile system can be sandwiched between two sheets of transparent material to make it more robust.

At present the new-fangled lens only works for monochromatic light and so is unlikely to replace the glass sort in smartphone cameras anytime soon. But it could revolutionise instruments that rely on single-colour lasers, by making further minaturisation possible while eliminating the optical aberrations inherent to glass lenses. Such devices include laser microscopes, which are used to capture high-resolution images of cells, or optical data storage, where a more accurate and smaller lens could help squeeze more information into ever less space.

First published on economist.com.


  1. Capasso et al., Aberration-Free Ultrathin Flat Lenses and Axicons at Telecom Wavelengths Based on Plasmonic Metasurfaces, Nano Letters2012.
  2. Capasso et al., Light Propagation with Phase Discontinuities: Generalized Laws of Reflection and Refraction, Science2011.

Also appeared in The Economist. Also available in audio here.

Image credit: Francesco Aieta

Printing at the highest resolution possible

How high can you get? Resolutionwise, that is. In 2010, when launching the Apple iPhone 4, Steve Jobs claimed that the 326 dots per inch (dpi) resolution of that machine’s display would make it impossible to pick the pixels apart. His reason was that this density of dots is at the limit of the resolving power of the human eye when something is held at reading distance from it. This limit is not, however, the theoretical maximum resolution of an image. That is about 100,000 dpi, a figure imposed by the laws of physics. Place any more dots in an inch and the light waves coming from them start to interfere with each other, leading to a loss of clarity.

Printing at 100,000 dpi using either the inkjet technique (in which droplets of liquid ink are laid down side by side) or the laserjet technique (in which static electricity is used to direct bits of powdered ink onto paper, where a laser melts them) is impossible. Neither can manage more than about 10,000 dpi. But Karthik Kumar, a material scientist at Singapore’s Agency for Science, Technology and Research, thinks he can do better. As he and his colleagues report in Nature Nanotechnology, they have a prototype that can manage the full 100,000. The catch is that it uses “ink” made out of silver and gold.

Actually, that is not the only catch. For the image has to be created using an electron beam, rather than a laser or an inkjet, and such beams are rather hard to handle. But as a proof of principle it is interesting, and it might lead to cheaper and faster methods.

Dr Kumar and his team start with a plate of silicon. The electron beam carves bits of this away, leaving a pattern of cylindrical posts each about 140 nanometres (billionths of a metre) across and 50 nanometres apart. That “about” is important, though. The exact diameters of the posts and the distances between them are crucial. Varying them changes the colour that forms between the posts.

To create this colour, the plate is coated with a layer of silver and another of gold. The outer electrons of the atoms of these heavy metals often come loose, to form a cloud akin to an electronic gas. When light falls on this gas, it absorbs all frequencies bar one, which is reflected. Exactly which frequency is reflected depends on the resonant frequency at which the electron gas vibrates. And that, in turn, depends on how far apart the silicon posts (which constrain the gas’s movements) are.

A coloured image can thus be made by varying the size and spacing of the posts. This, the team did. Specifically, they recreated a widely used test image: that of Lenna, a pin-up girl from the 1970s whose picture is reckoned (ahem) a challenge to reproduce because of its wide range of tones. Dr Kumar’s version of Lenna was only 100 microns (about the thickness of a human hair) across, but matched the original with reasonable fidelity.

Carving images on silicon using electron beams, and then coating the result with precious metals, is unlikely ever to be a viable technology for the mass printing of images. It might, though, be a good way of storing data permanently—better, in terms of density, at least, than existing optical techniques such as CDs, DVDs and Blu-ray discs. It is also strangely reminiscent of the Daguerreotype, an early form of photography that formed images of silver on a copper plate. Bearing in mind the multi-billion dollar industry that Louis Daguerre’s idea eventually turned into, perhaps Dr Kumar’s version is not so strange, after all.

Also published on economist.com.


  1. Kumar et al.Nature Nanotechnology, 2012
  2. Lenna Image
  3. Retina Display

Image from here.

The physics of sand castles: Just add water

A day out on the beach would be incomplete without a sand castle. The mightier the castle, the better. But sand is next to useless as a building material. Without water it simply spreads out as wide as possible. So in search of a good recipe Daniel Bonn, a physicist at the University of Amsterdam, and colleagues have stumbled upon a formula for making the perfect sandy redoubt.

As they reveal in a paper published this week in Scientific Reports the key is to use sand with only 1% water by volume. Wet sand has grains coated with a thin layer of water. Owing to water’s surface tension this thin coat acts like skin stretched over many grains, holding them together by creating bridges between the grains. The strength of these bridges is enough to fight Earth’s gravity and prevent the structures from buckling under their own weight.

An easy way to achieve the right amount of water, Dr Bonn suggests, is to tamp wet sand in a mould (open at the top and the bottom) with a thumper at least 70 times, as he did in his experiments.

As for the design itself, unsurprisingly, the wider the base the taller the castle. According to calculations, using ideally moist sand, a column with a three inch diameter could rise as high as two metres. At 12 metres, the current world record for the tallest sandcastle, set by Ed Jarrett in 2011, used a base of roughly 11 metres. If Dr Bonn is right, sand engineers could in principle beat that with a castle thrice the height upon the same foundation.

First published in The Economist.

Image from here.