I always enjoy reading The Economist’s Science and Technology section. Generally speaking, I find most of the articles interesting, even if they are not practically relevant to anything and I am working on. In a recent edition (27th of July) however I found the piece that absolutely fascinated me. Nothing to do with computers, or electronic money or digital identity. It was this piece about lenses.
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For a group of engineers at Columbia University, in New York, led by Nanfang Yu, has worked out how to make magnifying lenses that are flat, and thinner than a hair.
The invention of microscopically thin flat lenses that can be manufactured using the same nano lithographic techniques are used to making computer chips opens up all sorts of new technological advances in everything from cameras and contact lenses to microscopes and, of course, smart spectacles.
It can do this because its surface is covered with millions of tiny antennae. These antennae are of different designs, each with a cross section smaller than the average wavelength of the light it is interacting with, and are arranged in concentric circles (see picture). The antennae scatter the light falling on them in such a way that, when the individual changes are added up, the combined effect is the same as if different parts of the beam had passed through the lens at different speeds.
Dr Yu is not the first person to make a lens in this way, but previous efforts worked only with single colours, and also required the light to be polarised. Dr Yu’s lens works with all colours and in natural light, which is unpolarised.
In practice, few optical systems other than eyeglasses rely on single lenses. Usually, different lenses with different properties are stacked on top of each other to remove aberrations and achieve full-colour wide-angle images. Dr Yu’s lenses can be stacked in this way, too. By sandwiching three of them together, he has created a triplet that achieves almost all the control of light waves that would be expected of bigger and heavier glass-lens systems.
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Besides saving weight and volume, Dr Yu’s flat lenses also promise to be cheaper to mass produce than the conventional sort. Grinding and polishing a glass lens is complex and time-consuming. Flat lenses are made using nanolithographic techniques, which are also employed for making computer chips. Given these advantages, flat lenses could replace their bulkier counterparts anywhere that cost or weight is an issue—meaning pretty-well everywhere from microscopes and cameras, to pairs of spectacles.
The article caught my eye (nope unintended) because I've always found optics interesting. When I went to university to study Physics, one of the topics I was especially interested in was lasers and electrooptics. In fact, as I recall, one of the reasons that I chose Southampton University was that they had a research group in this area and when I was doing my UCCA forms (I don't know if they still have those) and my visits to universities — remember my I am from that generation who were the first in their family to go to university so I had no nothing to go on — it was the laser stuff going on there that grabbed me.
Although my final year dissertation was on the highly theoretical and mathematical topic of symmetry groups (I was very good at maths but very bad of physics, so this was a good choice for me), my final year practical project was on the construction and measurement of gas lenses. You make a gas lens by pumping gas down a heated tube so that the temperature gradient from the centre of the tube to the edge forms a continuously changing medium of varying refractive index. When you shine a laser down the middle of it, the differential refractive index serves to focus the laser beam.
(If it hadn't been for the invention of continuously-rolled glass fibre, gas lenses could have been huge! How else can you transmit laser beams across the Atlantic, for example!)
Working out how to predict the performance of the lens depends on some fiendishly complicated mathematical functions called "confluent hypergeometrics". My part of the project was to write Fortran to solve these equations to predict the characteristics of the lens, while my partner Kevin's part of the project was to actually build the damn thing out of bits of drainpipe and gaffer tape!
Astonishingly, the calculations and the reality were close enough to jazz and we got a passing grade that helped me to scrape an Honours degree.
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