People think I'm compensating, but I'm not. I just happen to like seeing tiny objects in exquisite detail. So my obsession—one that I inflict on others as often as possible—continues to grow. My microscopy obsession isn't all personal, though. The truth is that images are powerful. They explain, they inspire, and they help us cope with scales that would otherwise be incomprehensible. In short, images and imaging devices are awesome.

Making images better is perhaps the only thing more awesome than the awesomeness of images themselves. When a paper on the first functioning superoscillatory lens was published in Nature Materials, it proved irresistible to me.

I can see that perfectly, why can't you?

Before we get to the actual point of the article, let me entertain you by going on at length about the relationship between a lens and the smallest features we can see with that lens. The concept we need here is spatial frequencies. I think most of us are familiar with the idea of temporal frequencies. The notes on a piano are all at a well-defined set of temporal frequencies. The frequency corresponds to the time it takes for the pressure to go from high to low and back to high again. Higher frequencies correspond to a shorter time to complete a cycle.

We can do the same thing in space as well. If we freeze a light wave in time, then the distance between the peaks of the electric field of the wave provide a consistent spatial period, which we can turn into a spatial frequency. Unlike time, however, we are able to perceive three spatial dimensions—depending on how we look at it, a light wave can have three spatial frequencies. These frequencies will change depending on our point of view, but no matter which way we look at the wave, the frequencies must add up to the same maximum value.

To get an idea of how this limits the detail in an image, imagine a beam of light hitting an object, and collecting the scattered light with a lens. The scattered light carries the details of the object in its spatial frequencies. But from the point of view of the lens, the light waves with the very highest spatial frequencies are those that don't travel towards the lens; they travel parallel to it instead. The very highest spatial frequency information that is transmitted by the lens is given by those light waves that just barely pass through its edges.

Unfortunately, the very finest details of the object you're imaging are the ones that possess high spatial frequencies. In other words, to see detail, we need to collect high frequency information, but the lens cuts off the highest frequencies, blurring the image.

Even if we had a magic lens that collected all the scattered light, that maximum value—a value given by the wavelength of the light used to illuminate the object—would still limit the details we could perceive. Or at least under ordinary circumstances.

Effervescent evanescent waves

I need to confess something at this point: I lied. The maximum value for the spatial frequencies? That doesn't exist. Yet everything I said above is also true. So what happens to those light waves with spatial frequencies higher than the maximum value? These waves, called evanescent waves, simply don't propagate. Instead, their amplitude falls off exponentially with distance from the object. If you stuck your lens so close to the object (a distance of about one wavelength of light), then you would collect the evanescent waves and be able to perceive far more detail.

This isn't a very convenient way to image. Yet, collecting the contributions of evanescent waves is what a superoscillatory lens does.

It can do this because, although the amplitude of the evanescent wave drops very rapidly, it never quite reaches zero. For any normal lens, the contribution from evanescent waves is swamped by everything else. The job of the superoscillatory lens is to separate the contribution from these high frequency components so that they can be detected separately.

Do you remember how to superoscillate?

The potential for superoscillations to provide a high resolution imaging tool was pointed out by theoreticians Berry and Popescu. The trick, it seems, is to create a lens that gets all the contributions from the evanescent waves to add up in phase so that they produce an arbitrarily small spot.

But this spot will be surrounded by a very intense halo that corresponds to the light we normally image with. To make matters worse, the smaller that central spot, the weaker it becomes, making it harder and harder to implement a useful lens. But if the halo and the central spot can be separated, it may not matter how weak the central spot is.

And, in a sense, that is what the new paper is about. The superoscillatory lens consists of a series of rings milled into a piece of glass coated with aluminum. The light passing through the rings is scattered, and the interference between the light from the different rings produces a bright spot at a central focus, and a broad halo around the central focus. This focus is 10 micrometers from the lens, so the individual evanescent waves that make up that spot have an amplitude that is some 10 million times weaker than all the rest of the light. By adding them all in phase, the central spot isn't much weaker than the surrounding halo.

The researchers demonstrated the lens' imaging capabilities by snapping pictures of features that they couldn't resolve with conventional light-based microscopy. In the end, their lens topped out at about 100nm, which is a factor of three better than a normal microscope.

The best part is that this is just the beginning. Superoscillations were first proposed in 2006. The first evidence for the existence of superoscillations turned up in 2007. It has only taken six years to go from theory to the first lens that could conceivably be used in a device. I imagine that smaller and more detailed things are on the way.

Nature Materials, DOI: 10.1038/nmat3280