The late 20th and early 21st century have seen a revolution in the study of light. Far from the old days of seeing things dimly through microscopes, we are now in the position to freeze light, use it to make materials transparent, and watch it spiral around on a gold surface.

Watching light do its thing is very difficult. This sounds a bit silly, as we observe the world through the effects of light. But what we actually see is an average effect. Light, shade, colors, and texture all come to us via the intensity of light, provided by lots of individual photons. We are in no position to see the femtosecond flickering of the field that averages to our spectacular view of the world.

All the interesting stuff we see is related to the amplitude and phase of the light field, though. And the amplitude of a light wave changes very fast, going through a complete cycle in two to three femtoseconds. The wavefront (phase) also travels very fast, moving around 300 nanometers every femtosecond. Tracking this sort of motion is tricky, but it reveals all sorts of intriguing stuff.

Researchers in Germany and Ireland have demonstrated how to use a form of electron microscopy to image light. By combining the highly detailed images that can be obtained from electron microscopy with very short optical pulses to generate the electrons, the researchers were able to track the wavefronts of light as they spiraled into focus.

Help, the optical vortex is holding me prisoner

Ordinarily, light does not spiral. To cause spiral, you need a strange object called an optical vortex beam. To understand the beam, we should first take a step back and consider waves. If you watch waves rolling up a beach, you can see that the wave peak makes a rough line that travels up the beach as it breaks. This traveling line is the "wavefront" of the wave.

If you look a bit more carefully, though, you'll see that the wavefront is not a perfect line—it's curved and bent. The beach is not exactly the same everywhere, so the wave travels at different speeds on different parts of the beach. If you look even more carefully, you'll see that even though the average motion takes the wave up the beach, the wave is traveling perpendicular to the local line of the wavefront at every location.

Let's apply that idea to optics. If I hold a magnifying glass in the sunlight, I will get a bright spot at the focus of the lens. We can understand that focus in terms of wavefronts. As the light from the Sun enters the lens, the wavefronts are straight lines. Upon exiting, they form a part of a sphere that is centered on the focal point. The spherical wavefronts converge on the focus, and if there are no ants in the way and the light continues on past the focus, they're spread out in a spherical wave that still has the focal point as its center.

So wavefronts are what tell light where to go. Once you understand this principle, you can consider all sorts of strange optics. One is a spiral phase plate. After exiting a spiral phase plate, the wavefronts follow a corkscrew form. This creates an odd property: at the center, the wavefront should be in two places at the same time. Since this isn't possible, the amplitude of the light goes to zero at the center. If you look down the barrel of an optical vortex beam, you will briefly see a bright ring before you go blind.

A vortex beam is even stranger: even though the beam propagates forward, none of the wavefronts are actually pointed in the forward direction. If you were to label a small patch of wavefront and track it, you would find that it travels around the axis in a spiral. This is even odder when you consider that electromagnetic waves are made of photons. A naive picture of such a beam consists of photons corkscrewing through space, which is a bit disconcerting, considering that photons are supposed to travel in straight lines.

These beams are said to have orbital angular momentum, and you can measure the torque that a beam with orbital angular momentum applies to an object.

Light spiraling down a golden sink

Just to make the picture a little more complex, let's think about how electromagnetic waves travel along a metallic surface. These waves are called surface plasmon polaritons, which is a fancy way of saying that the electromagnetic wave movement is intrinsically tied to the motion of electrons.

When light shines on a metal, the electrons are driven into motion by the field. So an oscillating electric field sets the electrons oscillating. The electrons radiate light, and voila, your metal is a mirror.

If you arrange it exactly right, though, the electromagnetic wave and the electrons act together to generate a wave that travels along the surface of the metal. The field drives the electrons into motion, which radiates a field that in turn drives more electron motion. Electrons move slowly (compared to light in a vacuum), so the combined light and electron wave is a slow-moving streak of light traveling across the surface of the metal.

For a beam that has no orbital angular momentum, the wavefronts are a series of stripes. Each wavefront generates a charge wave that adds light to the next wavefront, building up a propagating wave. For a beam with orbital angular momentum, however, the wavefronts form a spiral that either focuses inward or flings itself outward in all directions. The surface wave can't propagate anywhere, but the energy will either flow inward to a ring around the center or outward and be lost.

That is what we expect, at least. But is that what really happens? Until now, we had to rely on calculations; any picture of a surface plasmon polariton with orbital angular momentum averaged the spiral motion, leaving only a set of rings.

Electrons reveal light

To image the motion of wavefronts, a team of researchers set up a very clever experiment. First, the surface plasmons were generated in gold using an extremely short pulse of light (just 20 femtoseconds in duration). Because of the short excitation, the surface plasmon builds up during the pulse but decays away after the pulse has vanished, allowing these two phases to be separated from each other.

To sense the wavefronts, the researchers used a second pulse of light (a copy of the first pulse) to excite electrons out of the gold surface. The photon energy of the light on its own is not sufficient to drive electrons out of the gold surface. However, the electrons that are part of the plasmon wavefront already have a lot of energy, so the light pulse is just the kick they need to get free of the gold.

So it becomes a question of imaging the source of electrons, which is exactly what an electron microscope is for. Placing the whole experiment in an electron microscope produces beautiful images of the wavefronts of a surface plasmon with orbital angular momentum.

The entire thing is basically stroboscopic imaging. The researchers excite the surface plasmon. After waiting a bit, the imaging pulse hits the surface plasmon. This produces a snapshot of the wavefronts in the form of loose electrons. By repeating the experiment with different delay times, the life, times, and death of the surface plasmon can all be captured.

The experiment reveals that the wavefront motion is quite complicated. During the surface plasmon formation phase, the wavefronts spiral inward, driving the energy in the surface plasmon polariton toward the center. At the peak of this process, the surface plasmon forms a tightly focused ring around the center of the vortex. But as decay sets in, a second wavefront forms and spirals in the opposite direction. This wavefront directs energy out of the center, where it is lost as heat.

The nice thing about this experiment is that it not only confirms that we understand what is going on when beams with orbital angular momentum are converted to surface plasmon polaritons, but we can also use the imaging technique to design and test new forms of optics that make use of these properties.

Science, 2017, DOI: 10.1126/science.aaj1699