Bringing Tiny Points of Darkness Into the Light

“Light is intriguing and still full of surprises, even though we use it every day to perceive the world around us,” says Lorenzo De Angelis, a PhD student at the Kavli institute of Nanoscience in Delft, the Netherlands. He speaks from experience. An unexpected aspect of light’s behavior was just uncovered by a team including De Angelis, Prof. Kobus Kuipers, and collaborators from Delft and the University of St. Andrews in the United Kingdom. Their work originated at AMOLF in Amsterdam and was published this week in the American Physical Society’s journal Physical Review Letters.

An artistic impression of the two kinds of tangles of darkness in a random light field.
Image Credit: Claudia Micheli.

Imagine shining a beam of laser light into a dark, reflective cavity. The light bounces off of the different surfaces inside, reflecting and interfering, and before long the cavity is filled with light randomly traveling in all different directions. One way to describe this situation is to talk about light as a field, similar to how you might talk about an electric field. Inside of an electric field, you can describe every point in space as having a value (strength) and a direction. Similarly, a light field describes how light is traveling at each point in space with a value (intensity) and direction.
In random light fields, an infinitely small dark point occurs anywhere the intensity is zero. Called phase singularities, these dark points are the result of light twisting like a corkscrew. Although light will continue traveling randomly in a cavity over time, phase singularities stay frozen. However, you can “unfreeze” the singularities by slowly changing the color of your laser light. On doing so, the phase singularities will start moving, and, as De Angelis says, tangled traces of darkness are left behind as they move around.

This illustration shows tangles of darkness in a random light field. Red represents “faithful” singularities and green the “unfaithful” singularities.
Image Credit: L. De Angelis, F. Alpeggiani, A. Di Falco, and L. Kuipers, Physical Review Letters.

These dark points can be destroyed, but only when they end up at the same location as another phase singularity that twists in the opposite direction. Similarly, new phase singularities can be created only in pairs. In this new research, the team studied the lifespan of these dark singularities—from birth to death. They also explored the influence of “fidelity” on the lifetime of phase singularities—in other words, whether it makes a difference if a point of darkness dies along with its birth partner versus another partner.

The team didn’t start out with this goal in mind. As De Angelis explains, “We were measuring the distribution of dark points in light, namely how far apart they like to be, and at which distance they still ‘feel’ the presence of other dark points. Then, we bumped into a paper from the famous scientist Michael Berry…”

In his paper, Berry suggested that singularities, like these dark points, could either stay loyal to the partner they were born with or move on to other partners throughout their life. He suggested that this property would contain important information on the type of randomness that governs the system. However, he pointed out, this is not an easy theory to explore and verify. “We saw a potential here,” says Kuipers, “because with our equipment and our expertise we could do experiments to address this problem, questioning light itself for an answer.”

An illustration of the evolution of dark points in a random light field. The red (green) circles highlight a pair of dark points being destroyed (created). Credit:
Image Credit: L. De Angelis, F. Alpeggiani, A. Di Falco, and L. Kuipers.

With Berry’s paper as motivation, the research project took a new turn. The team generated random light waves inside of a special kind of cavity and tracked the movements of the phase singularities at varying wavelengths of light, from birth to death. An experimental and data processing challenge to be sure, their results showed that once created, singularities only persist over a finite range of wavelengths.

Looking at the data more closely, they realized that the singularities fell into two general categories. Singularities that persisted over a larger range of wavelengths (about 0.6 nanometers) were destroyed at a one rate. Singularities that persisted over a much shorter range of wavelengths (about 0.03 nanometers) were destroyed at a different, faster rate.

Furthermore, when the researchers looked only at the faithful singularities—those who were destroyed with their birth partner—things were even more surprising. Compared to what simulations predicted, there were far too many faithful singularities among those that persisted over a short range of the wavelengths. As De Angelis summarizes, “the behavior of dark points that remain faithful to their creation partner is distinct from that of ‘promiscuous’ ones.”
Why? That’s a great question.

For several months the team tried to figure out what was wrong with their experiment, assuming that the simulations were right. In the end, however, they determined that the problem wasn’t in their experiment. Instead, it seems, there is some very real aspect of light missing from the simulations. The team hasn’t figured out exactly what that is and how it works yet, but their paper proposes some ideas that seem to be on the right track.

As this story reveals, light is a mysterious thing. On one hand, it is such a simple and foundational part of our existence that even young children grasp some of its nuances. On the other hand, light can be a fascinatingly complex phenomenon that we still don’t truly understand. As our knowledge and our experimental capacity grow, however, we are moving ever closer to bringing this mystery into the light.

Kendra Redmond

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