Points of darkness in light are singularities of wave optics, precisely they are singularities of light’s phase, or phase singularities. As light twists around these zeros of intensity, phase singularities are given a topological charge – positive or negative – defined by the direction of this twisting. Interestingly, this topological quantity seems by all means to be an actual charge, since phase singularities “feel” the charge in their surroundings. The way they feel it, is that one singularity of charge plus is always surrounded by a cloud of minuses, and vice-versa, so to try to maintain the total charge in a big box equal to zero. In atomic and molecular physics this process is called charge screening, and in fact we observe this screening to take place for singularities in random light as well.

However, in our recent publication we found something peculiar about this topological screening. To explain it we can play a little game. Let’s take a square box of side L, in which we observe an ensemble of charged entities:

In absence of screening the, total charge in the box would be zero, because every charge can randomly be a plus or a minus. But there will be an uncertainty on the total charge, which intuitiveley scales with total number of charges, i.e., with the area L*L of the box. Naive: the more particles I look at, the more likely it is to have more pluses than minuses.

In presence of perfect screening, the story changes. The total charge in the screen would still be zero, but with a smaller uncertainty! In fact we know that every charge is being compensated by a “cloud” of opposite ones, so to maintain the total charge zero. Nevertheless, this trick will not work at the edges of the screen… So there will still be an uncertainty on the total charge, given by the number of particles near the edges, i.e., proportional to the perimeter L.

Finally, we get to singularities in light. Weirdly enough singularities don’t show neither of the previous behaviours, but they do something in between. In our work we prove that the uncertainty on the topological charge for the singularities in a box of side L scales as ~ L log L, which is bigger than L but still smaller than L^2, proving that singularities do indeed undergo screening, although in a sort of imperfect way.

Reference

L. De Angelis, L. Kuipers. Screening and fluctuation of the topological charge in random wave fields, Optics Letters **43**, 12: 2740-2743 (2018)