October 29, 2013

Researchers shine light on knotty optics equations

Knotted structures of light could become a reality, according to a new study by University researchers.

Using pens, papers, computers, and math, fifth-year physics graduate student Hridesh Kedia, part of a lab led by Assistant Professor William Irvine, discovered new solutions to the famous Maxwell’s equations that have tied up scientists for 150 years.

The equations, named after 19th century physicist James Maxwell, describe light as made up of oscillating electric and magnetic fields, which twist around each other as the light propagates through space. These fields are described by field lines, which follow the direction of the field. Now, the physicists have found a way to shape these field lines into complicated, knotted structures that persist.

“People have been able to find solutions in which the field lines form such knots at an instant in time, but they would unravel,” Kedia said.

Kedia’s knots, meanwhile, are long-enduring, smooth, and contain no discontinuities that otherwise might make them impossible to produce in the real world.

“These are things that could be made in the lab, in principle,” he said.

The study of knots has historically been the domain of mathematicians, but now scientists are bringing knots into real-world materials.

Other recent work from Irvine's lab includes the production of a knotted vortex in water through 3D printing, and a paper proposing possible methods scientists could use to generate knotted light in the lab. Physicists could also use knotted light to induce knottiness in more exotic materials, like plasmas, which could have interesting properties when knotted. Knottiness might help to stabilize the plasma, making it easier to control, a property possibly useful for fusion research.

“People have thought about knots in physics for a long time, but only now we have the technology to start making them. So now people are starting to look at them in both theory and experiment,” Kedia said.