New York University physicists have invented a new method to create extended and knotted optical traps in three dimensions. The method for producing these “optical knots,” described in the Optical Society of America’s journal Optics Express, offers the potential to enable fusion energy as a practical power source.

The work, conducted in the laboratory of David Grier, chair of NYU’s Department of Physics, builds on an earlier Grier creation, “holographic optical traps,” which use computer-generated holograms to trap and move microscopic objects in three dimensions.

Unlike Gaussian laser beams, which focus to a spot, the holographically modified beams being used to create extended optical traps focus to curves, much like the bright patterns on the bottom of swimming pools. These bright curves, in turn, can be tied in knots.

Knotted traps are made by imprinting a computer-generated hologram on the wavefronts of an ordinary beam of light. When the modified beam is brought to a diffraction-limited focus with a high-power lens, the region of maximum intensity takes the form of a three-dimensional curve. This curve can cross over and through itself to trace out a knot. Moreover, the same hologram can redirect the light’s radiation pressure to have a component along the curve, so that the total optical force “threads the knot.”

Holographic optical traps can be used to confine and manipulate small objects—ranging in size from a few nanometers to several hundred micrometers—in 3D. This is a highly desirable capability for a wide range of research applications, including medical diagnostics and drug discovery.

Elisabeth Shanblatt, as an undergraduate student in NYU’s College of Arts and Science and one of the paper’s co-authors, was working on a project with Grier to create extended optical traps that follow arbitrary curves in 3D, when they discovered that the extended traps could cross through each other and thus form knots.

Extended holographic optical traps are especially useful, for example, for moving small objects such as biological cells through microfluidic lab-on-a-chip devices. They can also be used to measure small interactions among such objects, which is a useful basis for medical diagnostic tests.

To project their holograms, Shanblatt and Grier used a device called a “liquid-crystal spatial light modulator,” which is similar to a conventional LCD television screen. The spatial light modulator imprints a calculated pattern of phase shifts onto the wavelengths of the light. Rather than focusing to a spot of light, the modified beam focuses to a 3D curve that crosses over itself to form a knot.

The method has to potential to create knotted current loops of charged particles in high-temperature plasmas—a long-sought goal for developing fusion energy as a practical power source.

Fusion reactors work by smashing light atomic nuclei into each other so hard that the nuclei fuse into heavier elements, releasing lots of energy in the form of hot neutrons. The best way to accomplish this, Grier says, is to heat the light atoms to a high enough temperature so that their kinetic energy can overcome all of the barriers to fusion during random collisions. At these temperatures, the atoms’ electrons ionize and the gas becomes a plasma.

In addition, Grier adds, by passing large electric currents through the plasma, you can heat the plasma to greater temperatures. He notes that it’s possible to manipulate the currents with magnetic fields to contain the hot plasma, preventing it from destroying its physical container.

Typically, problems occur when currents flowing through plasma in a fusion reactor become unstable; this is similar to what occurs when the currents flowing through the plasma in a neon sign flicker. The currents thrash around, cool the plasma, damage the container, and generally prevent the process from generating useful energy.

“If the currents in a plasma are tied into a knot, the knot can eliminate most, if not all, of these instabilities because the magnetic field lines generated by the knotted current can’t pass though each other,” explains Grier.

Shanblatt and Grier believe that projecting a knotted optical force field into a plasma might prove to be a good way to initiate a knotted current loop.

The work was funded, in part, by a grant from the National Science Foundation.