Using Lagrange Points to Manipulate and Capture Light Beams with a Trojan Method

January 30, 2024 feature

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Article by Ingrid Fadelli, Phys.org

Various contemporary technologies, including communication and information processing systems, rely heavily on the accurate guidance and capture of optical waves. The most common method uses the total internal reflection of optical fibers. However, physicists have recently been studying techniques grounded in other physical mechanisms.

A novel technique for capturing light has been developed by researchers at the University of Southern California. This approach, published in Nature Physics, uses the unique properties of Lagrange points. These are the same equilibrium points that regulate the orbits of primitive celestial bodies like so-called Trojan asteroids in the sun-Jupiter system.

The paper's co-authors, Mercedeh Khajavikhan and Demetrios N. Christodoulides, explained to Phys.org that the discovery of Lagrange points dates back to the early work of Leonhard Euler and Joseph-Louis Lagrange. These points precisely balance the gravitational pull of two large bodies with centrifugal forces.

They said that although some Lagrange points are already used for strategic positioning in space for maintaining satellite stability while minimizing propellant consumption, their study investigates the fascinating properties of specific Lagrange points.

Trojan asteroids are a vast group of asteroids on the same orbit as the planet Jupiter. Lagrange points, named after Lagrange who discovered them, are positions where the gravitational force of two bodies in a system generate increased areas of attraction and repulsion.

Khajavikhan and Christodoulides used these unique physics to guide and trap light waves in their study. In the paper, they also illustrated that using certain Lagrange points for optical applications is akin to capturing Trojan asteroids within the sun-Jupiter orbit.

'A Lagrange optical waveguide is generated by running current through a helical wire in a treated silicon oil cylinder,' the co-authors explained.

'The thermo-optic effect thus creates a twisted index landscape where photon repulsion counterbalances with centrifugal force. A stable Lagrange point is surprisingly generated in this mountain-slope index profile, trapping a Trojan optical beam in two dimensions.'

In their laboratory, the researchers constructed a compact system to replicate the properties of Lagrange points. This system included a helically-shaped iron wire inserted into a medium with a temperature-dependent refractive index.

Passing electricity through the wire, they were able to heat this medium unevenly. This created what they referred to as a 'Trojan optical beam.'

The experiment yielded intriguing results as they discovered that in this refocusing refractive index setting, optical Trojan beams could be guided or trapped, which is not achievable under normal conditions.

'Moreover, the refractive index landscape where these optical beams are trapped is entirely bland. It does not contain any characteristics that would suggest a guiding response,' the researchers explained. 'In effect, the optical beam is trapped in a barren land—in nondescript regions without any standard waveguide structures.'

The team's recent work shows that the distinctive attributes of Lagrange points can be exploited to guide and trap light waves. This research may inspire future work and lead to new techniques for guiding optical waves in unconventional environments like liquids and gases where standard methods may not be effective.

'A possible avenue for further exploration could be the use of Trojan beams in amplifying (laser) systems, where optical gain or loss can establish alternative means for beam attraction or repulsion in fully dielectric media,' Khajavikhan and Christodoulides said.

So far, the researchers have only focused on the use of Lagrange points for guiding light beams. However, in the future the methodology they developed could also be tested in other areas of physics reaching beyond optics, for instance as a technique to guide acoustic waves or ultracold atoms.

'At this point, we plan to explore the possibility of guiding light in acoustic waves in both liquid and gaseous media,' Khajavikhan and Christodoulides added. 'Finally, of interest would be to observe for the first-time trapping and transporting dielectric micro- and nano-particles in Lagrange waveguides using optical tractor beams where multiple Lagrange points can be induced—an aspect that is not possible in celestial mechanics.'

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