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An interdisciplinary study on the properties of waves in symmetric metamaterials, or materials engineered to have properties that do not occur naturally, is set to unlock a new area of physics with a wide range of potential applications.

The Simons Collaboration on Extreme Wave Phenomena Based on Symmetries — a four-year, eight million dollar grant sponsored by the Simons Foundation — was launched this summer and brings together 14 professors from universities across the world, including Yale. The investigators’ fields of expertise range from theoretical physics and applied mathematics to modern optics and acoustics.

Many of the projects supported by the grant are based on the concept of parity-time, or PT, symmetry — the observation that certain systems are invariant when both space and time are reflected. In such systems, remarkable new properties arise, such as those pertaining to the propagation and transport of waves.

The field of PT symmetry was created in 1998 by Carl Bender, professor of physics at Washington University in St. Louis and an investigator on the Simons Collaboration. Bender, who is a mathematical physicist, told the News that he was surprised by the abundance of practical applications that have arisen from his theoretical work on PT symmetry.

“I never thought that anything I ever did, any paper that I ever wrote or any problem that I ever saw, would be testable in a laboratory,” Bender said. “And to my shock, this was a complete surprise, because about eight years after I published my paper on PT symmetry, there were experiments that started to be done.”

In explaining the concept of PT symmetry, Bender used the example of two glasses of water side-by-side, with one glass filling up and the other emptying out. When this system is reflected through space, the glasses swap positions, and when the system is reflected through time, the glass that was originally filling up is now emptying out, and vice versa. Since these reflections return the system to its original state, the system is considered PT symmetric.

Yale applied physics professor A. Douglas Stone, who is another investigator on the grant, told the News that his work is centered on what he calls “reflectionless scattering modes.” He said his main research goal is to construct waves that are absorbed in certain optical devices without being reflected.

Stone hopes to form a group with other scientists within the Simons Collaboration who work on similar topics to pursue further investigations, such as “controlling light in optical fibers and chips for communication and processing purposes.” He also commented on the role of symmetry in his research.

“Symmetry in physics is always a core principle which, if present, allows us to solve mathematically the equations of electromagnetism and quantum mechanics, which determine the propagation of waves in matter,” Stone wrote in an email to the News. “We are typically studying man-made structures with complex geometry. We then can choose to make the structure symmetric, so that it looks the same when reflected through a mirror at its center, and then the structure may guide waves in a very orderly manner.”

Stone noted that there are new, subtle symmetries impacting wave behavior that scientists are just beginning to understand. He said that this recent realization was a reason why the Simons Foundation funded the timely collaboration.

Stone further remarked that recent technological advances have facilitated his research.

“These new developments go hand in hand with the relatively recent ability of physical scientists to fabricate micro and nano scale devices, structures and materials to test or apply these and other theoretical ideas,” Stone wrote.

Katia Bertoldi, who is a professor of applied mechanics at the Harvard John A. Paulson School of Engineering and Applied Sciences and another investigator for the Simons Collaboration, wrote in an email to the News that her group has been focused in recent years on designing structures that support the breaking of symmetry caused by mechanical instability.

Bertoldi noted that it was difficult to predict how the project would evolve but offered some of her goals for the future collaboration.

“The effect of these symmetry breaking on wave propagation has not been fully studied and this is one of the focuses of this project,” she wrote.

Andrea Alù, professor of physics at the CUNY Graduate Center, proposed the grant and serves as its director.

In an email to the News, Alù expressed his excitement for the project, mentioning its potential applications in fields as diverse as biomedical imaging, wireless communications, energy harvesting and computing.

“I am very excited to be able to lead this collaborative effort and work with our team members towards this vision,” Alù wrote. “We have put together a team of outstanding scientists and seminal contributors to the field of metamaterials and wave physics to enable a thorough exploration of these opportunities and establish the foundations of a unified theory for extreme wave phenomena based on symmetries.”

Alù, whose own group has been investigating for many years the role of symmetry and symmetry-breaking in controlling extreme wave phenomena, told the News that the Simons Foundation’s mission to support this kind of fundamental research inspired him to propose the project.

Alù further emphasized his vision of collaboration by bringing together experts in a wide range of fields.

“Coming together in this long-term collaborative effort will certainly open new synergies for great discoveries,” Alù wrote. “We recently had the kick-off meeting of this project, which has already jumpstarted several interesting opportunities for discussion and collaborations.”

Bender echoed these hopes of collaboration, noting in particular the wonderful research that emerges when theorists and experimentalists work together.

He also emphasized that the ongoing project is not the solution to a specific problem, but rather a framework under which new developments can be made.

“There are so many new things that you could study, it’s just wonderful,” Bender said. “It’s like, you know, a kid who has a couple of toys and is getting tired of playing with them. And all of a sudden you take them to a great big toy shop, filled with new toys to play with.”

The Simons Foundation was founded in 1994 by Marilyn and James Harris Simons.

Zhemin Shao |

Zhemin Shao covers the University's endowment, finances and donations. He previously covered the Office of Career Strategy. Originally from Seattle, WA, he is a sophomore in Silliman College.