ARCHIVE. Compared to studies in the fields of biology and engineering, nonlinear dynamics might not be so obvious in terms of its worth. In reality, it is an area of physics research that permeates the natural world and a field integral to so many others. Dr. Milivoj Belic won the 2012 QNRF Research Team of the Year Award for his prolific contributions in this field, accounting for more than ten percent of Texas A&M at Qatar’s publications. His team’s specific focus is nonlinear optics, wherein they research the behavior of materials and laser light as they interact.

“What we do is manipulate photons, which are particles of light that can also be considered waves,” Dr. Belic said, “and we consider processes that happen in material when you shine laser light on them. So in essence we play with the wave phenomena. This is under the umbrella of quantum mechanics, but we do not do quantum mechanics; we do nonlinear optics.”

In linear optics photons do not “talk to” each other; however, in nonlinear optics they do, through the medium. Understanding the conversations—through the evolving language of nonlinear equations, i.e., nonlinear dynamics—helps researchers understand the material under study.

“In physics, very few things are done and finished once and for all, at least what has been done within the last century,” Dr. Belic said. “Most of those things are a never-ending story. Bit by bit you discover new things. But the problems and topics of research are there … an immense number of unsolved questions and half-baked answers.”

By running lasers through different types of materials such as gases, photo-refractive crystals, and nematic liquid crystals, Dr. Belic and his team observe the entire system as the light propagates, to get an idea of the material's response and the processes at play. The equations describing these processes are linked to waves and light and also with the response of the material—so it is both the response of the material and the behavior of the laser light, together, that are studied.

“We attack nonlinear equations; so it’s a mathematical physics problem. Now with such equations, it’s not like ‘aha, that’s it, we solved it!’—most often, it cannot be solved, at least not analytically. You have to try something different. Still, for many such equations we found ways to treat them analytically and this is something for which my team is becoming known internationally.”

The mathematical language around many physical phenomena is based on differential equations. A classic example would be the Schrödinger equation, which describes how the state of a quantum system changes over time. This is useful in linear systems and quantum mechanics. However, Dr. Belic explained that nonlinear dynamics is even more challenging than quantum mechanics. Specifically, it involves nonlinear Schrödinger equations and relies heavily on computers to crunch numbers because the responses in nonlinear systems are sometimes so erratic, evading analysis through the equations used in more predictable systems. Interestingly, most natural systems and materials require nonlinear thinking.

“Laws of physics are laws of nature,” Belic explained. “You have to master them and you have to know how to apply them. Mathematics is the language of nature. Things in nature are best explained through mathematics. Physics is essentially applied mathematics. In theoretical physics, you have to reason. But then you have experimental physics, so you have to experiment—to make a model, make predictions and test them. This can also turn out the other way around, where somebody finds something experimentally and then explains it.”

Whereas research in many fields is goal or product oriented, Dr. Belic said his team’s research is often curiosity-driven. A co-evolution of experiment and theory, the research requires a constant striving into the unknown.

“We are always trying to understand things, to contribute to a bank of understanding about nature at the basic level,” Dr. Belic explained. “We don’t produce gadgets—we want to know how they work. Here in Qatar, we had to start from scratch, so we started with theory. Some of our experiments are performed in other places such as Australia, the US, Serbia, France and Germany … we have a lot of collaborators.

“This work could contribute to other fields, not tomorrow, not today but in the foreseeable future,” he continued. “Newton formulated his laws in mathematical terms, and at the time people were asking ‘what is this for?’ It was a hundred years before people realized how useful they were.”

What excites Dr. Belic now is the potential to collaborate with researchers in other fields, enriching findings with the basic knowledge of physics and properties of materials.

“Before, physicians were doing their thing, mathematicians were doing their thing, chemists were doing their thing, and that approach was disjointed. But now we realize that if you want to make progress in brain research you cannot do so by the medical profession alone. For example, one of my collaborators is making a mathematical model of a brain cancer tumor. We all have to work together and that is the idea. And that is really the push nowadays with the funding agencies. Our team would like to go and collaborate with the Qatar Foundation institutes and has begun discussions with many of them.”

Establishing homegrown teams that are capable of producing great research requires a long period of cultivation. Qatar Foundation and TAMUQ have chosen this path and have generously supported the creation of high-quality team-oriented research centers. This turns the spotlight toward Qatar Foundation and TAMUQ as well as the whole Middle Eastern region. We greatly appreciate the strong support we have been given by TAMUQ and QNRF, and look forward to a bright future,” Dr. Belic said.

NPRP 25-6-7-2

Nonlinear Photonics for All-optical Telecommunication and Information Technologies.