Nonlinear Optics & Photonics

The primary goal of Arizona Center For Mathematical Sciences - ACMS, Director : Dr. J. V. Moloney, is to provide an environment for research and learning in the Mathematical Sciences. Its basic research themes are the modeling, understanding and applicability of nonlinear processes in optics, fluids, neural networks, and random distributed systems with continuing investigations into pattern dynamics, percolation, behavior of lattice gasses, nonlinear stability, low dimensional chaos, turbulence, dynamical systems and the nature of integrable systems of differential equations.

Research and learning takes place at all levels. The breadth of activity and spectrum of interest and talent among visiting collegaues serves to stimulate interdisciplinary work and promote the cross fertilization of ideas. Graduate students interested in applied mathematics enjoy a unique environment in which they can experience first hand the unity in the approaches (modeling, simulation, analysis, and involvement in experiments) with which mathematical scientists tackle a diverse set of problems from all areas of the physical sciences. There are several ongoing weekly working seminars in addition to regular departmental colloquia. These are in the areas of applied analysis, computation, dynamical systems, nonlinear optics, neural networks, integrable systems, and mathematical physics.

Nonlinear Optics has attained a special status at ACMS and the exceptional multidisciplinary culture at Arizona provides a unique environment for collaborative research with colleagues at the Optical Sciences Center, and the Program in Applied Mathematics. Graduate students in Applied Mathematics, Optical Sciences and Physics work together on research projects at the frontiers of this exciting field. Tucson's designation as "Optics Valley", reflects the large concentration of Optics industries in the region and provides a strong industrial link to the University of Arizona.


The study of propagation of light pulses in nonlinear optical media is of great technological interest. It also leads to some beautiful and sophisticated mathematics. The interplay of nonlinearity (the index of refraction depends on the intensity of the light) and randomness (the presence of loss and quantum mechanical effects lead to noise, and medium imperfections as well as the random nature of the data stream) leads to nontrivial problems in stochastic partial differential equations. Nanophotonics is a rapidly developing new area of science of great importance for technology and basic science. It is based on new materials incorporating inclusions of nanoscale size. These materials do not exist in nature and they display exotic properties which can be used for design of new optical devices with superb characteristics. Nanophotonics studies the interaction of light with structures formed by nanoparticles.These subjects must be studied using a combination of mathematical analysis, ideas from theoretical physics, quantum mechanics and numerical simulation. Professors Gabitov and Indik use a 48 node beowulf cluster together with such analytical methods to study these problems. The group runs the "Nonlinearity Randomness and Waves" seminar that meets Wednesdays at 3PM. dispersion managed bit sequence The figure shows the way that a short bit sequence will propagate over one period in a fiber with strong dispersion management. The horizontal axis represents time (in the traveling frame) and the vertical axis is propagation distance.


Moysey Brio, Ildar Gabitov, Robert Indik, J.V.Moloney