The Department of Electrical Engineering

My research focuses on nonlinear optics within the broader context of general wave physics. The emphasis is on propagation problems that are universal to wave systems, taking advantage of the fact that optical systems allow easy control of the input and direct imaging of the output. Using a healthy mix of theory and experiment, my group studies both basic nonlinear physics and advanced design issues for photonic applications.

As a prime example, my group is developing optical hydrodynamics in which the nonlinear propagation of light is described in terms of the equations for ideal fluid flow.    In this case, the light intensity acts as a fluid density while the direction of the wavefront gives an effective velocity. Such a fluid interpretation was the historical starting point for the wave theory of light as envisioned by Huygens, but its consequences have been underappreciated in the nonlinear case. For example, our work on optical shock waves has enabled a nonlinear generalization of Huygens’ principle: Superposition holds when two waves meet, but the combined field acts as a nonlinear source for new waves.           

Other examples follow by adding structure to the light. Propagation in waveguide arrays can be interpreted in terms of solid-state physics, while interactions between array sites can be described by coarse-grained hydrodynamics. Shock waves in photonic lattices provide a very efficient way to disperse energy, while the general behavior relates to waves in granular and molecular media, bubbly fluids, etc. Similarly, cascaded wave mixing can be viewed as a form of optical turbulence, and the propagation of statistical light can be treated as a photonic plasma.      

 

There are two primary results of these mappings: (1) optical modeling and observation of condensed-matter behavior that is difficult, if not impossible, to see by other means, and (2) a framework for the discovery of new optical physics. This latter consequence is particularly important, as better understanding of optical dynamics inevitably leads to the design of new photonic devices. Active areas along these lines include advanced waveguide systems, improved holographic techniques, and all-optical image/signal processing.