Prof. Gauthier is interested in a broad range of topics in the fields of nonlinear and quantum optics, biophysics, and nonlinear dynamical systems.

In the area of optical physics, his group is studying the fundamental characteristics of highly nonlinear light-matter interactions and is using this understanding to develop practical devices. Recently, they have been interested in tailoring the group velocity of laser-driven materials to achieve group velocities that are much greater than or much less than the speed of light in vacuum (so-called fast and slow light). They are measuring the speed at which information travels through fast- and slow-light media to test our understanding of the special theory of relativity, and they are transitioning the slow-light technology to telecommunications applications such as all-optical signal regeneration and processing. Another recent interest is the development of the world's most sensitive all-optical switch. Currently, they have observed switching with an energy density as low as a few hundred yoctoJoules per atomic cross-section, indicating that the switch should be able to operate at the single-photon level.

In the area of biophysics, his group is investigating the electrical activity of the heart from a nonlinear dynamics perspective. It is a multi-disciplinary effort consisting of faculty and students from the departments of Biomedical Engineering, Mathematics, and Physics. They are developing techniques for controlling cardiac dynamics using real-time closed-loop feedback, with the long-term goal of realizing an implantable ultra-low-energy cardiac defibrillator for people at high risk of sudden cardiac death. They are also developing new experimental methods for characterizing the nonlinear response of cardiac tissue and using the resulting data to guide the development of mathematical models for describing the generation and propagation of electrical waves in the heart.

In the area of nonlinear dynamics, his group is interested in the control and synchronization of chaotic devices, especially optical and radio-frequency electronic systems.  They are developing new methods for private communication of information using chaotic carriers, using chaotic elements for distance sensing (e.g., low-probability-of-detection radar), using networks of chaotic elements for remote sensing, and using chaotic elements for generating truly random numbers at high data rates.