The investigator proposes an analysis of coupled oscillators motivated by problems occurring in the study of lasers. Coupled oscillator models may result from coupling individual laser devices or from a modal decomposition of a multimode laser. For the models under consideration, the amplitude of the oscillations is an important dynamical variable; this is in contrast to limit-cycle oscillators where the amplitude is often slave to the phase, hence reducing the dimension of the dynamical system. Thus, even if the system maintains a desired phase-locked state, amplitude instabilities can limit the usefulness of the device in certain parameter regimes. Also of importance is that the use of lasers as a component of a communications system requires actively modulating the laser output. Dissipation is typically very weak, so excitation can lead to long undesirable transients or to sustained chaos. Thus, the effect of excitations ranging from periodic to impulsive must be well understood. Finally, the laser models are highly singular due to time scales ranging from milliseconds to nanoseconds; this provides both analytical and numerical challenges in their study. The investigator will apply such tools as asymptotic analysis, local and global bifurcation theory, and numerical simulation and data analysis techniques to investigate modulation effects, amplitude and phase control, and localization dynamics in coupled solid- state lasers and multimode fiber lasers.
Coupled lasers are being used in applications such as space communications, optical interconnects, fiber-optic communications, and optical beam steering. Some important design goals of coupled laser systems are to obtain higher output intensity of the system or achieve beam steering. The problems investigated in this proposal will further the understanding of these often unstable systems and lead to the achievement of control of the desired laser output. Furthermore, wide-ranging system configurations and many different coupling mechanisms (ranging from nearest neighbor, to non-local, to global) allow this work to aid not only laser technology, but also the study of coupled oscillators appearing in other applications.
