Coupled Lugiato-Lefever equation for nonlinear frequency comb generation at an avoided crossing of a microresonator

Guided-mode coupling in a microresonator generally manifests itself through avoided crossings of the corresponding resonances. This coupling can strongly modify the resonator local effective dispersion by creating two branches that have dispersions of opposite sign in spectral regions that would otherwise be characterized by either positive (normal) or negative (anomalous) dispersion. In this paper, we study, both analytically and computationally, the general properties of nonlinear frequency comb generation at an avoided crossing using the coupled Lugiato-Lefever equation. In particular, we find that bright solitons and broadband frequency combs can be excited when both branches are pumped for a suitable choice of the pump powers and the detuning parameters. A deterministic path for soliton generation is found.Comment: 9 pages, 5 figure

Spatiotemporal Model for Kerr Comb Generation in Whispering Gallery Mode Resonators

We establish an exact partial differential equation to model Kerr comb generation in whispering-gallery mode resonators. This equation is a variant of the Lugiato-Lefever equation that includes higher-order dispersion and nonlinearity. This spatio-temporal model, whose main variable is the total intracavity field, is significantly more suitable than the modal expansion approach for the theoretical understanding and the numerical simulation of wide-span combs. It allows us to explore pulse formation in which a large number of modes interact cooperatively. This versatile approach can be straightforwardly extended to include higher-order dispersion, as well as other phenomena like Raman, Brillouin and Rayleigh scattering. We demonstrate for the first time that when the dispersion is anomalous, Kerr comb generation can arise as the spectral signature of dissipative cavity solitons, leading to wide-span combs with low pumping.Comment: 5 pages, 2 figure

Effects of Birefringence and Nonlinearity on Optical Pulse Propagation in New Types of Optical Fibers

The purpose of this grant was to allow us to complete work that we had already begun on spun optical fibers and to begin studies of holey and photonic crystal optical fibers. The work on spun optical fibers was completed with great success. It led to several publications in collaboration with our co-workers at the Universita di Padova, and the student who carried out this work received a major award from the Universita di Padova. The work on holey and photonic crystal fibers has proceeded more slowly, but, in collaboration with Korean co-workers at the Gwangju Institute of Science and Technology, we have developed three different computational models that allow us to calculate the modes of these fibers: a Galerkin model, a plane wave model, and a multipole model. We have applied these models to the study of mode coupling in periodic gratings. In collaboration with scientists at the Naval Research Laboratory, we have also applied these models to the study of pulse compression in tapered fibers and the development of nonlinear fibers that are capable of handling large powers in high-index and chalcogenide glasses. European and Asian countries have made large investments in the development of these new glass technologies, while the United States has not. As a consequence, the United States is falling behind in what we believe will prove to be a critical area of nanotechnology. It is our view that by investing in this project, the Department of Energy has helped lay the groundwork for future development of special fiber technology in the United States, once the decision has been made that the United States cannot continue to stand on the sidelines as this technology--which appears to have great commercial and military value--is developed elsewhere