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

Nonlinear Stabilization of High-Energy and Ultrashort Pulses in Passively Modelocked Lasers with Fast Saturable Absorption

The two most commonly used models for passively modelocked lasers with fast saturable absorbers are the Haus modelocking equation (HME) and the cubic-quintic modelocking equation (CQME). The HME corresponds to a special limit of the CQME in which only a cubic nonlinearity in the fast saturable absorber is kept in the model. Here, we use singular perturbation theory to demonstrate that the CQME has a stable high-energy solution for an arbitrarily small but non-zero quintic contribution to the fast saturable absorber. As a consequence, we find that the CQME predicts the existence of stable modelocked pulses when the cubic nonlinearity is orders of magnitude larger than the value at which the HME predicts that modelocked pulses become unstable. This intrinsically larger stability range is consistent with experiments. Our results suggest a possible path to obtain high-energy and ultrashort pulses by fine tuning the higher-order nonlinear terms in the fast saturable absorber.Comment: 8 pages, 6 figures, submitted to PR

Solitary waves due to x(2):x(2) cascading

Solitary waves in materials with a cascaded x(2):x(2) nonlinearity are investigated, and the implications of the robustness hypothesis for these solitary waves are discussed. Both temporal and spatial solitary waves are studied. First, the basic equations that describe the x(2):x(2) nonlinearity in the presence of dispersion or diffraction are derived in the plane-wave approximation, and we show that these equations reduce to the nonlinear Schrödinger equation in the limit of large phase mismatch and can be considered a Hamiltonian deformation of the nonlinear Schrödinger equation. We then proceed to a comprehensive description of all the solitary-wave solutions of the basic equations that can be expressed as a simple sum of a constant term, a term proportional to a power of the hyperbolic secant, and a term proportional to a power of the hyperbolic secant multiplied by the hyperbolic tangent. This formulation includes all the previously known solitary-wave solutions and some exotic new ones as well. Our solutions are derived in the presence of an arbitrary group-velocity difference between the two harmonics, but a transformation that relates our solutions to zero-velocity solutions is derived. We find that all the solitary-wave solutions are zero-parameter and one-parameter families, as opposed to nonlinear-Schrödinger-equation solitons, which are a two-parameter family of solutions. Finally, we discuss the prediction of the robustness hypothesis that there should be a two-parameter family of solutions with solitonlike behavior, and we discuss the experimental requirements for observation of solitonlike behavior.Peer ReviewedPostprint (published version

Trapping of light beams and formation of spatial solitary waves in quadratic nonlinear media

Summary form only given. In this paper we report the outcome of our comprehensive investigations to study the dynamics of the beam trapping in both bulk crystals and optical planar waveguides made of quadratic nonlinear media in second-harmonic generation configurations. We address and discuss the suitable experimental conditions required to form spatial solitary waves in critical phase-matching and quasi-phase-matching settings.Peer ReviewedPostprint (published version

A fourth-order Runge-Kutta in the interaction picture method for coupled nonlinear Schrodinger equation

A fourth-order Runge-Kutta in the interaction picture (RK4IP) method is presented for solving the coupled nonlinear Schrodinger equation (CNLSE) that governs the light propagation in optical fibers with randomly varying birefringence. The computational error of RK4IP is caused by the fourth-order Runge-Kutta algorithm, better than the split-step approximation limited by the step size. As a result, the step size of RK4IP can have the same order of magnitude as the dispersion length and/or the nonlinear length of the fiber, provided the birefringence effect is small. For communication fibers with random birefringence, the step size of RK4IP can be orders of magnitude larger than the correlation length and the beating length of the fibers, depending on the interaction between linear and nonlinear effects. Our approach can be applied to the fibers having the general form of local birefringence and treat the Kerr nonlinearity without approximation. For the systems with realistic parameters, the RK4IP results are consistent with those using Manakov-PMD approximation. However, increased interaction between the linear and nonlinear terms in CNLSE leads to increased discrepancy between RK4IP and Manakov-PMD approximation.Comment: 12 pages, 4 figures, 1 Table, submitted to Optics Express

Speech Communication

Contains report on one research project.U. S. Air Force (Electronics Systems Division) under Contract AF 19(628)-5661National Institutes of Health (Grant 2 ROI NB-04332-06)Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DA 28-043-AMC-02536(E