Jeffrey L. Rogers

Synchronization by nonlinear frequency pulling.

We analyze a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling motivated by the physics of arrays of nanoscale oscillators. We study the model for the mean field case of all-to-all coupling, deriving results for the onset of synchronization as the coupling or nonlinearity increase, and the fully locked state when all the oscillators evolve with the same frequency.

200 W self-organized coherent fiber arrays

We report producing 200 W coherent fiber laser arrays without active control. This outcome is obtained via self-organization using a non-fiber coupler for two- to ten-laser arrays.

Self-organized coherence in fiber laser arrays

Self-organized coherence between fiber lasers has been reported both via all-fiber 2x2 directional coupler trees and in spatially multi-core fibers. We have taken this a major step forward, coupling together a number of independent fiber lasers to obtain a spatially and spectrally coherent far field, with no active length, polarization, or amplitude control. The near field output comes from a spatial array rather than from a single fiber, making this approach scalable to extremely high power.

Synchronization by reactive coupling and nonlinear frequency pulling.

We present a detailed analysis of a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling. We study the model for the mean field case of all-to-all coupling, deriving results for the initial onset of synchronization as the coupling or nonlinearity increase, and conditions for the existence of the completely synchronized state when all the oscillators evolve with the same frequency. Explicit results are derived for the Lorentzian, triangular, and top-hat distributions of oscillator frequencies. Numerical simulations are used to construct complete phase diagrams for these distributions.

Exploiting Nonlinearity to Provide Broadband Energy Harvesting

Energy harvesters are a promising technology for capturing useful energy from the environment or a machine’s operation. In thispaperwehighlight ideasthatmight leadtoenergyharvesters that more efficiently harvest a portion of the considerable vibrational energy that is present for human-made devices and environments such as automobiles, trains, aircraft, watercraft, machinery, and buildings. Specifically, we consider how to exploit ideas based on properties of nonlinear oscillators with negative linear stiffness driven by periodic and stochastic inputs to design energy harvesters having large amplitude response over a broad range of ambient vibration frequencies. Such harvesters could improve upon proposed harvesters of vibrational energy based on linear mechanical principles, which only give appreciable response if the dominant ambient vibration frequency is close to the resonance frequency of the harvester.

Model for high-gain fiber laser arrays

Recent experiments have shown that a small number of fiber lasers can spontaneously form coherent states when suitably coupled. The observed synchrony persisted for a long time without any active control. In this paper, we develop a dynamical model for fiber laser arrays that is valid in the high gain regime. In the limiting case of a single laser analysis and simulations are presented that agree with physical expectations. Using simulations to examine array behavior we report results that are in qualitative agreement with laboratory observations.

Pattern formation in vertically oscillated convection

A fluid layer driven out of equilibrium by both a thermal gradient and time-periodic vertical oscillations displays a number of interesting behaviour. Here we review results from the first experimental investigation of this system as well as a number of related and novel numerical findings. At primary onset these results include modulation-enhanced conduction stability as well as fluid motion in either harmonic or subharmonic resonance with the drive frequency. In the nonlinear parameter range we find a wide variety of singly resonant states, a region where both temporal responses coexist, and a number of novel coexistence patterns–including quasiperiodic crystals and superlattices. Four-wave interactions between harmonic and subharmonic modes are shown to select the structure of these complex patterns. The role of inversion symmetry in the emerging planforms is discussed.

Coherence between two coupled lasers from a dynamics perspective

We compare a simple dynamical model of fiber laser arrays with independent experiments on two coupled lasers. The degree of agreement with experimental observations is excellent. Collectively the evidence presented supports this dynamical approach as an alternative to the traditional static eigenmode analysis of the coupled laser cavities.

Effect of Gain-Dependent Phase Shift on Fiber Laser Synchronization

Recent experiments have demonstrated synchronization of fiber laser arrays at low and moderate pump levels. It has been suggested that a key dynamical process leading to synchronized behavior is the differential phase shift induced by the gain media. We explore theoretically the role of this effect in generating inphase dynamics. We find that its presence can substantially enhance the degree of inphase stability to an extent that could be practically important. At the same time, our analysis shows that a gain-dependent phase shift is not a necessary ingredient in the dynamical selection of the inphase state, thus, leading us to reconsider the essential mechanism behind inphase selection in fiber laser arrays.

Vortices and the entrainment transition in the two-dimensional Kuramoto model

We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling K is larger than a threshold K{E} , there is a macroscopic cluster of frequency-synchronized oscillators. We explain why the macroscopic cluster disappears at K{E} . We view the system in terms of vortices, since cluster boundaries are delineated by the motion of these topological defects. In the entrained phase (K>K{E}) , vortices move in fixed paths around clusters, while in the unentrained phase (K<K{E}) , vortices sometimes wander off. These deviant vortices are responsible for the disappearance of the macroscopic cluster. The regularity of vortex motion is determined by whether clusters behave as single effective oscillators. The unentrained phase is also characterized by time-dependent cluster structure and the presence of chaos. Thus, the entrainment transition is actually an order-chaos transition. We present an analytical argument for the scaling K{E}∼K{L} for small lattices, where K{L} is the threshold for phase locking. By also deriving the scaling K{L}∼log N , we thus show that K{E}∼log N for small N , in agreement with numerics. In addition, we show how to use the linearized model to predict where vortices are generated.