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T. M. Schneider

Publications and source records attributed to T. M. Schneider.

2 recordsLinked to original sources

Bifurcation structure of soliton self-injection locking in microresonators

Self-injection locking (SIL) of a diode laser to a high quality-factor microresonator has recently become increasingly important in hybrid integrated photonics, providing access to compact sub-Hz linewidth lasers. It was also shown to facilitate the access to dissipative Kerr solitons - the key to a low-noise coherent frequency comb on a photonic chip. However, the existence and stability ranges of SIL soliton states in experimentally controlled parameters are still not fully understood. Here we study the bifurcation structure of solutions in a model of soliton SIL in the weak-backscattering limit. We show that SIL produces soliton-number-dependent existence ranges of multi-soliton solutions in free-laser detuning and feedback phase parameters. We identify exclusive single-soliton existence regions and demonstrate dynamical access to single solitons in this region by direct numerical simulations using prescribed parameter sweeps.

physics.optics↗

Basin boundary, edge of chaos, and edge state in a two-dimensional model

In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the laminar flow, one notes a a qualitative change in its lifetime, from smoothly varying and short one on the laminar side to sensitively dependent on initial conditions and long on the turbulent side. The point of transition defines a point on the edge of chaos. Since it is defined via the lifetimes, the edge of chaos can also be used in situations when the turbulence is not persistent. It then generalises the concept of basin boundaries, which separate two coexisting attractors, to cases where the dynamics on one side shows transient chaos and almost all trajectories eventually end up on the other side. In this paper we analyse a two-dimensional map which captures many of the features identified in laboratory experiments and direct numerical simulations of hydrodynamic flows. The analysis of the map shows that different dynamical situations in the edge of chaos can be combined with different dynamical situations in the turbulent region. Consequently, the model can be used to develop and test further characterisations that are also applicable to realistic flows.

nlin.CD↗