相关论文: Explicit centre manifold reduction and full bifurc…
We consider damped driven Maxwell-Bloch equations for a single-mode Maxwell field coupled to a two-level molecule. The equations are used for semiclassical description of the laser action. Our main result is the construction of solutions…
In this paper, we consider an equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in systems of functional differential equations respecting $\Gamma \times S^1$-spatial symmetries. The existence of branches…
Topological lasers are of growing interest as a way to achieve disorder-robust single mode lasing using arrays of coupled resonators. We study lasing in a two-dimensional coupled resonator lattice exhibiting transitions between trivial and…
The Maxwell-Bloch dissipative equations describe laser dynamics. Under a simple condition on the parameters there exist two time dependent first integrals, that allow a nonstandard separation of variables in the equations. That condition…
We show the possibility of achieving experimentally a Takens-Bogdanov bifurcation for the nonlinear interaction of two transverse modes ($l = \pm 1$) in a $CO_2$ laser. The system has a basic O(2) symmetry which is perturbed by some…
We consider a delay differential equation (DDE) model for mode-locked operation in class-A semiconductor lasers containing both gain and absorber sections. The material processes are adiabatically eliminated as these are considered fast in…
A 1:2 internally resonant mechanical system can undergo secondary Hopf (Neimark-Sacker) bifurcations, resulting in a quasi-periodic response when the system is subject to harmonic excitation. While these quasi-periodic orbits have been…
The direct parametrisation method for invariant manifolds is adjusted to consider a varying parameter. More specifically, the case of systems experiencing a Hopf bifurcation in the parameter range of interest are investigated, and the…
In Part I of this paper, we have used spectral submanifold (SSM) theory to construct reduced-order models for harmonically excited mechanical systems with internal resonances. In that setting, extracting forced response curves formed by…
We study a three-dimensional dynamical system in two slow variables and one fast variable. We analyze the tangency of the unstable manifold of an equilibrium point with "the" repelling slow manifold, in the presence of a stable periodic…
Ring quantum cascade lasers have recently gained considerable attention, showing ultrastable frequency comb and soliton operation, thus opening a way to integrated spectrometers in the midinfrared and terahertz fingerprint regions. Thanks…
Studying time-dependent behavior in lasers is analytically difficult due to the saturating non-linearity inherent in the Maxwell-Bloch equations and numerically demanding because of the computational resources needed to discretize both time…
In this work, a numerical modal decomposition approach is applied to model the optical field of laser light after propagating through a highly multi-mode fiber. The algorithm for the decomposition is based on the reconstruction of measured…
Local bifurcation control is a topic of fundamental importance in the field of nonlinear dynamical systems. We discuss an original example within the context of storage-ring free-electron laser physics by presenting a new model that enables…
Self-tuning optical systems are of growing importance in technological applications such as mode-locked fiber lasers. Such self-tuning paradigms require {\em intelligent} algorithms capable of inferring approximate models of the underlying…
The dynamics of a model, originally proposed for a type of instability in plastic flow, has been investigated in detail. The bifurcation portrait of the system in two physically relevant parameters exhibits a rich variety of dynamical…
We investigate the dynamics of a two-photon laser under conditions where the spatial variation of the cavity field along the cavity axis is important. Main attention is paid to linear stability analysis and numerical investigation of a…
Period-doubling bifurcation is a universal dynamic of nonlinear systems, which has been extensively investigated in laser systems with a single transverse mode. This study presents an experimental observation and theoretical investigation…
We study the 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allow us to show that a…
In this Letter, we present a rigorous method to study the stability of periodic lasing systems. In a linear model, the presence of a continuum of modes (with arbitrarily close lasing thresholds) gives the impression that stable single-mode…