Numerical Bifurcation Analysis for Multisection Semiconductor Lasers

Sieber, Jan

doi:10.1137/s1111111102401746

Cited by 52 publications

(63 citation statements)

References 26 publications

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“…It should be noted that there exists a generalized (Bautin) Hopf bifurcation (not shown) on each Hopf curve when they start to approach each other in the low pump region. At this codimension-2 bifurcation point, the supercritical Hopf bifurcation becomes subcritical [37], thus no stable period orbit can be found when crossing the Hopf curve.…”

Section: Bifurcation Scenariosmentioning

confidence: 98%

Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers

Susanto

Cemlyn

et al. 2017

Phys. Rev. A

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A detailed stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers (VCSELs) is presented. We consider both steady-state and dynamical regimes. In the case of steady-state operation, we carry out a small-signal (asymptotic) stability analysis of the steady-state solutions for a representative set of spin-VCSEL parameters. Compared with full numerical simulation, we show this produces surprisingly accurate results over the whole range of pump ellipticity, and spin-VCSEL bias up to 1.5 times the threshold. We then combine direct numerical integration of the extended spin-flip model and standard continuation technique to examine the underlying dynamics. We find that the spin VCSEL undergoes a period-doubling or quasiperiodic route to chaos as either the pump magnitude or polarization ellipticity is varied. Moreover, we find that different dynamical states can coexist in a finite interval of pump intensity, and observe a hysteresis loop whose width is tunable via the pump polarization. Finally we report a comparison of stability maps in the plane of the pump polarization against pump magnitude produced by categorizing the dynamic output of a spin VCSEL from time-domain simulations, against supercritical bifurcation curves obtained by the standard continuation package AUTO. This helps us better understand the underlying dynamics of the spin VCSELs.

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Section: Bifurcation Scenariosmentioning

confidence: 98%

Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers

Susanto

Cemlyn

et al. 2017

Phys. Rev. A

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“…We show multipulse excitability here for the example of an optically injected semiconductor laser, but, in fact, this phenomenon may occur in any at least three-dimensional system with Belyakov bifurcation points. Other examples of systems with Belyakov points are an atmospheric circulation model [10], a tritrophic food chain model [11], and a reduced model of a multisection semiconductor laser [12].We work with an optically injected single-mode semiconductor laser because it is a technologically important example of a forced nonlinear oscillator [13] for which astonishingly accurate experimental verification of various types of dynamics was demonstrated, both at local and global scale [14]. A single-mode class-B laser with optical injection is described well by the rate equations…”

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confidence: 99%

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confidence: 99%

Multipulse Excitability in a Semiconductor Laser with Optical Injection

2002

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An optically injected semiconductor laser can produce excitable multipulses. Homoclinic bifurcation curves confine experimentally accessible regions in parameter space where the laser emits a certain number of pulses after being triggered from its steady state by a single perturbation. This phenomenon is organized by a generic codimension-two homoclinic bifurcation and should also be observable in other systems. DOI: 10.1103/PhysRevLett.88.063901 PACS numbers: 42.65.Sf, 05.45. -a, 42.55.Px A system is called excitable when it produces a large nonlinear response to a small but sufficiently large perturbation from its stable equilibrium. When perturbed above a certain threshold, an excitable system makes a large excursion in phase space leading to a large amplitude pulse. It then settles back to the stable equilibrium in what is called the refractory period. Here we use the example of an optically driven semiconductor laser to show that an excitable response to a single stimulus may have a form of not just a single pulse but of a certain fixed number of pulses. How many pulses are produced depends on the laser's operating conditions.The notion of excitability was first introduced in biology to describe the spiking behavior of nerve cells [1] and later found in reaction-diffusion systems [2]. More recently different types of excitability were found in optical systems, ranging from nonlinear cavities with temperaturedependent absorption [3] to lasers with saturable absorber [4], optical feedback [5], and optical injection [6]. In lasers essentially two types of excitability are found [4]: the classic case of excitability on an invariant circle, and excitability in the vicinity of a homoclinic bifurcation, found first in lasers with saturable absorber [4] and then in multisection distributed feedback lasers [7]. All these examples of excitability were associated with a single-pulse response to a single perturbation. A double-pulse excitable response observed in a laser with optical feedback was explained as the result of noise on a two-dimensional model [5].Our main result is that a multipulse response to a single perturbation is a natural and deterministic phenomenon. It is an example of excitability near a homoclinic bifurcation, but in this case near an n-homoclinic bifurcation, where the homoclinic orbit (to a saddle focus) closes up not after the first but after the nth global loop; see Figs. 2 and 4 below. The key element is a generic bifurcation structure of tongues formed by n-homoclinic bifurcation curves in parameter space. These tongues are organized by special points called Belyakov bifurcation points [8,9], and inside each such tongue a different number of pulses will be triggered. We show multipulse excitability here for the example of an optically injected semiconductor laser, but, in fact, this phenomenon may occur in any at least three-dimensional system with Belyakov bifurcation points. Other examples of systems with Belyakov points are an atmospheric circulation model [10], a tritrophic food ch...

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“…5. The inspection of the changing optical spectra and the bifurcation analysis of the similar narrow waveguide multisection edge-emitting semiconductor lasers [6,31,34] allows us to identify it as a saddle-node bifurcation. This suggestion is supported also by the type of transient P out (t) just before the bifurcation (see Fig.…”

Section: Results Of Numerical Simulationsmentioning

confidence: 99%

Numerical Algorithms for Simulation of Multisection Lasers by Using Traveling Wave Model

Čiegis

Radziunas

Lichtner

2008

Mathematical Modelling and Analysis

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Abstract. Sequential and parallel algorithms for the simulation of the dynamics of high-power semiconductor lasers is presented. The model equations describing the multisection broad-area semiconductors lasers are solved by the finite difference scheme, which is constructed on staggered grids. This nonlinear scheme is linearized applying the predictor-corrector method. The algorithm is implemented by using the ParSol tool of parallel linear algebra objects. For parallelization we adopt the domain partitioning method, the domain is split along the longitudinal axis. Results of computational experiments are presented, the obtained speed-up and efficiency of the parallel algorithm agree well with the theoretical scalability analysis.

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Numerical Bifurcation Analysis for Multisection Semiconductor Lasers

Cited by 52 publications

References 26 publications

Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers

Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers

Multipulse Excitability in a Semiconductor Laser with Optical Injection

Numerical Algorithms for Simulation of Multisection Lasers by Using Traveling Wave Model

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