Modeling of Passively Mode‐Locked Semiconductor Lasers

Vladimirov, Andrei; Рачинский, Дмитрий; Wolfrum, Matthias

doi:10.1002/9783527639823.ch8

Cited by 22 publications

(13 citation statements)

References 59 publications

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“…Similar periodic pulsating solutions have been previously found in the laser model (1.1) and its variations [40,41]. The main advance of this work is a detailed asymptotic analysis of the pulses and linear stability analysis near the bifurcation point.…”

Section: Resultssupporting

confidence: 79%

Periodic pulsating dynamics of slow–fast delayed systems with a period close to the delay

2017

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We consider slow–fast delayed systems and discuss pulsating periodic solutions, which are characterised by specific properties that (a) the period of the periodic solution is close to the delay, and (b) these solutions are formed close to a bifurcation threshold. Such solutions were previously found in models of mode-locked lasers. Through a case study of population models, this work demonstrates the existence of similar solutions for a rather wide class of delayed systems. The periodic dynamics originates from the Hopf bifurcation on the positive equilibrium. We show that the continuous transformation of the periodic orbit to the pulsating regime is simultaneous with multiple secondary almost resonant Hopf bifurcations, which the equilibrium undergoes over a short interval of parameter values. We derive asymptotic approximations for the pulsating periodic solution and consider scaling of the solution and its period with the small parameter that measures the ratio of the time scales. The role of competition for the realisation of the bifurcation scenario is highlighted.

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Section: Resultssupporting

confidence: 79%

Periodic pulsating dynamics of slow–fast delayed systems with a period close to the delay

2017

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“…The linearization at the equilibrium (4) with A = 0 leads to the same characteristic equation ( 8) for the eigenvalues. Hence, this equilibrium looses stability at the threshold and then undergoes a cascade of Hopf bifurcations at the same points (12) and with the same frequencies (11) as model ( 1)-( 3) with increasing the bifurcation parameter g 0 . If, instead of (17), we assume the relation…”

Section: Variations Of the Main Modelmentioning

confidence: 90%

“…which is dual to formulas (11), (12). The curve (13) carrying the eigenvalues simply moves to the right with increasing g 0 , see Figure 2a.…”

Section: Main Prototype Modelmentioning

confidence: 96%

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Pulsating dynamics of slow-fast population models with delay

Kravetc,

Rachinskii,

Vladimirov

2016

Preprint

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We discuss a bifurcation scenario which creates periodic pulsating solutions in slow-fast delayed systems through a cascade of almost simultaneous Hopf bifurcations. This scenario has been previously associated with formation of pulses in a delayed model of mode-locked semiconductor lasers. In this work, through a case study of several examples, we establish that a cascade of Hopf bifurcations can produce periodic pulses, with a period close to the delay time, in population dynamics models and explore the conditions that ensure the realization of this scenario near a transcritical bifurcation threshold. We derive asymptotic approximations for the pulsating solution and consider scaling of the solution and its period with the small parameter that measures the ratio of the time scales. The role of competition for the realization of the bifurcation scenario is highlighted.

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“…Semiconductor mode locked lasers are compact reliable low-cost devices that emit short optical pulses at high repetition rates suitable for applications in telecommunications, machining, probing, all optical systems, etc. [50]. We use a delay differential model of a passively mode-locked laser proposed in [51].…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers

2018

J. Nonlinear Var. Anal.

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The goal of this paper is to study the equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in a system of five identical passively mode-locked semiconductor lasers coupled in the S 5-equivariant fashion. Each laser is described by a delay differential model respecting a spacial S 1-symmetry. The existence of branches of relative periodic solutions together with their symmetric classification is established using the equivariant twisted S 5 × S 1-degree with one free parameter. Theoretical results are supported by numerical simulations.

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Modeling of Passively Mode‐Locked Semiconductor Lasers

Cited by 22 publications

References 59 publications

Periodic pulsating dynamics of slow–fast delayed systems with a period close to the delay

Periodic pulsating dynamics of slow–fast delayed systems with a period close to the delay

Pulsating dynamics of slow-fast population models with delay

Hopf bifurcation of relative periodic solutions in a system of five passively mode-locked lasers

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