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Nelin. Dinam., 2019, Volume 15, Number 4, Pages 429–455 (Mi nd672)  

Complex Dynamics Induced by Asymmetry in Coupled Laser Systems

A. Bountisa, Ya. Kominisb, J. Shenac, V. Kovanisd

a Department of Mathematics, School of Science and Humanities, Nazarbayev University, Kabanbay batyr 53, Nur-Sultan, 010000 Republic of Kazakhstan
b School of Applied Mathematical and Physical Science, National Technical University of Athens, 9 Iroon Polytechneiou, Zographou, Athens 15773, Greece
c National University of Science and Technology MISiS, Leninsky prosp. 4, Moscow, 119049, Russia
d Bradley Department of Electrical and Computer Engineering, Virginia Tech, 1185 Perry Street, 453 Whittemore (0111), Blacksburg, VA 24061, USA

Abstract: Coupled semiconductor lasers are systems possessing complex dynamics, which makes them interesting for many applications in photonics. In this paper, we first review our results on the existence and stability of asymmetric phase-locked states of a single dimer consisting of two coupled semiconductor lasers. We show that stable phase-locked states of arbitrary asymmetry exist, whose field amplitude ratio and phase difference can be dynamically controlled by appropriate electronic current injection. Moreover, we obtain stable limit cycles with asymmetric characteristics, emerging through Hopf bifurcations from these phase-locked states. Also, we emphasize the importance of exceptional points, and we show that asymmetry enables their existence in extended regions of parameter space. The dynamics of asymmetric dimers under small signal modulation of the pumping current is also investigated and the occurrence of antiresonances and sharp resonances with very high frequencies is demonstrated. Finally, we describe our recent findings on optically coupled arrays of coupled dimers and explore their fascinating nonlinear dynamics. In particular, we couple in an appropriate way a large number of dimers and show that, depending on their degree of asymmetry, they exhibit organized high amplitude oscillations, or oscillate very close to phase-locked states, suggesting that such photonic networks may prove useful in a variety of beam forming and beam shaping applications.

Keywords: coupled mode equations, semiconductor laser arrays, Hopf bifurcations, limit cycle oscillations, coherence in photonic arrays

Funding Agency Grant Number
Ministry of Education and Science of the Republic of Kazakhstan 339/76-2015
This research is partly supported by the ORAU grant entitled Taming Chimeras to Achieve the Superradiant Emitter, funded by Nazarbayev University, Republic of Kazakhstan. This work was partially also supported by the Ministry of Education and Science of the Republic of Kazakhstan via Contract No. 339/76-2015.


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MSC: 34C05, 34D23, 37C27, 37G15
Received: 22.09.2019

Citation: A. Bountis, Ya. Kominis, J. Shena, V. Kovanis, “Complex Dynamics Induced by Asymmetry in Coupled Laser Systems”, Nelin. Dinam., 15:4 (2019), 429–455

Citation in format AMSBIB
\by A.~Bountis, Ya.~Kominis, J.~Shena, V.~Kovanis
\paper Complex Dynamics Induced by Asymmetry in Coupled Laser Systems
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 4
\pages 429--455

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