Dynamics of a semiconductor laser array with delayed global coupling.
Dynamics of a semiconductor laser array with delayed global coupling.
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DOI：
10.1103/physreve.64.016613
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发表时间：
2001-06
期刊：
影响因子：
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通讯作者：
G. Kozyreff;A. Vladimirov;P. Mandel
中科院分区：
文献类型：
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作者：
G. Kozyreff;A. Vladimirov;P. Mandel
我们研究了全局单模半导体激光器阵列的动力学，但通过公共外部反馈镜和最近邻相互作用进行弱耦合。我们试图确定阵列中所有激光器同相的条件，无论是稳定、周期性、准周期还是混沌状态，以便最大化输出远场强度。我们证明延迟可能是实现同相同步的有用控制参数。对于同相稳态，导致同相周期状态的延迟引起的 Hopf 分岔和导致反相周期状态的延迟无关的 Hopf 分岔之间存在竞争。这两种状态都经过分析描述，并且发现了准周期解的二次 Hopf 分岔。接近稳定状态时，阵列由一组场相位的 Kuramoto 方程描述。在第一个 Hopf 分岔之上，这些方程通过添加相位的二阶和三阶时间导数来推广。
We study the dynamics of an array of single mode semiconductor lasers globally but weakly coupled by a common external feedback mirror and by nearest neighbor interactions. We seek to determine the conditions under which all lasers of the array are in phase, whether in a steady, periodic, quasiperiodic, or chaotic regime, in order to maximize the output far field intensity. We show that the delay may be a useful control parameter to achieve in-phase synchronization. For the in-phase steady state, there is a competition between a delay-induced Hopf bifurcation leading to an in-phase periodic regime and a delay-independent Hopf bifurcation leading to an antiphased periodic regime. Both regimes are described analytically and secondary Hopf bifurcations to quasiperiodic solutions are found. Close to the stable steady state, the array is described by a set of Kuramoto equations for the phases of the fields. Above the first Hopf bifurcation, these equations are generalized by the addition of second and third order time derivatives of the phases.