Codimension Two Bifurcation in a Laser with Injected Signal

G. Oppo, H. Solari
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Abstract

The equations of a laser with injected signal have attracted interest not only in optics but also from the community of nonlinear dynamics physicists. After the pioneering works of Ref. [1] and [2] where the proper set of Maxwell-Bloch equations has been derived and integrated numerically, interesting dynamical effects ranging from the coexistence of conservative and dissipative behaviours [3] to the existence of codimension two bifurcations (CTB) [4] have been analysed. In Ref. [4], for example, a CTB was recognised to be responsible of the appearance of frequency pushed solutions which are counter-intuitive in a problem majorly related to locking phenomena. Recently, partial attempts of characterizing the degenerate nature of the CTB have been published [5]. However a complete unfolding of the CTB capable of showing analytically all the dynamical behaviours of the solutions is presently lacking.
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注入信号激光中的余维二分岔
注入信号激光器的方程不仅引起了光学学界的兴趣,而且引起了非线性动力学物理学家的兴趣。在文献[1]和文献[2]的开创性工作之后,推导了麦克斯韦-布洛赫方程的适当集合并进行了数值积分,分析了从保守和耗散行为的共存[3]到余维二分岔(CTB)的存在[4]等有趣的动力学效应。例如,在文献[4]中,人们认为CTB负责频率推解的出现,这在主要与锁定现象相关的问题中是反直觉的。最近,已经发表了部分描述CTB简并性的尝试[5]。然而,目前还缺乏能够解析显示解的所有动力学行为的完整的CTB展开。
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