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Routes to Chaos of a Semiconductor Laser Subjected to External Optical Feedback: A Review
摘要： This paper reviews experimental investigations of the route to chaos of a semiconductor laser subjected to optical feedback from a distant reflector. When the laser is biased close to threshold, as the feedback strength is increased, an alternation between stable continuous wave (CW) behavior and irregular, chaotic fluctuations, involving numerous external-cavity modes, is observed. CW operation occurs on an external-cavity mode whose optical frequency is significantly lower than that of the solitary laser. The scenario is significantly different for larger currents as the feedback level is increased. At low feedback, the laser displays periodic or quasiperiodic behavior, mostly around external-cavity modes whose frequency is slightly larger than that of the solitary laser. As the feedback level increases, the RF and optical frequencies involved progressively lock until complete locking is achieved in a mixed external-cavity mode state. In this regime, the optical intensity and voltage oscillate at a frequency that is also equal to the optical frequency spacing between the modes participating in the dynamics. For even higher feedback, the locking cannot be maintained and the laser displays fully developed coherence collapse.
关键词： chaos,nonlinear dynamics,semiconductor laser,bifurcations,optical feedback
更新于2025-09-19 17:13:59
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[Springer Tracts in Modern Physics] Parity-time Symmetry and Its Applications Volume 280 || Krein Signature in Hamiltonian and P T $$\mathbb {PT}$$ -Symmetric Systems
摘要： We explain the concept of Krein signature in Hamiltonian and PT -symmetric systems on the case study of the one-dimensional Gross–Pitaevskii equation with a real harmonic potential and an imaginary linear potential. These potentials correspond to the magnetic trap, and a linear gain/loss in the mean-?eld model of cigar-shaped Bose–Einstein condensates. For the linearized Gross–Pitaevskii equation, we introduce the real-valued Krein quantity, which is nonzero if the eigenvalue is neutrally stable and simple and zero if the eigenvalue is unstable. If the neutrally stable eigenvalue is simple, it persists with respect to perturbations. However, if it is multiple, it may split into unstable eigenvalues under perturbations. A necessary condition for the onset of instability past the bifurcation point requires existence of two simple neutrally stable eigenvalues of opposite Krein signatures before the bifurcation point. This property is useful in the parameter continuations of neutrally stable eigenvalues of the linearized Gross–Pitaevskii equation.
关键词： Hamiltonian systems,Instability bifurcations,PT -symmetry,Gross–Pitaevskii equation,Krein signature
更新于2025-09-10 09:29:36
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Nonlinear Stark--Wannier Equation
摘要： In this paper we consider stationary solutions to the nonlinear one-dimensional Schr¨odinger equation with a periodic potential and a Stark-type perturbation. In the limit of large periodic potential the Stark–Wannier ladders of the linear equation become a dense energy spectrum because a cascade of bifurcations of stationary solutions occurs when the ratio between the e?ective nonlinearity strength and the tilt of the external ?eld increases.
关键词： nonlinearity,PDEs,bifurcations
更新于2025-09-10 09:29:36