By Sylvia Schikora
The stabilization of risky states hidden within the dynamics of a method, particularly the keep watch over of chaos, obtained a lot awareness within the final years. during this paintings, a widely known keep watch over approach referred to as behind schedule suggestions regulate is utilized for the 1st time solely within the all-optical area. A multisection semiconductor laser gets optical suggestions from an exterior Fabry-Perot interferometer. The keep watch over sign is a phase-tunable superposition of the laser sign, and provokes the laser to function in an in a different way risky periodic kingdom with a interval equivalent to the time hold up. The keep an eye on is noninvasive, as the mirrored sign has a tendency to 0 while the objective nation is reached.
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Additional info for All-Optical Noninvasive Delayed Feedback Control of Semiconductor Lasers
Perturbations acting on the phase Φ inﬂuence the movement along the direction of the orbit. peak in the powerspectrum. Weak perturbations in ﬁrst approximation only affect the phase of an oscillator, not the amplitudes. Thus, weak noise mainly affects the movement of a trajectory along an orbit (Fig. 7). 1) with Ω0 the freerunning oscillation frequency and ε(t) the effective noise. In a linear approximation assuming weak phase ﬂuctuations and a weak control force, the diffusion constant D of the controlled oscillator is obtained as D = D0 · (1 + K/2 · τ cos(Ω0 τ))2 .
In case of a real positive Λ0,k with ωk = 0, solutions leave x∗ straight in one direction (Fig. 1 (a)). For a complex conjugate pair Λ0,k = λk ±iωk the solution would spiral in a plane around x∗ (Fig. 1 (b)). In the latter case, x∗ is called a ‘focus‘. Fig. 1 (c) demonstrates the functional principle of DFC of an unstable focus. One question is how to choose the delay time τ when controlling a stationary state. The dynamic system departs from an unstable focus along spirals, with the intrinsic focus period T0 .
Beyond the bifurcation, the RO amplitude starts to grow rapidly, while the width stays on a minimum value. 3: Supercritical Hopf bifurcation in the freerunning ITL. Width (circles) and height (squares) of the dominant peak in the power spectrum of the solitary ITL versus phase current. Dashed: guide for the eye. Solid: linear ﬁt for determining the Hopf bifurcation (H). DFB currents: I1 = 30 mA, I2 = 45 mA. changed to a stable selfpulsation, and the focus is now unstable. 1 mA. Coupling of the Fabry-Perot Etalon The unstable focus behind the Hopf bifurcation shall be stabilized by all-optical DFC.