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[CrossRef]

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[CrossRef]

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[CrossRef]

D. C. DeMott, D. J. Ulness, A. C. Albrecht, “Femtosecond temporal probes using spectrally tailored noisy quasi-cw laser light,” Phys. Rev. A 55, 761–771 (1997).

[CrossRef]

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[CrossRef]

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[CrossRef]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).

[CrossRef]
[PubMed]

G. L. Lippi, S. Barland, F. Monsieur, “Invariant integral and the transition to steady states in separable dynamical systems,” Phys. Rev. Lett. 85, 62–65 (2000).

[CrossRef]
[PubMed]

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[CrossRef]

G. L. Lippi, N. Dokhane, X. Hachair, S. Barland, J. R. Tredicce, “High speed direct modulation of semiconductor lasers,” in Semiconductor Lasers and Optical Amplifiers for Lightwave Communication Systems, R. P. Mirin, C. S. Menoni, eds., Proc. SPIE4871, 103–114 (2002).

[CrossRef]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).

[CrossRef]
[PubMed]

E. Benkler, M. Kreuzer, R. Neubecker, T. Tschudi, “Experimental control of unstable patterns and elimination of spatiotemporal disorder in nonlinear optics,” Phys. Rev. Lett. 84, 879–882 (2000).

[CrossRef]
[PubMed]

G. K. Harkness, G.-L. Oppo, E. Benkler, M. Kreuzer, R. Neubecker, T. Tschudi, “Fourier space control in an LCLV feedback system,” J. Opt. B: Quantum Semiclassical Opt. 1, 177–182 (1999).

[CrossRef]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).

[CrossRef]
[PubMed]

L. Bickers, L. D. Westbrook, “Reduction of transient laser chirp in 1.5 μm DFB lasers by shaping the modulation pulse,” IEE Proc. J 133, 155–162 (1986).

S. Bielawski, D. Derozier, P. Glorieux, “Experimental characterization of unstable periodic orbits by controlling chaos,” Phys. Rev. A 47, R2492–R2495 (1993).

[CrossRef]
[PubMed]

M. E. Bleich, D. Hochheiser, J. V. Moloney, J. E. S. Socolar, “Controlling extended systems with spatially filtered, time-delayed feedback,” Phys. Rev. E 55, 2119–2126 (1997).

[CrossRef]

F. T. Arecchi, S. Boccaletti, P. L. Ramazza, “Pattern formation and competition in nonlinear optics,” Phys. Rep. 318, 1–83 (1999).

[CrossRef]

M. Brambilla, A. Gatti, L. A. Lugiato, “Optical pattern formation,” Adv. At. Mol. Opt. Phys. 40, 229–306 (1998).

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).

[CrossRef]

T. Brixner, N. H. Damrauer, P. Niklaus, G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).

[CrossRef]
[PubMed]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).

[CrossRef]
[PubMed]

M. Bruensteiner, G. C. Papen, “Extraction of VCSEL rate-equation parameters for low-bias system simulation,” IEEE J. Sel. Top. Quantum Electron. 5, 487–494 (1999).

[CrossRef]

T. C. Weinacht, J. Ahn, P. H. Bucksbaum, “Controlling the shape of a quantum wavefunction,” Nature 397, 233–235 (1999).

[CrossRef]

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, T. Erneux, “Chaos and coherence in coupled lasers,” Phys. Rev. E 55, 3865–3869 (1997).

[CrossRef]

L. M. Pecora, T. L. Carroll, “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824 (1990).

[CrossRef]
[PubMed]

V. N. Chizevsky, E. V. Grigorieva, S. A. Kashchenko, “Optimal timing for targeting periodic orbits in a loss-driven CO2 laser,” Opt. Commun. 133, 189–195 (1997).

[CrossRef]

V. N. Chizhevsky, P. Glorieux, “Targeting unstable periodic orbits,” Phys. Rev. E 51, R2701–R2704 (1995).

[CrossRef]

J. L. Herek, W. Wohlleben, R. J. Cogdell, D. Zeidler, M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002).

[CrossRef]
[PubMed]

P. Colet, C. Mirasso, M. San Miguel, “Memory diagram of single-mode semiconductor lasers,” IEEE J. Quantum Electron. 29, 1624–1630 (1993).

[CrossRef]

T. Brixner, N. H. Damrauer, P. Niklaus, G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).

[CrossRef]
[PubMed]

M. Danielsen, “A theoretical analysis for gigabit/second pulse code modulation of a semiconductor laser,” IEEE J. Quantum Electron. QE-12, 657–660 (1976).

[CrossRef]

G. J. de Valcàrcel, K. Staliunas, “Excitation of phase patterns and spatial solitons via two-frequency forcing of a 1:1 resonance,” Phys. Rev. E 67, 026604 (2003).

[CrossRef]

L. Larger, J.-P. Goedgebuer, F. Delorme, “Optical encryption system using hyperchaos generated by an optoelectronic wavelength oscillator,” Phys. Rev. E 57, 6618–6624 (1998).

[CrossRef]

D. C. DeMott, D. J. Ulness, A. C. Albrecht, “Femtosecond temporal probes using spectrally tailored noisy quasi-cw laser light,” Phys. Rev. A 55, 761–771 (1997).

[CrossRef]

M. Schwab, M. Sedlatschek, B. Thüring, C. Denz, T. Tchudi, “Origin and control of dynamics of hexagonal patterns in a photorefractive feedback system,” Chaos Solitons Fractals 10, 701–707 (1999).

[CrossRef]

S. Juul Jensen, M. Schwab, C. Denz, “Manipulation, stabilization, and control of pattern formation using Fourier space filtering,” Phys. Rev. Lett. 81, 1614–1617 (1998).

[CrossRef]

S. Bielawski, D. Derozier, P. Glorieux, “Experimental characterization of unstable periodic orbits by controlling chaos,” Phys. Rev. A 47, R2492–R2495 (1993).

[CrossRef]
[PubMed]

N. Dokhane, G. L. Lippi, “Faster modulation of single-mode semiconductor lasers through patterned current switching: numerical investigation,” IEE Proc.-J Optoelectron. 151, 61–68 (2004).

[CrossRef]

N. Dokhane, G. L. Lippi, “Improved direct modulation technique for faster switching of diode lasers,” IEE Proc.-J Optoelectron. 149, 7–16 (2002).

[CrossRef]

N. Dokhane, G. L. Lippi, “Chirp reduction in semiconductor lasers through injection current patterning,” Appl. Phys. Lett. 78, 3938–3940 (2001).

[CrossRef]

G. L. Lippi, S. Barland, N. Dokhane, F. Monsieur, P. A. Porta, H. Grassi, L. M. Hoffer, “Phase space techniques for steering laser transients,” J. Opt. B: Quantum Semiclassical Opt. 2, 375–381 (2000).

[CrossRef]

G. L. Lippi, N. Dokhane, X. Hachair, S. Barland, J. R. Tredicce, “High speed direct modulation of semiconductor lasers,” in Semiconductor Lasers and Optical Amplifiers for Lightwave Communication Systems, R. P. Mirin, C. S. Menoni, eds., Proc. SPIE4871, 103–114 (2002).

[CrossRef]

N. Dokhane, “Amélioration de la modulation logique directe des diodes laser par la technique de l’espace des phases,” Ph.D. dissertation (in French) (Université de Nice-Sophia Antipolis, Valbonne, France, 2000).

J.-P. Eckmann, D. Ruelle, “Ergodic theory of chaos and strange attractors,” Rev. Mod. Phys. 57, 617–656 (1985).

[CrossRef]

P. Torphammar, R. Tell, H. Eklund, A. R. Johnston, “Minimizing pattern effects in semiconductor lasers at high rate pulse modulation,” IEEE J. Quantum Electron. QE-15, 1271–1276 (1979).

[CrossRef]

K. S. Thornburg, M. Möller, R. Roy, T. W. Carr, R.-D. Li, T. Erneux, “Chaos and coherence in coupled lasers,” Phys. Rev. E 55, 3865–3869 (1997).

[CrossRef]

G.-L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, W. J. Firth, “Control of spatiotemporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

G. K. Harkness, G.-L. Oppo, R. Martin, A. J. Scroggie, W. J. Firth, “Elimination of spatiotemporal disorder by Fourier space techniques,” Phys. Rev. A 58, 2577–2586 (1998).

[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, W. J. Firth, “Spatial soliton pixels in semiconductor devices,” Phys. Rev. Lett. 79, 2042–2045 (1997).

[CrossRef]

R. Martin, A. J. Scroggie, G.-L. Oppo, W. J. Firth, “Stabilization, selection, and tracking of unstable patterns by Fourier space techniques,” Phys. Rev. Lett. 77, 4007–4010 (1996).

[CrossRef]
[PubMed]

M. Möller, B. Forsmann, W. Lange, “Instabilities in coupled Nd:YVO4 microchip lasers,” J. Opt. B: Quantum Semiclassical Opt. 10, 839–848 (1998).

R. Olshansky, D. Fye, “Reduction of dynamic linewidth in single-frequency semiconductor lasers,” Electron. Lett. 20, 928–929 (1984).

[CrossRef]

M. Brambilla, A. Gatti, L. A. Lugiato, “Optical pattern formation,” Adv. At. Mol. Opt. Phys. 40, 229–306 (1998).

T. Brixner, N. H. Damrauer, P. Niklaus, G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).

[CrossRef]
[PubMed]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).

[CrossRef]
[PubMed]

T. Ackemann, B. Giese, B. Schäpers, W. Lange, “Investigations of pattern forming mechanisms by Fourier filtering: properties of hexagons and the transition to stripes in an anisotropic system,” J. Opt. B: Quantum Semiclassical Opt. 1, 70–76 (1999).

[CrossRef]

B. Ségard, S. Matton, P. Glorieux, “Targeting steady states in a laser,” Phys. Rev. A 66, 053819 (1–5) (2002).

[CrossRef]

V. N. Chizhevsky, P. Glorieux, “Targeting unstable periodic orbits,” Phys. Rev. E 51, R2701–R2704 (1995).

[CrossRef]

S. Bielawski, D. Derozier, P. Glorieux, “Experimental characterization of unstable periodic orbits by controlling chaos,” Phys. Rev. A 47, R2492–R2495 (1993).

[CrossRef]
[PubMed]

J.-P. Goedgebuer, L. Larger, H. Laporte, “Optical crypto-system based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80, 2249–2252 (1998).

[CrossRef]

L. Larger, J.-P. Goedgebuer, F. Delorme, “Optical encryption system using hyperchaos generated by an optoelectronic wavelength oscillator,” Phys. Rev. E 57, 6618–6624 (1998).

[CrossRef]

G. L. Lippi, S. Barland, N. Dokhane, F. Monsieur, P. A. Porta, H. Grassi, L. M. Hoffer, “Phase space techniques for steering laser transients,” J. Opt. B: Quantum Semiclassical Opt. 2, 375–381 (2000).

[CrossRef]

P. A. Porta, L. M. Hoffer, H. Grassi, G. L. Lippi, “Analysis of nonfeedback technique for transient steering in Class B lasers,” Phys. Rev. A 61, 033801 (1–10) (2000).

[CrossRef]

G. L. Lippi, P. A. Porta, L. M. Hoffer, H. Grassi, “Control of transients in ‘lethargic’ systems,” Phys. Rev. E 59, R32–R35 (1999).

[CrossRef]

P. A. Porta, L. M. Hoffer, H. Grassi, G. L. Lippi, “Control of turn-on in Class B lasers,” Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, 1811–1819 (1998).

[CrossRef]

V. N. Chizevsky, E. V. Grigorieva, S. A. Kashchenko, “Optimal timing for targeting periodic orbits in a loss-driven CO2 laser,” Opt. Commun. 133, 189–195 (1997).

[CrossRef]

G. L. Lippi, N. Dokhane, X. Hachair, S. Barland, J. R. Tredicce, “High speed direct modulation of semiconductor lasers,” in Semiconductor Lasers and Optical Amplifiers for Lightwave Communication Systems, R. P. Mirin, C. S. Menoni, eds., Proc. SPIE4871, 103–114 (2002).

[CrossRef]

G. K. Harkness, G.-L. Oppo, E. Benkler, M. Kreuzer, R. Neubecker, T. Tschudi, “Fourier space control in an LCLV feedback system,” J. Opt. B: Quantum Semiclassical Opt. 1, 177–182 (1999).

[CrossRef]

G.-L. Oppo, R. Martin, A. J. Scroggie, G. K. Harkness, A. Lord, W. J. Firth, “Control of spatiotemporal complexity in nonlinear optics,” Chaos Solitons Fractals 10, 865–874 (1999).

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On the basis of general principles63 one prefers the opposite approach, fixing V1 and V2 and varying t1 and t2. If the instrumentation allows it, this is certainly preferred. However, we see that even the opposite one, imposed by our generator, produces successful results.

In general, it is not meaningful to attempt a number of levels much larger than 100, no matter what system is taken into consideration. Maximum estimates of the number of trials can therefore be based on this worst-case assumption if other information is missing.

If the generator’s time resolution is small compared with the time interval to be explored, we come back to the considerations already made79 and consider that 100 trials are more than enough for a scan of the parameter space. In such a case, if no other restrictions are applied, the amount of data to be analyzed may rapidly become too large to be practicable. A way of reducing the portion of parameter space to analyze is presented in Subsection 5.B.

The time estimate for one loop can be obtained on the basis of the following considerations. For 1 kbyte the typical access time for a hard disk is nowadays ≈15 μs, while a standard GIPB interface is currently capable of transferring the same amount of data in ≈150 μs. Choosing a large safety factor in the duty cycle, to make sure that the measurement is not affected by external factors influencing the laser (e.g., heating, memory effects), we can set the signal frequency to ≈10 kHz; thus the waiting time to synchronize the cycles is at most 100 μs. In addition we have to take into account the time Labview takes to update the parameters and send them to the generator, and to activate it, and for the oscilloscope to trigger and store the data in memory. Given the speed of computer clocks, even if the program is not written in an efficient way, the bottleneck of the operation is the arbitrary waveform generator’s reaction time in responding and sending out the signal. In our measurements this time was particularly long (3 s) because of the very old technology of the apparatus. With sufficient error margin we can generically assume modern generators to be ~50 times faster; therefore we arrive at an estimated cycle time of ≈0.06 s.

Although we have not used this option in our measurements, most modern oscilloscopes offer a window discrimination or smart trigger on the data acquired. This option can be used for prefiltering the data. Alternatively this filtering can be done on the computer, once the data are transferred from a lower-class oscilloscope or from an older model, before the information is stored on the hard disk.

This statement is valid with the assumption that the range of values over which the steering parameter (voltage in our system) can be varied above and below threshold covers a comparable range. In our device the laser response above threshold grows considerably more for 1.8 V ≤ V≲ 3.5 V than for 3.5 V ≲ V≤ 5 V. Thus we can consider that the range of below-threshold voltages ΔVbt≈1.8 V is of the same order as the main contribution in the above-threshold interval ΔVat≈ 1.7 V. This response can be tested a priori in each system, and a weighted version of our statement can be used as an educated guess for determining a reasonable interval of ratios between t1 and t2 to be tested.

In all cases in which the time resolution of the arbitrary function generator is sufficiently fine, one would effectively invert the roles of the scans on the time values, t1 and t2, and voltage values, V1 and V2. In this latter case the number of voltage values to be chosen could also be rather small, since one would immediately start by considering in a preliminary run only those that are sufficiently close to Vmax for V1 and to Vmin for V2.

This situation is represented graphically by the trajectory labeled A in Fig. 7 in Ref. 62 when the target point in the phase space is approached from below.

This corresponds to the part of the composite trajectory that approaches the saddle point in phase space,55 starting from the initial operating point (with the laser switched off). It is in the neighborhood of this point that the laser field grows rapidly out of the intrinsic noise (not shown in the figures in Ref. 55).

In the phase-space picture55,60 this phase corresponds to aiming at the fixed point, thereby removing the oscillations.

For simplicity, in this discussion we assume that the laser is switched on from below threshold. One can easily introduce a generalization to consider the transition between states where the laser is active with different output power levels. (This has been discussed for telecommunication semiconductor lasers.60)

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The step that we describe in detail in Section 4 is necessary for laser systems, i.e., devices that package together both the laser and some controls (e.g., electronic, optical, or others). If one desires to optimize a Class B laser with no additional elements, the general considerations of Refs. 55, 60, and 64 apply directly. The procedure that we propose in this paper can still be applied and is likely to provide faster results, but the tests described in detail in Section 4 become unnecessary.

Although some degree of steering is possible in an oscillator, one can show that the time necessary to attain the new equilibrium state cannot be shortened, contrary to what happens in Class B lasers, and in the more complex device that we analyze here.

Embedding techniques amount to generating N-dimensional spaces starting from a one-dimensional data sequence by constructing vectors with elements shifted by an arbitrary number of elements. For a discussion see Refs. 74 and 75.

Compare Fig. 14 in Ref. 60 with Fig. 1.55 From the latter the presence of the saddle point is much more readily recognized.

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