Experimental and theoretical study of filtered optical feedback in a semiconductor laser

Fischer, A.; Andersen, O. K.; Yousefi, M.; Stolte, S.; Lenstra, D.

doi:10.1109/3.825886

Cited by 72 publications

(49 citation statements)

References 14 publications

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“…In the context of semiconductor lasers, it has been shown both theoretically and experimentally that delayed, bandpass filtered optical feedback is able to suppress the undamping of relaxation oscillations [36,40]. Recently, filtering of an optical feedback signal [41] was also investigated for laser models of Lang-Kobayashi type [42].…”

Section: Control Loop Latencymentioning

confidence: 99%

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Control of unstable steady states by extended time-delayed feedback

2007

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Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This system represents a generic model of an unstable steady state which can be found for instance in a Hopf bifurcation. In addition to the original controller design, we investigate effects of control loop latency and a bandpass filter on the domain of control. Furthermore, we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase. We present an analysis of the domain of control and support our results by numerical calculations.

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Section: Control Loop Latencymentioning

confidence: 99%

“…In optical systems like semiconductor lasers with external optical feedback [36,37], this feedback phase can be seen as the phase of the electric field. Experimentally, this phase of the feedback can be varied by tuning an external Fabry-Perot cavity.…”

Section: Phase Dependent Couplingmentioning

confidence: 99%

Control of unstable steady states by extended time-delayed feedback

2007

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“…We finish this introduction with a brief review of other work on the FOF laser. Experimental studies in comparison with results from numerical integration of the governing rate equations can be found in [8,34,35]. As was mentioned, FOs were first found in an experiment reported in [9].…”

mentioning

confidence: 80%

Bifurcation Analysis of a Semiconductor Laser with Filtered Optical Feedback

Erzgräber¹,

Krauskopf²,

Lenstra³

2007

SIAM J. Appl. Dyn. Syst.

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Abstract. We study the dynamics and bifurcations of a semiconductor laser with delayed filtered feedback, where a part of the output of the laser re-enters after spectral filtering. This type of coherent optical feedback is more challenging than the case of conventional optical feedabck from a simple mirror, but it provides additional control over the output of the semiconductor laser by means of choosing the filter detuning and the filter width. This laser system can be modelled by a system of delay differential equations with a single fixed delay, which is due to the travel time of the light outside the laser.In this paper we present a bifurcation analysis of the filtered feedback laser. We first consider the basic continuous wave states, known as the external filtered modes (EFMs), and determine their stability regions in the parameter plane of feedback strength versus feedback phase. The EFMs are born in saddle-node bifurcations and become unstable in Hopf bifurcations. We show that for small filter detuning there is a single region of stable EFMs, which splits up into two separate regions when the filter is detuned.We then concentrate on the periodic orbits that emanate from Hopf bifurcations. Depending on the feedback strength and the feedback phase two types of oscillations can be found. First, there are undamped relaxation oscillations, which are typical for semiconductor laser systems. Secondly, there are oscillations with a period related to the delay time, which have the remarkable property that the laser frequency oscillates while the laser intensity is almost constant. These frequency oscillations are only possible due to the interaction of the laser with the filter. We determine the stability regions in the parameter plane of feedback strength versus feedback phase of the different types of oscillations. In particular, we find that stable frequency oscillations are dominant for nonzero values of the filter detuning.

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“…In this respect FOs are very different from the well-known relaxation oscillations (ROs) that are a typical feature of semiconductor lasers. In fact, in light of the strong amplitude-phase coupling of semiconductor lasers, the existence of FOs in the FOF laser-first reported in [6]-has been somewhat surprising. Their existence has been explained by the influence of the filter dispersion, which effectively compensates for the dynamics in the laser intensity [8].…”

mentioning

confidence: 99%

“…These two parameters offer additional control over the feedback light, which may be used to influence the dynamics of the laser; see also, for example, [1-4] for other optical feedback schemes. The dynamics of the FOF laser has been considered in a number of experimental and theoretical studies; see, for example, [5][6][7][8]. Their focus has been on the influence of the detuning, the feedback strength, and the external round-trip time.…”

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confidence: 99%

Dynamics of a filtered-feedback laser: influence of the filter width

Erzgräber

Krauskopf

2007

Opt. Lett.

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The behavior of a semiconductor laser subject to filtered optical feedback is studied in dependence on the width of the filter. Of special interest are pure frequency oscillations where the laser intensity is practically constant. We show that frequency oscillations are stable in a large region of intermediate values of the filter width, where the dispersion of the filter is able to compensate for the well-known phase-amplitude coupling of the semiconductor laser. Our stability diagram covers the entire range from a very narrow filter, when the system behaves like a laser with monochromatic optical injection, to a very broad filter, when the laser effectively receives conventional (i.e., unfiltered) optical feedback. © 2007 Optical Society of America OCIS codes: 140.5960, 190.3100, 000.4430. We consider a semiconductor laser with filtered optical feedback (FOF), where a part of the laser light is spectrally filtered and reinjected into the laser after the round-trip time of the feedback loop. In an experimental setup spectral filtering can be realized, for example, by a Fabry-Perot interferometer where optical isolators prevent unwanted reflections; see Fig. 1. The filter itself is characterized by the detuning ⌬ between the laser frequency and the filter center frequency, and by the filter width ⌳. These two parameters offer additional control over the feedback light, which may be used to influence the dynamics of the laser; see also, for example, [1-4] for other optical feedback schemes. The dynamics of the FOF laser has been considered in a number of experimental and theoretical studies; see, for example, [5][6][7][8]. Their focus has been on the influence of the detuning, the feedback strength, and the external round-trip time. By contrast, studies of the influence of the filter width ⌳ have focused so far on the two limiting cases of an extremely narrow filter and of an extremely broad filter. Namely, the narrow-filter limit reduces to a laser with optically injected light at the filter frequency, while in the broad-filter limit spectral filtering is lost so that the system reduces to a laser with conventional optical feedback [9-11]; in both limits spectral filtering can be neglected. However, in a real system where the feedback light is subject to spectral filtering, intermediate filter widths are of interest.In this paper we study how the behavior of the FOF laser is influenced by the filter width ⌳ over several orders of magnitude, ranging from zero up to 4 GHz. This is motivated by recent experimental measurements in [12], where the vital influence of ⌳ in an intermediate range was revealed by changing the distance between the two mirrors of the FabryPerot interferometer. Of special interest are frequency oscillations (FOs) of the system, which are characterized by an absence of oscillations of the power of the laser. In this respect FOs are very different from the well-known relaxation oscillations (ROs) that are a typical feature of semiconductor lasers. In fact, in light of the strong amplitude-...

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Experimental and theoretical study of filtered optical feedback in a semiconductor laser

Cited by 72 publications

References 14 publications

Control of unstable steady states by extended time-delayed feedback

Control of unstable steady states by extended time-delayed feedback

Bifurcation Analysis of a Semiconductor Laser with Filtered Optical Feedback

Dynamics of a filtered-feedback laser: influence of the filter width

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