Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback

Sano, Takuya

doi:10.1103/physreva.50.2719

Cited by 247 publications

(149 citation statements)

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“…The upper half of the fixed points on the ellipse, denoted by stars, all exhibit a saddle-node instability and can be regarded as the destructive interference solutions in the passive case. They are often called antimodes [14]. The other fixed points, denoted by open circles, can be regarded as the constructive interference solutions in the passive case.…”

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confidence: 99%

“…Sano [14] was the first to recognize the role of the antimodes in LFF and proposed that LFF is a form of chaotic itinerancy [3] among the attractor ruins of the destabilized compound cavity modes, where each dropout is associated with the trajectory approaching too close to one of the (many) antimodes. It was shown by Van Tartwijk, Levine, and Lenstra [15] that on each attractor ruin the power is organized in irregular pulses.…”

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Fast Pulsing and Chaotic Itinerancy with a Drift in the Coherence Collapse of Semiconductor Lasers

et al. 1996

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We report the first experimental observation of irregular picosecond light pulses within the coherence collapse of a semiconductor laser subject to delayed moderate optical feedback. This pulsing behavior agrees with the recent explanation of low frequency fluctuations as chaotic itinerancy with a drift. Theory and experiments show very good agreement. PACS numbers: 42.65.Sf, 05.45.+b, 42.55.Px Delayed feedback-induced instabilities have been studied since the late 1970s in various dynamical systems. Besides these very early interests they are nowadays of particular interest because of their intrinsic high dimensionality and, related to that, their rich variety of dynamical phenomena [1]. Optical systems have played an important role for these investigations, and have boosted the interest in high-dimensional nonlinear dynamics [2][3][4].A very popular delay system is the semiconductor laser subject to external optical feedback, because of its high sensitivity to external signals [5]. Semiconductor lasers show a sudden increase in their spectral linewidth from about 100 MHz to typically several tens of GHz for delay times not much smaller than the relaxation oscillation period and for moderate feedback levels. This phenomenon has been called coherence collapse [6], and has attracted a lot of research (e.g., [7-11]).One dynamical phenomenon within the coherence collapse regime frequently attributed to is the so-called low frequency fluctuations phenomenon (LFF). It refers to fluctuations in the emitted light intensity with distinctly lower frequencies in comparison to the underlying relaxation oscillation frequencies and mode beating frequencies [12 -14]. Recently, LFF has been explained as chaotic itinerancy with a drift [15]. This theory predicts erratic picosecond pulsing of the output power. In this paper we give experimental evidence confirming these predictions. We do this by comparing measured intensity pulses with pulse trains obtained by numerical modeling. The very good agreement supports the recent identification of the essential physical mechanism leading to the LFF behavior.The dynamics of a single-mode semiconductor laser subject to moderate amounts of optical feedback from an external reflection is modeled by the following delaydifferential rate equations [5]:Here we have written the complex optical field as E ͑t͒ E͑t͒ exp͑iv 0 t͒ p P͑t͒ exp͑iv 0 t͒, where v 0 is the optical angular frequency of the stand-alone (solitary) laser, P͑t͒ is the photon number, and n͑t͒ is the excess number of electron-hole pairs with respect to the solitary value N 0 . The parameters in (1a) and (1b) have their usual meaning: j is the bulk differential gain, e accounts for gain saturation, a is the linewidth enhancement factor, G 0 is the inverse photon lifetime, pJ th is the electrical pump current (J th is its value at threshold), and T 1 is the electron-hole pair lifetime. The feedback is accounted for via the delay time t and the feedback rate g. The dimensionless effective feedback strength is defined as C ϵ gt p...

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Fast Pulsing and Chaotic Itinerancy with a Drift in the Coherence Collapse of Semiconductor Lasers

et al. 1996

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“…We speculate that the observed dark pulse is a kind of temporal cavity soliton formed in the laser. Semiconductor lasers subject to optical feedback from an external mirror have been extensively investigated both theoretically [1][2][3] and experimentally. 4,5 It has been shown that as a result of the delayed feedback, the lasers can exhibit a variety of interesting features, including the destabilization of relaxation oscillations, 6-9 coherence collapse, 10 and low-frequency fluctuations (LFF) or dropouts.…”

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confidence: 99%

“…4,5 It has been shown that as a result of the delayed feedback, the lasers can exhibit a variety of interesting features, including the destabilization of relaxation oscillations, 6-9 coherence collapse, 10 and low-frequency fluctuations (LFF) or dropouts. 1,11 Physically, a nonlinear system with delayed feedback has infinite solutions, whose behaviors need to be explained in terms of the nonlinear dynamics. Theoretical studies on the semiconductor lasers with delayed feedback based on the Lang-Kobayashi (LK) equations 2 or their simplfied form 12 have shown that multiple attractors can coexist in the system.…”

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Periodic dark pulse emission induced by delayed feedback in a quantum well semiconductor laser

Tang

et al. 2012

AIP Advances

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“…Noise-driven models have been proposed to describe the LFF effect [3]. A deterministic approach, based on the single mode Lang-Kobayashi (LK) equations [4], was proposed in [5] to explain the LFF as a chaotic itinerancy with a drift [6]. Recently, there have been strong indications that the LFF need not be irregular: the laser can produce a train of equally spaced pulses [7].…”

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Low Frequency Fluctuations in a Multimode Semiconductor Laser with Optical Feedback

Viktorov

Mandel

2000

Phys. Rev. Lett.

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We study a multimode semiconductor laser subject to a moderate optical feedback. The steady state is destabilized by either a simple Hopf bifurcation leading to in phase dynamics or by a degenerate Hopf bifurcation leading to antiphase dynamics. The degenerate bifurcation is also a source of multiple coexisting attractors. We show that a simple interpretation of the low frequency fluctuations in the multimode regime is provided by a chaotic itinerancy among the many coexisting unstable attractors produced by the degenerate Hopf bifurcation. PACS numbers: 42.55.Px, 42.60.Mi Semiconductor lasers are prone to instabilities when subjected to an optical feedback. In most applications, the optical feedback is difficult to avoid and may lead to a loss of useful properties. An example is the occurrence of low frequency fluctuations (LFF) which are observed near the lasing threshold. This phenomenon is characterized by intensity dropouts with an average time between dropouts much longer than either relaxation oscillation periods or mode beating characteristic times. The LFF regime has been observed experimentally first using a bandwidth limited detector [1], and recently confirmed by means of high bandwidth streak camera experiments [2]. The modelization of this behavior is difficult because the characteristic time scales involved in the laser dynamics are too short to allow a direct detection by electronic means. Noise-driven models have been proposed to describe the LFF effect [3]. A deterministic approach, based on the single mode Lang-Kobayashi (LK) equations [4], was proposed in [5] to explain the LFF as a chaotic itinerancy with a drift [6]. Recently, there have been strong indications that the LFF need not be irregular: the laser can produce a train of equally spaced pulses [7]. Most studies of the LFF have been limited so far to single mode models. However, recent experiments have demonstrated the growing importance of a multimode operation in the LFF regime [8]. A key result for the modelization is the experimental evidence that the dynamics of the modal intensities can be antiphased: the characteristic nonoptical frequencies are still controlled by the external cavity round-trip time, but the oscillation phases differ from mode to mode [9]. A phenomenological multimode model has recently been proposed in [10]. It describes a multimode operation, but in the time-dependent regime the modes are always in phase. The goal of this Letter is to introduce a multimode extension of the LK model which accounts for the possibility of antiphase dynamics. We achieve this goal by taking into account the grating associated with a Fabry-Perot configuration. This model is able to describe both the in phase and the out of phase dynamics which are observed experimentally. It predicts two possible instabilities for the steady states: a standard self-pulsing instability where all modes are in phase, and a new ͑N 2 1͒-degenerate Hopf bifurcation where N is the number of lasing modes. Depending on the experimental conditions, eithe...

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Antimode dynamics and chaotic itinerancy in the coherence collapse of semiconductor lasers with optical feedback

Cited by 247 publications

References 19 publications

Fast Pulsing and Chaotic Itinerancy with a Drift in the Coherence Collapse of Semiconductor Lasers

Fast Pulsing and Chaotic Itinerancy with a Drift in the Coherence Collapse of Semiconductor Lasers

Periodic dark pulse emission induced by delayed feedback in a quantum well semiconductor laser

Low Frequency Fluctuations in a Multimode Semiconductor Laser with Optical Feedback

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