Bistability and low-frequency fluctuations in semiconductor lasers with optical feedback: a theoretical analysis

Mørk, Jesper; Tromborg, B.; Christiansen, Peter Leth

doi:10.1109/3.105

Cited by 178 publications

(73 citation statements)

References 34 publications

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“…3(b) shows quasi-periodic behavior of the ECL, which is confirmed by the spectra of I and V that both show the presence of two incommensurate frequencies, in the form of a central peak at 8.74 GHz, and sidebands offset by 0.35 GHz from the central peak. This quasi-periodic behavior is expected to occur on the route to chaos for an ECL [10], where the central peak frequency is close to that of the relaxation-oscillation frequency f RO and that the side-peak separation is close to f τ . The undamping of these two frequencies probably results from two successive Hopf bifurcation in Ref.…”

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confidence: 99%

“…The undamping of these two frequencies probably results from two successive Hopf bifurcation in Ref. 10 and Ref.…”

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confidence: 99%

“…In addition to the interest in optical microwave generation of periodic [1] and shapedpulse [2] signals, there has also been a stream of work on the generation of broadband chaotic signals through the use of electro-optic modulators subjected to feedback [7,8] of a laser diode (LD) subjected to optoelectronic [9] or optical feedback [10,11] (ECL), or to optical injection [12,13]. It is notable that certain applications [14] of chaotic laser dynamics, and in particular chaotic radar [15] and ultrahigh-rate random-bit generation [16][17][18], do not intrinsically make use of the chaotic optical signal, but of an electrical signal detected by one or more PDs.…”

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A multi-GHz chaotic optoelectronic oscillator based on laser terminal voltage

Chang

Choi

Locquet

et al. 2016

Applied Physics Letters

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A multi-GHz chaotic optoelectronic oscillator based on an external cavity semiconductor laser (ECL) is demonstrated. Unlike standard optoelectronic oscillators for microwave applications, we do not employ the dynamic light output incident on a photodiode to generate the microwave signal, but instead generate the microwave signal directly by measuring the terminal voltage V (t) of the laser diode of the ECL under constant-current operation, thus obviating the photodiode entirely.

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“…The undamping of these two frequencies probably results from two successive Hopf bifurcation in Ref. 10 and Ref.…”

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confidence: 99%

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confidence: 99%

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A multi-GHz chaotic optoelectronic oscillator based on laser terminal voltage

Chang

Choi

Locquet

et al. 2016

Applied Physics Letters

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“…It was already concluded from theory in 1990 that, under conditions of coherence collapse (or, for that matter, conditions of low-frequency f luctuations), 2 stable operation with high power and narrow linewidth should occur. 3 Recently, this property was rederived by an asymptotic approximation technique, 4 and the physical consequences were discussed.…”

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Prevention of coherence collapse in diode lasers by dynamic targeting

1997

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We numerically show that a laser that would suffer from coherence collapse if precautions were not taken can be made to operate with a small linewidth and a stable maximum output power by application of a new dynamic targeting technique. © 1997 Optical Society of America Optical feedback is a well-known effect that must be taken into account when analyzing the behavior of a semiconductor laser. Even for external ref lections of less than 1%, the laser can operate in the coherencecollapse regime characterized by chaotic behavior of the output power and a linewidth increased by a factor of 1000.

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“…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].…”

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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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Bistability and low-frequency fluctuations in semiconductor lasers with optical feedback: a theoretical analysis

Cited by 178 publications

References 34 publications

A multi-GHz chaotic optoelectronic oscillator based on laser terminal voltage

A multi-GHz chaotic optoelectronic oscillator based on laser terminal voltage

Prevention of coherence collapse in diode lasers by dynamic targeting

Low Frequency Fluctuations in a Multimode Semiconductor Laser with Optical Feedback

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