Low-frequency Fluctuation Regime Research Articles

Experimental and Numerical Study of Locking of Low-Frequency Fluctuations of a Semiconductor Laser with Optical Feedback

We study the output of a semiconductor laser with optical feedback operated in the low-frequency fluctuations (LFFs) regime and subject to weak sinusoidal current modulation. In the LFF regime, the laser intensity exhibits abrupt drops, after which it recovers gradually. Without modulation, the drops occur at irregular times, while, with weak modulation, they can lock to the external modulation and they can occur, depending on the parameters, every two or every three modulation cycles. Here, we characterize experimentally the locking regions and use the well-known Lang–Kobayashi model to simulate the intensity dynamics. We analyze the effects of several parameters and find that the simulations are in good qualitative agreement with the experimental observations.

Locking Phenomena in Semiconductor Lasers near Threshold with Optical Feedback and Sinusoidal Current Modulation

The dynamics of semiconductor lasers with optical feedback and current modulation has been extensively studied, and it is, by now, well known that the interplay of modulation and feedback can produce a rich variety of nonlinear phenomena. Near threshold, in the so-called low frequency fluctuations regime, the intensity emitted by the laser, without modulation, exhibits feedback-induced spikes, which occur at irregular times. When the laser current is sinusoidally modulated, under appropriate conditions, the spikes lock to the modulation and become periodic. In previous works, we studied experimentally the locked behavior and found sub-harmonic locking (regular spike timing such that a spike is emitted every two or three modulation cycles), but we did not find spikes with regular timing, emitted every modulation cycle. To understand why 1:1 regular locking was not observed, here, we perform simulations of the well-known Lang–Kobayashi model. We find a good qualitative agreement with the experiments: with small modulation amplitudes, we find wide parameter regions in which the spikes are sub-harmonically locked to the modulation, while 1:1 locking occurs at much higher modulation amplitudes.

Experimental study of modulation waveforms for entraining the spikes emitted by a semiconductor laser with optical feedback.

The entrainment phenomenon, by which an oscillator adjusts its natural rhythm to an external periodic signal, has been observed in many natural systems. Recently, attention has focused on which are the optimal conditions for achieving entrainment. Here we use a semiconductor laser with optical feedback, operating in the low-frequency fluctuations (LFFs) regime, as a testbed for a controlled entrainment experiment. In the LFF regime the laser intensity displays abrupt spikes, which can be entrained to a weak periodic signal that directly modulates the laser pump current. We compare the performance of three modulation waveforms for producing 1:1 locking (one spike is emitted in each modulation cycle), as well as higher order locking regimes. We characterize the parameter regions where high-quality locking occurs, and those where the laser emits spikes which are not entrained to the external signal. The role of the modulation amplitude and frequency, and the role of the dc value of the laser pump current (that controls the natural spike frequency) in the entrainment quality are discussed.

Low-frequency fluctuations in an external-cavity laser leading to extreme events.

We experimentally investigate the dynamical regimes of a laser diode subject to external optical feedback in light of extreme-event (EE) analysis. We observe EEs in the low-frequency fluctuations (LFFs) regime. This number decreases to negligible values when the laser transitions towards fully developed coherence collapse as the injection current is increased. Moreover, we show that EEs observed in the LFF regime are linked to high-frequency pulsing events observed after a power dropout. Finally, we prove experimentally that the observation of EEs in the LFF regimes is robust to changes in operational parameters.

Chaotic light at mid-infrared wavelength.

The onset of nonlinear dynamics and chaos is evidenced in a mid-infrared distributed feedback quantum cascade laser both in the temporal and frequency domains. As opposed to the commonly observed route to chaos in semiconductor lasers, which involves undamping of the laser relaxation oscillations, quantum cascade lasers first exhibit regular self-pulsation at the external cavity frequency before entering into a chaotic low-frequency fluctuation regime. The bifurcation sequence, similar to that already observed in class A gas lasers under optical feedback, results from the fast carrier relaxation dynamics occurring in quantum cascade lasers, as confirmed by numerical simulations. Such chaotic behavior can impact various practical applications including spectroscopy, which requires stable single-mode operation. It also allows the development of novel mid-infrared high-power chaotic light sources, thus enabling secure free-space high bit-rate optical communications based on chaos synchronization.

Analysis of the Spike Rate and Spike Correlations in Modulated Semiconductor Lasers With Optical Feedback

We investigate experimentally how changes in the external cavity length and dc current affect the mean interspike-interval (ISI) in a modulated semiconductor laser with optical feedback operating in the low-frequency fluctuations regime. The variation of the mean ISI with the modulation frequency is shown to be more pronounced when time delay and dc current allow for low spike rate. We use the method of ordinal symbolic analysis to examine how time correlations (among three, four and five consecutive laser spikes) change with the spike rate. This method is able to capture subtle changes, otherwise hidden in the dynamics. We find that higher spike rates wash out the effects of the modulation in the time correlations. Simulations using the Lang and Kobayashi model are in good qualitative agreement with the experimental observations.

Effects of periodic forcing on the temporally correlated spikes of a semiconductor laser with feedback.

Optical excitable devices that mimic neuronal behavior can be building-blocks of novel, brain-inspired information processing systems. A relevant issue is to understand how such systems represent, via correlated spikes, the information of a weak external input. Semiconductor lasers with optical feedback operating in the low frequency fluctuations regime have been shown to display optical spikes with intrinsic temporal correlations similar to those of biological neurons. Here we investigate how the spiking laser output represents a weak periodic input that is implemented via direct modulation of the laser pump current. We focus on understanding the influence of the modulation frequency. Experimental sequences of inter-spike-intervals (ISIs) are recorded and analyzed by using the ordinal symbolic methodology that identifies and characterizes serial correlations in datasets. The change in the statistics of the various symbols with the modulation frequency is empirically shown to be related to specific changes in the ISI distribution, which arise due to different phase-locking regimes. A good qualitative agreement is also found between simulations of the Lang and Kobayashi model and observations. This methodology is an efficient way to detect subtle changes in noisy correlated ISI sequences and may be applied to investigate other optical excitable devices.

Characterizing the deterministic nature of individual power dropouts in semiconductor lasers subject to delayed feedback

We implement a method to identify the deterministic nature of specific events in the dynamics of a semiconductor laser subject to time-delayed optical feedback. Specifically, we study the power dropouts in the low-frequency fluctuations regime on an individual event basis and identify whether the underlying dominant mechanism is deterministic. Our approach is based on sychronization with a twin system in a symmetric relay configuration. We investigate the dependence of the fraction of deterministically driven (i.e., synchronized) dropouts on the laser's pump current as a key parameter. Our experimental results are corroborated by numerical modeling based on rate equations. Our numerical findings also provide insights into the influence of spontaneous emission noise.

Language organization and temporal correlations in the spiking activity of an excitable laser: Experiments and model comparison

We introduce a method, based on symbolic analysis, to characterize the temporal correlations of the spiking activity exhibited by excitable systems. The technique is applied to the experimentally observed dynamics of a semiconductor laser with optical feedback operating in the low-frequency fluctuations regime, where the laser intensity displays irregular trains of sudden dropouts that can be interpreted as excitable pulses. Symbolic analysis transforms the series of interdropout time intervals into sequences of words, which represent the local ordering of a certain (small) number of those intervals. We then focus on the transition probabilities between pairs of words, showing that certain transitions are overrepresented (resulting in others being underrepresented) with respect to the surrogate series, provided the laser injection current is above a critical value. These experimental observations are in very good agreement with numerical simulations of the delay-differential Lang-Kobayashi model that is commonly used to describe this laser system, which supports the fact that the language organization reported here is generic and not a particular feature of the specific laser employed or the experimental time series analyzed. We also present results of simulations of the phenomenological nondelayed Eguia-Mindlin-Giudici(EMG) model and find that in this model the agreement between the experiments and the simulations is good at a qualitative, but not at a quantitative, level.

Experimental control of power dropouts by current modulation in a semiconductor laser with optical feedback

The injection current of an external-cavity semiconductor laser working in a regime of low-frequency fluctuations (LFFs) is modulated at several MHz. The rate of power dropouts in the laser emission is correlated with the amplitude and frequency of the modulating signal. The occurrence of dropouts becomes more regular when the laser is driven at 7 MHz, which is close to the dominant frequency of dropouts in the solitary laser. Driving the laser at 10 MHz also induces dropouts with a periodicity of 0.1 μs, resulting in LFFs with two dominant frequencies.

Quantifying stochasticity in the dynamics of delay-coupled semiconductor lasers via forbidden patterns

We quantify the level of stochasticity in the dynamics of two mutually coupled semiconductor lasers. Specifically, we concentrate on a regime in which the lasers synchronize their dynamics with a non-zero lag time, and the leader and laggard roles alternate irregularly between the lasers. We analyse this switching dynamics in terms of the number of forbidden patterns of the alternate time series. The results reveal that the system operates in a stochastic regime, with the level of stochasticity decreasing as the lasers are pumped further away from their lasing threshold. This behaviour is similar to that exhibited by a single semiconductor laser subject to external optical feedback, as its dynamics shifts from the regime of low-frequency fluctuations to coherence collapse.

The impact of regime shifts on the performance of management strategies for the Gulf of Alaska walleye pollock (Theragra chalcogramma) fishery

Climate variability affects marine ecosystems. The mechanisms relating low-frequency environmental fluctuations (regime shifts) and their impacts on marine populations are not well established for most species, but there is an expectation that the accuracy of scientific advice provided to fisheries management would be improved if management strategies incorporated the effects of regime shifts on stocks. Management strategy evaluation is used to examine the impact of regime shifts in average recruitment on the performance of management strategies for the fishery for walleye pollock, Theragra chalcogramma , in the Gulf of Alaska. The current and four alternative management strategies are evaluated. The alternatives include management strategies with different definitions of the average recruitment used when calculating management reference points, e.g., a 25-year sliding-window method and a “dynamic B0” method. The current management strategy, which ignores the possibility of future regime shifts, kept the spawning biomass higher relative to the target level than the other management strategies and had the lowest risk of fishing mortality exceeding the overfishing limit. The sliding-window management strategy achieved the highest catches and the lowest interannual variation in catch, although at the cost of a higher risk of the fishing mortality exceeding the overfishing limit.

Two distinct regimes of turbulence in HL-2A tokamak plasmas

Two distinct regimes of turbulence are identified with Langmuir probe arrays in the edge plasmas of the HuanLiuqi (HL)-2A tokamak for the first time. The spatial and temporal coherent characteristics of the low frequency fluctuations (LFFs) of 20–100 kHz are found in significant contrast to the high frequency ambient turbulence (HFAT) of 100 kHz or higher. In the LFF regime, the deviations from the regular linear dispersion relations of the HFAT are observed. The poloidal and toroidal correlation lengths of the former are measured one order of magnitude longer than that of the latter. The ratio of the temporal scales of the fluctuations in the LFF and HFAT regimes is estimated to be of the same order as that for the spatial scales. The LFF may coexist with and differentiate from the geodesic acoustic modes. The bispectrum analysis of the data indicates that nonlinear three wave coupling between the LFF and HFAT is a possible creation mechanism for the former. The possible correlation of the results with the theory and simulation predictions on quasimodes is discussed.

Dynamics of a multimode semiconductor laser with optical feedback

A new model of a multi-longitudinal-mode semiconductor laser with weak optical feedback is proposed. This model generalizes the well-known Tang-Statz-deMars equations, which are derived from the first principles and adequately describe solid-state lasers to a semiconductor active medium. Steady states of the model and the spectrum of relaxation oscillations are found, and the laser dynamics in the chaotic regime of low-frequency fluctuations of intensity is investigated. It is established that the dynamic properties of the proposed model depend mainly on the carrier diffusion, which controls mode-mode coupling in the active medium via spread of gratings of spatial inversion. The results obtained are compared with the predictions of previous semiphenomenological models and the scope of applicability of these models is determined.

多模半导体激光器在光反馈条件下的低频波动

Dynamics of a semiconductor laser subject to moderate optical feedback operating in the low-frequency fluctuation regime is numerically investigated. Multimode Lang-Kobayashi (LK) equations show that the low-frequency intensity dropout including the total intensity and sub-modes intensity is accompanied by sudden dropout simultaneously, which is in good agreement with experimental observation. The power fluctuation is quite annoying in practical applications, therefore it becomes important to study the mechanism of power fluctuation. It is also shown that many factors, such as spontaneous emission noise and feedback parameter, may influence power fluctuation larger than previously expected.

Power dropout control by optical phase modulation in a chaotic semiconductor laser

The effect of periodic phase modulation of light on a chaotic external-cavity semiconductor laser working in a regime of low-frequency fluctuations (LFFs) is studied numerically. It is observed that the phase modulation changes the time period between consecutive dropouts in the emitted laser intensity. A new variable ΦL is defined as the phase of the laser's LFFs, which increases in time with 2π after each power dropout event. The phase ΦPM of the periodic phase modulator is unfolded on the real axis and increases linearly at a rate given by the modulating frequency. It is shown that the phase difference between the laser and the modulator ΔΦ(t)=mΦL(t)−nΦPM(t), where m and n are integers, remains constant in time, leading to phase-synchronized states, for specific values of the modulating frequency and amplitude.

Two-mode chaos synchronization using a multimode external-cavity laser diode and two single-mode laser diodes

Strong optical injection and optical frequency matching have been used to effect an experimental demonstration of two-mode synchronization using a multimode external-cavity chaotic transmitter laser and two single-mode stand-alone receiver lasers. It is shown by means of synchronization diagrams and measured cross-correlation functions that the longitudinal modes of the receiver lasers have been successfully synchronized to frequency matched modes of the transmitter laser operating in the low frequency fluctuation regime.

Dynamics of semiconductor lasers with optical feedback: Comparison of multimode models in the low-frequency fluctuation regime

The role of spontaneous emission noise and gain line profile in the dynamics of a multimode semiconductor laser with weak-to-moderate optical feedback is studied. Two models of such a laser are compared. If the gain profile is flat and in the absence of noise, model A predicts that all modal intensities are in phase, and model B predicts antiphase dynamics of the modal intensities. Noise induces out-of-phase solutions in model A and hardly affects model B. Weakly curved gain profile determines the number of lasing modes but otherwise has little effect on the laser dynamics in both models.

Dynamics of self-pulsing semiconductor lasers with optical feedback

We analyse the dynamics of a self-pulsating semiconductor laser with optical feedback. Without re-injection of light the laser displays periodic oscillations. At very weak feedback levels we observe an amplitude instability whose frequency increases with the feedback level until the laser enters the low frequency fluctuation regime commonly observed in cw lasers with optical feedback. We show that such behaviour can be observed within the framework of the Lang–Kobayashi equations for self-pulsating semiconductor lasers.

Delay-induced resonances in an optical system with feedback.

We study the influence of the delay time in the response of a delayed feedback system to external periodic driving. The nonlinear system we consider is a semiconductor laser with optical feedback operating in the low-frequency fluctuation regime. We numerically examine the consequences of varying the external cavity length of the system when a weak modulation is introduced through the laser's pump current. The harmonic modulation is seen to lead to a partial periodic entrainment of power dropouts, and the distribution of time intervals between the dropouts exhibits resonances with certain delay times. In other words, the response of the system to the external modulation is enhanced for particular values of the external cavity length. The same effect can be observed in the presence of noise, indicating that stochastic resonance can be enhanced or degraded depending on the feedback time.