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

Abstract

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...

Entraining power-dropout events in an external-cavity semiconductor laser using weak modulation of the injection current

“…The usual phase-space model of LFF [15] based on the Lang-Kobayashi equations shows that the dynamics evolve along the external cavity modes of the system, which are the steady-state solutions of (5) and (6). These states can be characterized in terms of and the dimensionless photon number, carrier number, and optical angular frequency shift, respectively, where and represents the dimensionless optical angular frequency.…”

“…To determine whether the Lang-Kobayashi model with modulation can give rise to qualitatively similar behavior to that seen in the experiments, we numerically integrate (5) and (6). The temporal evolution of the power emitted by the ECSL is shown for no modulation in Fig.…”

Interspike-interval correlations induced by two-state switching in an excitable system

“…1(a). Even though this behavior is the result of delay-induced instabilities and is thus high-dimensional in nature [9,10], experimental and theoretical studies have shown that the power dropouts can be interpreted as excitable pulses [11,12], which have even been reproduced with low-dimensional models [13]. Therefore, here we use this system as a test bed to study the emergence of interspike interval correlations in generic excitable systems.…”

Low Frequency Fluctuations in a Multimode Semiconductor Laser with Optical Feedback

“…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.…”