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Two-parameter bifurcation diagrams of an optically injected (a), (c) shallow-dot and (b), (d) deep-dot QD laser. The color code denotes the number of intensity extrema found at each (K,Δνinj) parameter point, using the MBBE model (a), (b) and the MBBE with an α-factor (c), (d), respectively. The solutions were obtained numerically by sweeping the injection detuning outwards from Δνinj = 0. The light-blue to light-yellow shaded region shows the increasing laser intensity in the phase-locked region, where the QD laser emits cw light. The other color code denotes periodic oscillations (orange to dark blue), as well as chaotic or quasi-periodic behavior (white). The hatched region denotes phase-bounded oscillation, where the mean output frequency is equal to νinj. The solid and dashed lines denote SNIC and Hopf bifurcation lines, respectively, delimiting the phase-locked region. J = 2Jth.
Source publication
We employ a nonequilibrium energy balance and carrier rate equation model based on microscopic semiconductor theory to describe the quantum-dot (QD) laser dynamics under optical injection and time-delayed feedback. The model goes beyond typical phenomenological approximations of rate equations, such as the alpha-factor, yet allows for a thorough nu...
Citations
... General dynamical features have been identified in nanolasers [13][14][15][16][17][18][19][20][21][22], together with dynamics induced by feedback [23][24][25][26][27][28][29][30][31][32], mode competition [33][34][35][36], mode coupling, and synchronization [37]. Sensing [38] and generation of low-coherence light [39] have been recently proposed as a result of the dynamical features that are typical of these devices. ...
Chaos in semiconductor lasers or other optical systems has been intensively studied in the past two decades. However, modulation around threshold has received much less attention, in particular, in gain-modulated semiconductor lasers. In this paper, we investigate the bifurcation sequence that appears with pump modulation in the threshold region with a large amplitude and different values of modulation frequency. Modulation around threshold necessarily includes “below-threshold” dynamics, which can be effectively displayed only through a nonlinear visualization of the oscillations. The irregular temporal behavior is examined at various modulation frequencies and amplitudes, highlighting a possible route to chaos for very large amplitude modulation in the near-threshold region. The addition of (average) spontaneous emission to the lasing mode enables a coupled dynamics between photons and carriers even below threshold, thus extending the pump range in which modulation actively modifies the laser behavior. We also report on the existence of a transition between similar attractors characterized by a temporal transient that depends on the amplitude of the modulation driving the pump.
... The emission from ES significantly alters the symmetry of the gain spectrum hence ballooning the -factor to larger values (Newell et al., 1999;Dagens et al., 2005;Mi, Bhattacharya, and Fathpour, 2005). Prior studies revealed that the off-resonant states affect the -factor by mainly changing the refractive index variation (Lingnau, Lüdge, et al., 2012;Lingnau, Weng W Chow, et al., 2013) (Uskov et al., 2004). The carrier plasma effect in QW based on Drude formula is described as follows (Hegarty et al., 2005): ...
Silicon photonics is promising for high-speed communication systems, short-reach optical interconnects, and quantum technologies. Direct epitaxial growth of III-V materials on silicon is also an ideal solution for the next generation of photonic integrated circuits (PICs). In this context, quantum-dots (QD) lasers with atom-like density of states are promising to serve as the on-chip laser sources, owing to their high thermal stability and strong tolerance for the defects that arise during the epitaxial growth. The purpose of this dissertation is to investigate the nonlinear properties and dynamics of QD lasers on Si for PIC applications. The first part of this thesis investigates the dynamics of epitaxial QD lasers on Si subject to external optical feedback (EOF). In the short-cavity regime, the QD laser exhibits strong robustness against parasitic reflections hence giving further insights for developing isolator-free PICs. In particular, a near-zero linewidth enhancement factor is crucial to achieve this goal. The second part is devoted to studying the static properties and dynamics of a single-frequency QD distributed feedback (DFB) laser for uncooled and isolator-free applications. The design of a temperature-controlled mismatch between the optical gain peak and the DFB wavelength contributes to improving the laser performance with the increase of temperature. The third part of this dissertation investigates the QD-based optical frequency comb (OFC). External control techniques including EOF and optical injection are used to optimize the noise properties, reduce the timing-jitter, and increase the frequency comb bandwidth. In the last part, an investigation of the optical nonlinearities of the QD laser on Si is carried out by the four-wave mixing (FWM) effect. This study demonstrates that the FWM efficiency of QD laser is more than one order of magnitude higher than that of a commercial quantum-well laser, which gives insights for developing self-mode-locked OFCs based on QD. All these results allow for a better understanding of the nonlinear dynamics of QD lasers and pave the way for developing high-performance classical and quantum PICs on Si.
... These devices are extremely stable in feedback configurations 8 and offer genuine promise of isolator free operation [9][10][11] . In the optical injection configuration they are significantly more stable than conventional semiconductor lasers, allowing for phase locked operation over a much larger area of control parameters and with a marked reduction in areas displaying chaotic operation [12][13][14][15][16][17] . They also display many unique dynamics such as canard phenomena and a multitude of excitable regimes [16][17][18][19][20][21][22] . ...
... All of their results are numerical but they consider carefully the experimental results of 81 . They also perform successful analyses for the GS only situation using such a model in 14,85,86 . Rather than having an explicit α, they extract the frequency shift of the GS field brought about by changes in the full carrier ...
We review results on the optical injection of dual state InAs quantum dot-based semiconductor lasers. The two states in question are the so-called ground state and first excited state of the laser. This ability to lase from two different energy states is unique amongst semiconductor lasers and in combination with the high, intrinsic relaxation oscillation damping of the material and the novel, inherent cascade like carrier relaxation process, endows optically injected dual state quantum dot lasers with many unique dynamical properties. Particular attention is paid to fast state switching, antiphase excitability, novel information processing techniques and optothermally induced neuronal phenomena. We compare and contrast some of the physical properties of the system with other optically injected two state devices such as vertical cavity surface emitting lasers and ring lasers. Finally, we offer an outlook on the use of quantum dot material in photonic integrated circuits.
... The influential research in optical bistability (OB) by Bonifacio and Lugiato [1,2] undergirds the many investigations of the active counterpart of OB, the laser with injected signal (LIS). The LIS system is well-studied and covers a broad range of active systems, including CO2, diode [3][4][5], and quantum dot lasers [6,7]. It is replete with interesting dynamics from chaos to coexisting attractors [8][9][10]. ...
Universal, predictive attractor patterns configured by Lyapunov exponents (LEs) as a function of the control parameter are shown to characterize periodic windows in chaos just as in attractors, using a coherent model of the laser with injected signal. One such predictive pattern, the symmetric-like bubble, foretells of an imminent bifurcation. With a slight decrease in the gain parameter, we find the symmetric-like bubble changes to a curved trajectory of two equal LEs in one attractor, while an increase in the gain reverses this process in another attractor. We generalize the power-shift method for accessing coexisting attractors or periodic windows by augmenting the technique with an interim parameter shift that optimizes attractor retrieval. We choose the gain as our parameter to interim shift. When interim gain-shift results are compared with LE patterns for a specific gain, we find critical points on the LE spectra where the attractor is unlikely to survive the gain shift. Noise and lag effects obscure the power shift minimally for large domain attractors. Small domain attractors are less accessible. The power-shift method in conjunction with the interim parameter shift is attractive because it can be experimentally applied without significant or long-lasting modifications to the experimental system.
... Figure 3 shows maps of P and η calculated for three different values of γ 21 (10 ns −1 , 50 ns −1 and 150 ns −1 ) for the following set of parameters: γ n =1 ns −1 , γ 0 =400 ns −1 , γ s = 10 ns −1 , γ p =20 ns −1 , α=3, k=250 ns −1 and h 1 =1.1995. These are in the range of previously reported values [38][39][40]. It is noted that works [26,40], on the α factor for QD lasers have challenged conventional practices of using the same value for both ES and GS emission. ...
... These are in the range of previously reported values [38][39][40]. It is noted that works [26,40], on the α factor for QD lasers have challenged conventional practices of using the same value for both ES and GS emission. Additionally, the reported values for QD lasers vary from very small [19,41], to very large values [24,28]. ...
We investigate numerically the chaotic dynamics of optically pumped quantum-dot (QD) spin vertically coupled surface emitting lasers (VCSELs) accounting for both ground state (GS) and excited state (ES) energy levels through the elaboration of the spin-flip model (SFM). The intensity dynamics associated with ES and GS transitions are studied by means of the largest Lyapunov exponent (LLE) and stability maps in terms of operational parameters (pump ellipticity and pump intensity), as well as material parameters (ES–GS intraband relaxation rate, spin relaxation rate and birefringence), are produced. It is established that although both ES and GS dynamics exhibit the same kind of nonlinear dynamics for a given set of control parameters, the ES and GS dynamics are weakly uncorrelated. This can be the basis for the realization of various functionalities including reservoir computing.
... QD lasers are less sensitive to optical feedback than quantum-well (QW) semiconductor lasers [6,7]. Nevertheless, rich nonlinear dynamics of QD lasers with optical feedback or injection have been reported [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Theoretical analysis of bifurcation toward chaotic dynamics has been significantly investigated in QD lasers with optical feedback or injection [6][7][8][9][10][11][12][13]. ...
... Nevertheless, rich nonlinear dynamics of QD lasers with optical feedback or injection have been reported [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. Theoretical analysis of bifurcation toward chaotic dynamics has been significantly investigated in QD lasers with optical feedback or injection [6][7][8][9][10][11][12][13]. Compared with intensive theoretical and numerical examinations, experimental investigations of the nonlinear dynamics of QD lasers with optical feedback are noticeably limited [14][15][16][17][18]. ...
We experimentally investigate the complex dynamics of a multi-mode quantum-dot semiconductor laser with time-delayed optical feedback. We examine a two-dimensional bifurcation diagram of the quantum-dot laser as a comprehensive dynamical map by changing the injection current and feedback strength. We found that the bifurcation diagram contains two different parameter regions of low-frequency fluctuations. The power-dropout dynamics of the low-frequency fluctuations are observed in the sub-GHz region, which is considerably faster than the conventional low-frequency fluctuations in the MHz region. Comparing the dynamics of quantum-dot laser with those of single- and multi-mode quantum-well semiconductor lasers reveals that the fast low-frequency fluctuation dynamics are unique characteristics of quantum-dot lasers with time-delayed optical feedback.
... Despite this simplification, this assumption is sufficient to reproduce the experimental findings. g g 0 and g e 0 are gain coefficients, and β models the effect of inhomogeneous broadening [41,49]. The primary laser control parameters are ε and ≡ ω i − ω g , respectively, the injection strength and the detuning between the frequency of the injected light and that of the GS. ...
One of the defining characteristics of excitability is the existence of an excitable threshold: the minimum perturbation amplitude necessary to produce an excitable response. We analyze an optically injected dual state quantum dot laser, previously shown to display a dual state stochastic excitable dynamic. We show that deterministic triggering of this dynamic can be achieved via optical phase perturbations. Further, we demonstrate that there are in fact two asymmetric excitable thresholds in this system corresponding to the two possible directions of optical phase perturbations. For fast enough perturbations, an excitable interval arises, and there is a limit to the perturbation amplitude, above which excitations no longer arise, a phenomenon heretofore unobserved in studies of excitability.
... An important step towards improving the resistance of semiconductor lasers to optical feedback and other perturbations was the fabrication and subsequent employment of self-assembled semiconductor quantum dots (QDs) as the active medium in lasers (Bimberg et al. 1999;Bimberg and Pohl 2011). In addition to their reduced threshold current and temperature stability, QD lasers are more robust against such perturbations (Otto et al. 2010(Otto et al. , 2012aGlobisch et al. 2012;Lingnau et al. 2013;Duan et al. 2019;O'Brien et al. 2004;Huyet et al. 2004). As we will see later on, this robustness is facilitated by a change of the internal dynamical timescales due to the presence of the QDs. ...
... Short delay, in this context means that the roundtrip time in the external cavity t is not larger than the RO period T = 2p/o RO . The most general formulation of the dynamic equation of the electric field then reads (van Tartwijk and Agrawal 1998;Lingnau et al. 2012Lingnau et al. , 2013: ...
... and significantly simplifies the dependence of the complex gain G = Re G + iIm G on the carrier density N. The simplified dynamic equation for the electric field then reads (van Tartwijk and Agrawal 1998;Ohtsubo 2013;Lingnau et al. 2013): ...
... For a QD laser the description of gain and refractive index is more complex and also for the latter mainly non-resonant states contribute to this. These effects are called instantaneous frequency shifts [11][12][13]. The band structure of a QD laser contains localized energy levels. ...
... Note that we describe the index shift by the linear relation δΩN. This has been derived from [12]. The ES is included in the carrier dynamics model and participates in the scattering processes but is not optically active. ...
We experimentally and analytically investigate the influence of temperature on the linewidth of an InP quantum dot (QD) laser. The full width half maximum of the peak in the optical spectrum strongly depends on the pump current and rebroadens at high injection levels. We show that with increasing temperature these effects are amplified. Applying a QD laser model including the excited and ground state with detailed balance scattering rates, we are capable of reproducing the experimentally observed data qualitatively and thus show that a relatively simple QD-laser model is capable of capturing this complex behavior. Additionally, we include a temperature dependent energy band gap reduction needed to fit the data and show that this effect enhances the rebroadening effect for higher temperatures.
... Nevertheless, previous works have shown, that exposing quantum dot lasers to external perturbations like optical feedback or injection, a rich variety of dynamics including oscillation bursts [9], externally activated pulse trains [10], regular pulse packages [11,12], nonlinear oscillations [13], excitability [14,15] and chaos [16][17][18] can be observed. ...
... To furthermore account for the varying sizes of the QDs and thus varying localization energies, i.e. the inhomogeneous broadening, the QDs are separated into a set of resonant and optically active QDs and a set of off-resonant and optically inactive QDs. The ratio between the two sets is extracted from a full Maxwell-Bloch model, which uses QD subgroups to describe the inhomogeneous broadening [17]. We use m ∈ {GS, ES} to denote the QD state, b ∈ {e, h} to denote the charge-carrier type and x ∈ {a, i} to denote either the active or inactive set of QDs. ...
We investigate the impact of short optical feedback on a two-state quantum dot laser. A region in the feedback parameter space is identified, where the laser emission periodically alternates between oscillation bursts from the quantum dot ground and excited state, i.e. two-color anti-phase oscillation bursts. We compare these results to the low-frequency fluctuations and regular pulse packages of single-color semiconductor lasers and show via an in-depth bifurcation analysis, that the two-color oscillation bursts originate from a torus-bifurcation of a two-state periodic orbit. A cascade of further period-doubling bifurcations produces chaotic dynamics of the burst envelope. Our findings showcase the rich dynamics and complexity, which can be generated via the interaction of electronic and photonic time scales in quantum dot lasers with optical feedback.
