Continued growth in demand for sensing, communication, and computing has given rise to photonic integrated circuits (PICs) for applications such as LiDAR for self-driving systems, next-generation artificial intelligence systems, data transmission in 5G/6G optical networks, and quantum communications [1–3]. Particularly, silicon-based PICs with dense integration of lasers, modulators, and passive components are evolving rapidly from proof-of-concept demonstrations to commercialized products due to their advantages in terms of size, weight, cost, and power consumption. One of the biggest challenges for PICs is optical feedback that comes from either unwanted parasitic reflections or leakage from other adjacent components. This feedback degrades the coherence of on-chip lasers and enhances relative intensity noise (RIN), leading to strong laser instability such as a chaotic state or coherent collapse [4,5]. To overcome this issue, optical isolators must be appended to on-chip lasers for practical applications. However, the integration of optical isolators on the silicon substrate is quite challenging due to their bulky size and incompatibility with CMOS fabrication techniques [6]. In this context, on-chip lasers with intrinsic insensitivity to optical feedback are desirable in isolator-free PICs for optical sensing, communication, and computing systems.

Quantum dot (QD) lasers are considered the most promising on-chip light sources because QD gain material is available for both hybrid and monolithic integration on silicon, due to its high tolerance to threading dislocation defects [7–11]. Furthermore, compared with their quantum well (QW) counterparts, the intrinsic tight three-dimensional carrier confinement in QDs leads to numerous outstanding laser characteristics such as low threshold current density [12–16], high temperature stability [17–20], and low optical noise [21,22]. For QW lasers, laser emission always comes from the ground state (GS) transition, which is not the case for QD lasers. By continuously increasing pump currents, QD lasers exhibit a propensity to operate in the dual state at elevated output power, wherein the coexistence of GS and excited state (ES) emissions is obtained. This unique peculiarity in QD lasers is attributed to the unclamped gain and cascade-like carrier relaxation process [23–25]. Compared with sole GS QD lasers, QD lasers operating on sole ES exhibit not only relatively wide modulation bandwidth [26] due to higher differential gain [27] and faster carrier relaxation rate [28], but also more complex routes to chaos due to a lower relaxation oscillation frequency (ROF) [29–31], which is of great interest for random number generation [32]. Furthermore, dual-state lasing QD lasers exhibit lower intensity noise and larger modulation bandwidth than that of sole GS or ES QD lasers, which is due to the quasi-antiphase dynamics in the carrier relaxation process [33–35]. Dual-state lasing dynamics has been theoretically proved to be governed by the effect of a phonon bottleneck and inhomogeneous broadening [36]. The dual-state emission character of QD lasers opens up the possibility of many external perturbation scenarios that are of interest for both physics and engineering; foremost among them is bistability with a switching mechanism [37]. For instance, a transition from full GS emission to full ES emission in QD lasers can be realized through optical injection [38,39]. The nature of this intrinsic bistability and Q-switching dynamics in QD lasers contributes to the development of optical storage elements [40–42], optical triggers [43–45], as well as all-optical gates [39].

For optical feedback, QD lasers emitting on the sole GS have been shown to be highly resistant to both long-delay and short-delay external feedback due to their low linewidth enhancement factor (αH-factor) and high damping factor [46]. These lasers also exhibit error-free transmission under optical feedback in both external modulation and direct modulation configurations [47–49]. In contrast, QD lasers emitting on sole ES are more sensitive to optical feedback, which is attributed to the smaller damping rate and stronger partition noise [29–31]. When QD lasers operate in the dual state, the introduction of optical feedback leads to bistable operation where a power drop in the GS and an intensity burst in the ES are obtained [50–52].

This paper presents an experimental and theoretical investigation on the reflection sensitivity of dual-state QD lasers when subjected to external optical feedback. Experiment results show that the critical feedback level of dual-state QD lasers strongly depends on the occurrence of ES, demonstrating that reflection tolerance is greatly degraded at the ES lasing threshold. To interpret the underlying mechanism of this phenomenon, we establish a three-level rate equations model of a dual-state QD laser, by taking into account the effect of optical feedback. To assess the feedback resistance of dual-state QD lasers, the critical feedback level is determined by analyzing the simulated bifurcation diagram. Theoretical results align well with experimental observations, demonstrating that the damping factor and ROF significantly decrease while the αH-factor substantially increases at the ES lasing threshold, which finally affects the laser resistance to external optical feedback. Furthermore, higher ES-GS energy separation exhibits a positive association with the ES-GS threshold ratio, which can strengthen feedback insensitivity. This paper provides an in-depth investigation into the reflection sensitivity of dual-state QD lasers, emphasizing the significance of energy-level engineering in fabricating feedback-insensitive dual-state QD lasers for PICs without on-chip isolators.

For the QD laser in this study, the active region consists of 10 QD layers grown by solid source molecular beam epitaxy (MBE) on n+ GaAs (100) substrates. The QDs are directly deposited on the GaAs matrix at 485°C by deposition of 2.5 monolayers (ML) InAs at the growth rate of 0.083 ML/s and then covered with a 5 nm thick In0.15Ga0.85As layer, which results in a surface density of about 3×1010 to 5×1010cm−2. The dimensions of the QDs are typically within 15 to 20 nm in diameter and 3 to 5 nm in height, while the GaAs spacer is 33 nm in thickness. The laser is processed to have a 1 mm long cavity with as-cleaved facets and a 2 μm wide waveguide etched through the active area. The laser has low threshold current density, high differential efficiency, and high characteristic temperature [53]. At room temperature of 20°C, the threshold currents of the QD laser for GS and ES transitions (IthGS, IthES) are 16.5 and 186 mA, respectively. The corresponding ratio between ES and GS threshold currents is 11.3. Dual-state lasing operation can be achieved by increasing the bias current of the QD laser, as depicted in Fig. 1. The red and yellow blocks in Fig. 1(a) highlight the optical gain of GS and ES transitions, respectively. Dashed lines (1) and (2) in Fig. 1(b) mark the bias currents in Figs. 1(a1) and 1(a2), respectively. The laser first exhibits GS lasing at lower bias currents while the peak wavelength is redshifted with the increase of current. The optical spectrum splits into two peaks separated by approximately 90 nm when the ES threshold current is exceeded.

The experiment setup for investigating the feedback sensitivity of QD lasers is depicted in Fig. 2. The light emitted from the QD laser is coupled by an anti-reflection-coated lens-end fiber and split by a 90/10 coupler into two paths; 90% of the coupled power is sent to the feedback path, while the remaining 10% is for detection. A backreflector (BKR) integrated with a mirror and variable attenuator is plugged to generate reflection. The polarization controller is inserted to compensate for fiber dispersion in the feedback path. In this case, the external cavity is composed of mentioned fiber components and necessary fiber optics patch cables, leading to a cavity length of 7 m, which corresponds to a long-delay feedback configuration [54]. The feedback strength (fext) is defined as the ratio between the power returned to the laser and emitted by the laser, which can be adjusted by the BKR. The maximal fext can reach −6.1dB in the measurement with the loss of laser-to-fiber coupling and fiber connection taken into account. An isolator can prevent additional feedback from the detection path. The feedback dynamics of a dual-state QD laser is investigated through an optical spectrum analyzer (OSA) and an electrical spectrum analyzer (ESA). Since the ROF of QD lasers is of the order of several GHz [27], the 12 GHz bandwidth of the photodiode (PD) is sufficient in the experiment.

Figure 3 depicts the optical and radio frequency (RF) spectrum mappings as a function of the feedback strength for different bias currents of 0.72×, 1×, and 1.25×IthES. The progression of the longitudinal mode of the gain peak and dynamical behavior in the RF domain is depicted in columns 1 and 2, respectively. With the increase of feedback strength, the narrow modal linewidth in optical spectra and the absence of coherence collapse in RF spectra can be maintained until the critical feedback level (rcrit) is exceeded. rcrit corresponds to the birth of laser destabilization, beyond which the laser is no longer stable against optical feedback where strong longitudinal mode broadening, the first Hopf bifurcation, and the onset of coherence collapse take place [47]. The QD laser exhibits weak resistance to optical feedback with rcrit=−24.0dB at the ES threshold current compared to the case of 0.72×IthES, which has larger rcrit of −15.9dB, meaning that the stability of GS lasing is degraded when approaching dual-state lasing. It is contributed by the lower damping factor and larger αH-factor, which is theoretically confirmed in Section 3.C. Once ES lasing occurs, the feedback resistance re-increases to rcrit=−14.8dB at 1.25×IthES, which results from a reduction of the αH-factor associated with the ES transition induced by the larger differential gain. In addition, it is important to stress that any further increase of the pump current also raises the damping factor accordingly, resulting in restabilization of the lasers against optical feedback. The whole process of rcrit variation with increasing bias current is shown later in Fig. 8 to compare with simulation results. Figure 4 compares the optical and RF spectra for high fext of −9.9dB and low fext of −29dB at the ES lasing threshold. At a high feedback level, the laser experiences the coherence collapse state with strong broadening of the Fabry-Perot (FP) modes in both GS and ES as well as intense chaotic oscillations observed in the RF domain. In the following section, the three-level rate equations are established to further investigate the complete optical feedback dynamics in dual-state QD lasers.

Figure 6 demonstrates the GS and ES threshold current as well as ES-GS threshold ratio versus ES-GS energy separation ranging from 40 to 110 meV. It is noteworthy that the ES-GS energy separations of the QD laser up to 108 meV in measurement [57] and 126 meV in theory [58] have been demonstrated. The GS transition energy is mostly determined by the vertical confinement and thus the thickness of the QD, while energy separation is related to QD lateral confinement. For large ES-GS energy separation, the ES threshold increases while the GS threshold decreases followed by the increase of the ES-GS threshold ratio. This effect implies that high ES transition energy favors the maintenance of sole GS emission and delays the appearance of ES lasing; hence a high ES-GS energy separation is beneficial to increase the ES-GS threshold ratio in the fabrication of QD lasers. It is noted that the dependence of feedback resistance on the threshold ratio has been experimentally proved in epitaxial QD lasers on silicon [59]. Thus, the effect of ES-GS energy separation on reflection sensitivity is theoretically investigated as follows.

The external cavity length is set to 30 cm in the simulation, in which case the QD laser is operated in the long-delay regime in line with the experiment [46,60,61]. Figure 7 shows bifurcation diagrams with respect to the normalized bias current I/IthES and ES-GS energy separation (ΔEGSES). The corresponding time series and GS phase portraits are demonstrated in the second and third columns, respectively. Three values of ES-GS energy separation are applied to investigate the impact of energy separation on laser feedback sensitivity. In Fig. 7(a), the ES-GS energy separation is set to ΔEGSES=65meV, corresponding to IthGS=37.0mA, IthES=319.5mA, and IthES/IthGS=8.64. The bifurcation diagram of GS lasing plots the case when the normalized bias current I/IthES=1.0, where the QD laser operates at the ES threshold. rcrit can be extracted from the first Hopf bifurcation, which is −26.3dB. The time series and phase portrait of GS lasing are plotted with the high feedback strength of −12.0dB, in which case the laser operates in a chaotic state with irregular time series peaks and overlapping phase portraits. Furthermore, the ES-GS energy separation is then set to ΔEGSES=80meV, corresponding to IthES/IthGS=11.5, and the normalized bias current is set to I/IthES=1.31 in Fig. 7(b). The QD laser operates in the dual-state lasing regime where both GS and ES show the same rcrit of −14.3dB. The time series with a feedback strength of −11.0dB illustrates that period-one periodic oscillation is taking place for both GS and ES; the corresponding GS portrait gives one closed circle approximating a line. Figure 7(c1) reveals the bifurcation diagram for large ΔEGSES of 110 meV at I/IthES=0.87, indicating that the laser operates at sole GS. The corresponding IthES/IthGS is 16.7, and rcrit is −20.3dB. Figures 7(c2) and 7(c3) show the time series and phase portrait for fext of −13.0dB, where the period-two periodic oscillation is found in the time domain with two closed circles in the phase portrait.

Figure 8 compares the critical feedback levels extracted at different bias currents between measurement and simulation. For the measurement, the minimum rcrit is found at the ES threshold current, while rcrit is enhanced regardless of whether the bias current is increased or decreased, which means that the QD laser has higher resistance to optical feedback at bias currents away from the ES threshold. The influence of ES-GS energy separation on the resistance to optical feedback is also demonstrated in Fig. 8. When the ES-GS energy separation is set to 65 meV, which is the same as the result of the QD material grown by the same technology [62], the simulation results are quantitatively in agreement with the measurement. Therefore, the validity of the dual-state QD lasers model under optical feedback is verified. The black arrow confirms that a large ΔEGSES strengthens the laser stability against optical feedback. For instance, at 1.05 ×IthES near the ES threshold, rcrit increases from −20.8dB for ΔEGSES=65meV to −17.7dB for ΔEGSES=110meV. In dual-state lasing operation, rcrit reaches −12.4dB for the laser with ΔEGSES of 110 meV at 1.27 ×IthES. Since IthES/IthGS is positively correlated with ΔEGSES, Fig. 8 also indicates that large ES-GS energy separation, which can be obtained by optimizing the size, composition, and strained buffer layer of the QDs [57,58,63,64], contributes to maintaining the sole GS emission at high bias current and attenuates the reflection sensitivity in the case of dual-state lasing.

The dynamic properties of QD lasers including αH-factor, damping factor, and ROF are investigated to explain the high feedback sensitivity at the ES threshold. Figure 9 displays that the dependence of normalized bias current on the αH-factor originates from the GS and ES. The αH-factors are obtained from the phase noise spectrum, while ΔEGSES is set to 50 meV [65]. The αH of GS grows from 0.7 at 0.2×IthES to 1.2 at 0.9×IthES and then exhibits a peak of 2.9 at the ES threshold current, which is attributed to the enhanced carrier variation in the RS and ES [26,66]. As the bias current continues to increase above the ES threshold, the carriers in ES are clamped, which suppresses the carrier variation in ES [67]. Therefore, GS αH decreases from 1.0 at 1.1×IthES to 0.6 at 1.8×IthES, while ES αH remains constant at about 0.57. This difference depicts that feedback sensitivity is mainly driven by the αH from the GS.

The damping factor and ROF extracted from the modulation transfer function of the laser system, are shown in Fig. 10 as a function of the normalized bias current. With the increase of bias current, the laser is overdamped with a high damping factor slightly increasing from 171 to 176 GHz, and the ROF increases to a maximum of 1.24 GHz. Nevertheless, a sharp decline in the damping factor is observed, reaching its minimum value of 9.4 GHz, and the ROF is also a minimum of 0.2 GHz. This remarkable reduction can be attributed to the predominant influence of ES spontaneous emission. As the ES lasing threshold is surpassed, the stimulated emission from ES becomes dominant, subsequently amplifying both the damping factor and the ROF. rcrit can be calculated by [4,68,69] rcrit=γ2(1+αH2)αH4τin2R4(1−R)2,(16)where γ is the damping factor. Therefore, it is verified that the local minimum value of rcrit at the ES threshold shown in Fig. 8 is driven by high αH-factor, low damping factor, and low ROF, which result in the reflection sensitivity of the QD laser.

We investigated the reflection sensitivity of dual-state QD lasers from both measurements and simulations. The experimental results demonstrate that the rcrit of dual-state QD lasers strongly depends on the occurrence of the ES, and the feedback tolerance is significantly degraded at the ES lasing threshold. The numerical model of dual-state QD lasers considering external optical feedback is established to investigate this phenomenon. rcrit extracted from the bifurcation diagram is in good agreement with the measurement, which confirms the validity of the model. Furthermore, the high ES-GS energy-level separation associated with the high ES-GS threshold ratio contributes to strengthening the feedback resistance. At the ES threshold, the burst αH-factor and the collapse damping factor make the QD laser more sensitive to external optical feedback. These findings bring new insights for understanding the physical mechanisms in QD lasers and highlight the importance of energy-level engineering in fabricating reflection-insensitive dual-state QD lasers for isolator-free PICs. Future work will focus on the optical noise properties of dual-state QD lasers under optical feedback.

Acknowledgment. We acknowledge Professor Dieter Bimberg from Technische Universität Berlin, Germany, and Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, China, for providing the high-quality QD laser sample.