Experimental Investigation on the Dynamics Characteristics of a Two-State Quantum Dot Laser under Optical Feedback

Abstract

We experimentally investigate the dynamics characteristics of a two-state quantum dot laser (TSQDL) subject to optical feedback. Firstly, we inspect the impact of the temperature on the power-current characteristics of the ground state (GS) lasing and the excited state (ES) lasing in the TSQDL operating at free-running. The results demonstrate that with the decrease in the temperature, the threshold current for GS lasing ($I_{th}^{GS}$) and the threshold current for ES lasing ($I_{th}^{ES}$) decrease very slowly. There exists a current for GS quenching ($I_Q^{GS}$), which is gradually increased with the decrease in the temperature. After introducing optical feedback, the overall trend of change is similar to those obtained under free-running. Next, through inspecting the time series and power spectrum of the output from the TSQDL under optical feedback, the dynamical characteristics of the TSQDL are investigated under different feedback ratios, and diverse dynamical states including quasi-chaos pulse package, chaos state, regular pulse package, quasi-period two, quasi-regular pulsing, and chaos regular pulse package have been observed. Finally, for the TSQDL biased at three different cases: lower than $I_{th}^{ES}$, slightly higher than $I_{th}^{ES}$, and higher than $I_{th}^{ES}$, nonlinear dynamic state evolutions with the increase in feedback ratio are inspected, respectively. The results show that, for the TSQDL biased at lower than $I_{th}^{ES}$, it presents an evolution route of stable state—quasi-chaos pulse package—chaos state—regular pulse package. For the TSQDL biased at slightly larger than $I_{th}^{ES}$, it presents an evolution route of stable state—quasi-regular pulsing—quasi-period two—chaos regular pulse package. For the TSQDL biased at higher than $I_{th}^{ES}$, the TSQDL always behaves stable state within the range of feedback ratio that the experiment can achieve. However, with the increase in optical feedback ratio, the number of longitudinal modes for GS lasing and ES lasing are changed.

1. Introduction

With the rapid advancement of science and technology, the quantum technology field has become a hotspot of research. Quantum dot lasers (QDLs), as a type of semiconductor lasers (SLs), possess a unique three-dimensional quantum confinement of carriers in the active region, which results in a discrete energy level structure [1]. As a result, QDLs exhibit some significant advantages over conventional quantum well lasers (QWLs), including large modulation bandwidth [2], low threshold current [3], high-temperature stability [4,5], and weak sensitivity to optical feedback [6,7]. These unique characteristics make QDLs excellent candidate light sources in many fields such as silicon photonic integrated circuits [8,9], optical switch [10,11], photonic microwave signal generation [12,13,14,15,16], and optical communications [17,18], etc. In particular, under introducing external perturbations such as optical injection, optical feedback, or optoelectronic feedback, QDLs may exhibit rich nonlinear dynamics [19,20], which can be applied in areas such as all-optical logic gates [21], optical memory [22], random number generation [23,24], chaotic secure communication [25,26], and so on.

For QDLs, the recombination of electrons and holes of the ground state (GS) leads to the GS lasing while the recombination of electrons and holes of the excited states (ES) can also lead to the lasing at lower wavelengths. Free-running QDLs may lase in a GS, an ES, or a coexistence state of GS and ES under different currents. Correspondingly, such QDLs are named as two-state QDLs (TSQDLs) [27,28,29,30]. However, through adopting some techniques to suppress one of the lasing patterns, QDLs can lase in GS or ES individually, and corresponding QDls are named ground-state quantum dot lasers (GSQDLs) [31] and excited-state quantum dot lasers (ESQDLs) [32], respectively. GSQDLs have relatively strong relaxation oscillation damping and low energy level structure, showing low threshold current and low sensitivity to optical feedback [33,34]. Compared with GSQDLs, ESQDLs exhibit a faster carrier capture rate and wider modulation bandwidth, which significantly improves the sensitivity of ESQDLs to optical feedback [35]. For TSQDLs, they show interesting lasing properties due to the interaction of the carriers and photons of two lasing modes. The experimental results demonstrate that, under a large current, the GS may be completely suppressed, which is called GS quenching [36]. Furthermore, the switching between multiple longitudinal modes and the multimodal dynamics of TSQDLs under external perturbations have received significant attention. In 2013, Virte et al. theoretically investigated the influence of optical feedback on ES and GS lasing in TSQDLs, and the results showed that the bistable switching between different emission states, as well as the selection of a lasing state, depends on the feedback intensity and injection current [37]. In 2016, Virte et al. experimentally and theoretically studied the multimode dynamics of a TSQDL under time-delayed optical feedback, and the results showed that the energy exchange between the longitudinal modes of the ES is triggered by changing the feedback phase [38]. In 2017, Pawlus et al. demonstrated experimentally and theoretically that, by introducing state-selective optical feedback, relative intensity noise (RIN) in a TSQDL can be reduced [39]. However, we have noticed that the dynamical characteristics of TSQDL are paid less attention.

In this work, we experimentally investigate the nonlinear dynamics and mode characteristics of a TSQDL under external optical feedback, and the effects of the optical feedback ratio and the bias current are analyzed.

2. Experimental Setup

The schematic diagram of the experimental setup is displayed in Figure 1, in which red and yellow lines represent the spatial and fiber optical path, respectively. The two-state quantum dot laser (TSQDL) utilized in this work is provided by Suzhou Institute of Nano and Bionics, Chinese Academy of Sciences, which is grown by molecular beam epitaxial (MBE) on Si-doped GaAs (100) substrate. The TSQDL possesses a Fabry-Perot (F-P) cavity with a length of 380 μm, and the center wavelength is about 1300 nm for ground state (GS) lasing and about 1210 nm for excited state (ES) lasing, respectively. The bias current and temperature of TSQDL are controlled by high-precision and low-noise current sources (ILX-Lightwave, LDC-3724C). The output light of TSQDL passes through an aspheric lens (AL) with a focal length of 2.50 mm and then is split into two parts by a 40:60 beam splitter 1 (BS1). The 60% emitted light first passes through a neutral density filter (NDF) and then is reflected by a plane mirror before being fed back into the laser. In this experiment, the external cavity length is fixed at 22 cm, and the corresponding external cavity frequency $f_{ext}$ = 0.58 GHz. Through adjusting NDF, the feedback ratio κ (=$P_{pm}/P_{tot}$, where $P_{pm}$ is the feedback power detected at point A in Figure 1, and $P_{tot}$ is the total output power of free-running TSQDL) can be controlled. The power is monitored by a power meter (PM1, Thorlabs PM100D). The 40% of the power output from BS1 is divided equally into two paths via a 50:50 beam splitter 2 (BS2). One path passes through a bandpass filter (BF) and then is sent to PM2 for measuring the output power, and the other path is directly coupled into optical fiber through a coupler (OC). The coupled signal is split into two parts by a 20:80 fiber coupler (FC), where 20% output enters an optical spectrum analyzer (OSA, Ando AQ6317C) for recording optical spectrum and 80% output is converted into electrical signal by a photodetector (PD, New Focus 1544B, 12-GHz bandwidth). The electrical signal output from PD is divided into two parts by a 50:50 electric power divider (EPD). One enters an electronic spectrum analyzer (ESA, FSW67, 67-GHz bandwidth, Rohde & Schwarz, Munich, Germany) for power spectrum measurement, and the other is used to record the time series by a digital storage oscilloscope (DSO, X91604A, 16 GHz bandwidth, Agilent, Santa Clara, CA, USA).

3. Results and Discussion

Figure 2(a1,a2) shows the power–current (P-I) curves of the TSQDL at different temperatures under free-running and optical feedback with a feedback ratio of κ = 0.208, respectively. From Figure 2(a1,a2), one can observe the threshold current for GS ${(I}_{th}^{GS})$ and ES lasing${(I}_{th}^{ES})$ and the current for GS quenching ($I_Q^{GS}$) under different temperatures, and the corresponding results are shown in Figure 2(b1,b2). For free-running TSQDL (as shown in Figure 2(a1,b1)), with the decrease in temperature, the values of $I_{th}^{GS}$ and $I_{th}^{ES}$ decrease slightly, and meanwhile the value of $I_Q^{GS}$ gradually increases. It is easy to understand that the threshold current decreases with the temperature, which is a common feature of semiconductor lasers. As for $I_Q^{GS}$ presenting an increased trend, it may have originated from the relaxation rate from GS to ES being slower under a lower temperature. As a result, the current required for GS intensity quenching (or completely being suppressed) increases. After introducing optical feedback with a feedback ratio of κ = 0.208 (as shown in Figure 2(a2,b2)), the overall trend is similar to that obtained under free-running. However, the output power is obviously increased due to the introduction of feedback.

Figure 2(a2,b2) are obtained at a fixed feedback ratio. Next, we will investigate the influence of feedback ratio on P-I characteristics of TSQDL, and the corresponding result is given in Figure 3. Here, the temperature of laser is fixed at 16 °C. From this diagram, it can be seen that, with the increase in the feedback ratio, both the GS threshold current and the ES threshold current gradually decrease, but the current for GS quenching ($I_Q^{GS}$) increases significantly. At the same time, a large feedback ratio may be helpful for achieving a large output power.

Then, we will examine the optical spectrum properties of TSQDL. Figure 4a shows the power–current (P-I) curve of the free-running TSQDL. It can be seen that the threshold currents of the GS and ES of the TSQDL are $I_{th}^{GS}$ = 25.00 mA and $I_{th}^{ES}$ = 70.00 mA, respectively. Figure 4(b1–b3) display the optical spectra of the TSQDL biased at 50.00 mA, 75.00 mA, and 85.00 mA, respectively. For the bias, current is set at 50 mA ($2\times I_{th}^{GS}$), GS exhibits multi-longitudinal mode lasing, while ES does not lase. For the current increases to 75.00 mA ($1.07\times I_{th}^{ES}$), ES begins to lase in a single longitudinal mode, while GS lasing is suppressed completely. For the current is 85.00 mA ($1.13\times I_{th}^{ES}$), ES lases in a multi-longitudinal mode, while GS lasing is still suppressed.

Finally, we will investigate the influence of optical feedback on the dynamic state of the TSQDL under the bias current taken 50.00 mA, 75.00 mA, and 85.00 mA, respectively.

For the TSQDL is biased at 50.00 mA lower than $I_{th}^{ES}$, Figure 5 shows the output optical spectrum (first column), time series (second column), and power spectra (third column) of some typical dynamical states under feedback ratio κ. Under this circumstance, the ES does not lase at all. For κ = 0 (without optical feedback), the optical spectrum (Figure 5(a1)) shows that multiple longitudinal modes with a mode interval of ${∆\lambda }_{GS}$ = 0.63 nm can be observed for GS lasing. Some tiny fluctuations emerge in the time series (Figure 5(b1)), which originated from laser noise. Accordingly, the power spectrum (Figure 5(c1)) almost coincides with the noise floor level. Therefore, the dynamic state of the TSQDL is a stable state (S). For κ = 0.097, one can observe that the time series (Figure 5(b2)) shows slowly varying envelope pulses and the power spectrum (Figure 5(c2)) shows two incommensurable frequencies. Thus, this dynamic state of the TSQDL corresponds to a quasi-chaotic pulse package (QCPP). For κ = 0.149, the number of longitudinal modes obviously increases for GS lasing. Random intensity oscillation is observed in the time series (Figure 5(b3)), and the corresponding power spectrum (Figure 5(c3)) covers a wide frequency range. As a result, the TSQDL exhibits a chaotic state(C). For κ = 0.206, from the optical spectrum (Figure 5(a4)), it can be seen that the number of longitudinal modes is significantly increased. The time series (Figure 5(b4)) behaves as regular pulse oscillations, and meanwhile, an equal-interval frequency distribution emerges in the power spectrum (Figure 5(c4)). Therefore, the TSQDL exhibits a regular pulse package (RPP), and its frequency is 0.58 GHz, which is identical to the external cavity frequency. In short, by gradually increasing the optical feedback ratio, an evolution route of S-QCPP-C-RPP is observed due to the competition between the relaxation oscillation frequency of the laser and the external cavity frequency. Moreover, only GS lasing is observed, and the reason may be as follows. For the TSQDL is biased at 50.00 mA lower than $I_{th}^{ES}$, the optical feedback results in the recombination of electrons and holes in GS, which makes the GS lasing be amplified. At the same time, the recombination of electrons and holes in GS accelerates the intraband transition from ES to GS, which makes the ES more difficult to lase. Under this case of relatively low current, optical feedback may be helpful for further enhancing the preponderance of the GS lasing while the ES cannot lase all the time.

For the TSQDL is biased at 75.00 mA slightly higher than $I_{th}^{ES}$, corresponding results are presented in Figure 6. For κ = 0 (free-running), only one longitudinal mode is observed in the optical spectrum of ES lasing (Figure 6(a1)), while GS lasing is quenching. The time series (Figure 6(b1)) and power spectrum (Figure 6(c1)) are similar to those in Figure 5(b1) and power spectrum Figure 5(c1). Therefore, the TSQDL operates at a stable state (S). For κ = 0.136, the optical spectrum (Figure 6(a2)) show that multiple longitudinal modes oscillation is observed for ES lasing and GS lasing. Periodic drops in intensity can be observed in the time series (Figure 6(b2)), and meanwhile multiple peaks emerge in the power spectrum (Figure 6(c2)). The fundamental frequency in power spectrum agrees with the external cavity frequency $f_{ext}$= 0.58 GHz. Therefore, it can be judged that the TSQDL operates at a quasi-regular pulsing (QRP). For κ = 0.161 (Figure 6(a3–c3)), the number of longitudinal modes of the ES remains almost unchanged, and the intensity of each longitudinal mode decreases. However, the number of longitudinal modes of the GS increases, and the intensity of each longitudinal mode increases. Combining the time series with the power spectrum, the dynamical state of the TSQDL is determined to be a quasi-period two (Q2). For κ = 0.215 (Figure 6(a4–c4), the ES lasing is completely suppressed, and much more longitudinal modes are observed for GS lasing. Regular oscillations with random intensity are shown in the time series, and the corresponding power spectrum covers a broad frequency range with multiple peaks. Therefore, the TSQDL presents a chaos regular pulse package (CRPP). The above results demonstrate that with the increase in feedback ratio, the GS lasing gradually becomes dominant and ES lasing is gradually suppressed. The reason may be explained as follows. Since the TSQDL is biased at 75.00 mA slightly higher than $I_{th}^{ES}$, the ES lasing has no obvious advantage over the GS lasing under free-running. After introducing optical feedback, with the increase in optical feedback, many more electrons and holes in ES are consumed by photons from the feedback light. As a result, with the increase in feedback strength, the preponderance of ES lasing is gradually weakened while the GS lasing is gradually strengthened. If the feedback strength is strong enough, the GS lasing becomes the dominant lasing pattern, and the ES lasing vanishes.

As for the TSQDL is biased at 85.00 mA higher than $I_{th}^{ES}$, the experimental results show that the TSQDL under optical feedback always operates at a stable state but the number of longitudinal modes varies with the feedback ratio. The corresponding results are shown in Figure 7. In order to better judge whether a longitudinal mode appears, we draw two vertical gray dashed lines in the optical spectrum of Figure 7(a1–a6) corresponding to wavelengths ${\lambda }_{ES}$ = 1208.62 nm and ${\lambda }_{GS}$ = 1317.34 nm. As shown in Figure 7(a1), without optical feedback (κ = 0), the ES lasing includes multiple longitudinal modes with a mode interval of ${∆\lambda }_{ES}$ = 0.51 nm, the GS does not lase. After introducing optical feedback with κ = 0.162 (Figure 7(a2)), a part of longitudinal modes for ES lasing are suppressed, only three longitudinal modes with a mode interval of ${2\times ∆\lambda }_{ES}$ can be observed, and the GS does not lase. For κ = 0.183 (Figure 7(a3)), compared with Figure 7(a2), the longitudinal mode in ES lasing with the longest wavelength is suppressed and the other two longitudinal modes are enhanced due to mode competition. For κ = 0.207 (Figure 7(a4)), only one longitudinal mode with a wavelength of 1208.05 nm remains in the ES lasing, and the GS is still suppressed. For κ = 0.222 (Figure 7(a5)), there are only two longitudinal modes with a mode interval of ${2\times ∆\lambda }_{ES}$ in ES lasing, and meanwhile a longitudinal mode emerges in the GS lasing. For k = 0.238 (Figure 7(a6)), it was observed in the ES lasing that the longitudinal mode of wavelength ${\lambda }_{ES}$ is completely suppressed, and only one longitudinal mode with a wavelength of 1208.05 nm can be observed. Meanwhile, for GS lasing, the longitudinal mode is located at 1319.29 nm lases. In short, due to the gain distribution and mode competition influenced by optical feedback, the number of longitudinal modes for GS and ES lasing in TSQDL varies with the feedback ratio. Similar to the results obtained under the current of 75.00 mA (Figure 6), with the increase in feedback strength, the energy of TSQDL is gradually transferred from ES lasing to GS lasing, the reason is the same as those explained above. However, the ES lasing is not completely suppressed even if k = 0.238 due to the large bias current (85.00 mA) making ES lasing an absolute predominance over GS lasing.

4. Conclusions

In summary, the evolution of the nonlinear dynamic state and longitudinal mode structure of TSQDL under plane mirror optical feedback is experimentally investigated. The results showed that for free-running TSQDL, with the increase in the temperature, the threshold currents of ES and GS lasing ($I_{th}^{GS}\mathrm{a}\mathrm{n}\mathrm{d}{I}_{th}^{ES}$) decrease, and the current for GS quenching increases. After introducing optical feedback, similar trend can be found. For the TSQDL biased at 50 mA (lower than $I_{th}^{ES}$) and 75 mA ($1.07\times I_{th}^{ES}$), the dynamical characteristics of the TSQDL under optical feedback are determined via optical spectra, time series, and power spectra, and various dynamical states including quasi-chaos pulse package (QCPP), chaotic state (C), regular pulse package (RPP), quasi-regular pulsing (QRP), quasi-period two (Q2), and chaos regular pulse package (CRPP), have been observed. For the TSQDL biased at 85.00 mA ($1.13\times I_{th}^{ES}$), with the increase in feedback ratio, the number of longitudinal modes for ES lasing decreases. When the feedback strength is strong enough, the longitudinal mode of GS lasing is activated. This research demonstrates that TSQDL possesses unique advantages in controlling the laser lasing of GS and ES by adjusting the biased current or feedback ratio, and the introduction of optical feedback is helpful for enhancing the GS lasing and suppressing the ES lasing. We hope that this work will provide an effective method to control the operation of TSQDL in a desired state under special circumstances. Additionally, this work may exhibit some potential applications in optical switching, multi-wavelength transmission, and optical logic gates.