This work experimentally investigates the optical feedback sensitivity of InAs/GaAs quantum dot (Qdot) lasers epitaxially grown on Ge substrate. In comparison with a Qdot laser on GaAs substrate with identical epilayer and cavity structures, the Ge-based laser is found to exhibit lower sensitivity to the optical feedback, although it has a higher epitaxial defect density. Theoretical analysis proves that the high defect density strongly increases the damping factor while slightly reduces the linewidth broadening factor, which lead to high tolerance to the optical feedback. This work suggests the high potential of Qdot lasers on Ge for isolator-free operation in photonic integrated circuits.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The development of photonic integrated circuits (PICs) on the silicon platform is strongly driven by the applications in data centers and in high-performance computings. For achieving large-scale PICs, the integration of III-V semiconductor lasers on Ge or Si (Ge/Si) is a crucial issue, which can be solved by the flip-chip bonding, the wafer bonding, or the direct epitaxial growth technique [1–4]. While the former two methods already become commercially available, the latter one offers merits of low cost, high scalability, and high yield [4, 5]. However, the epitaxial growth approach produces high density of defects such as threading dislocations and antiphase domains, due to the material mismatch between the III-V compound and Ge/Si (including different lattice constants, thermal expansion coefficients, and polar/nonpolar natures), which limit the laser performances [4, 6]. In recent years, researchers have devoted a lot of efforts to improving the quality of InAs/GaAs quantum dot (Qdot) lasers epitaxially grown on Ge/Si, which successfully show low threshold current density , high operation temperature , and long aging lifetime . Based on the improved steady-state performances of Ge/Si-based Qdot lasers, the dynamic characteristics are beginning to draw more and more attentions. D. Inoue et al. demonstrated a directly-modulated Si-based Qdot laser with a small-signal 3-dB bandwidth of 6.5 GHz and a large-signal modulation rate of 12.5 Gbps . In addition, J. Norman et al. reported a Qdot laser on Si with an extremely small linewidth broadening factor (LBF) as low as 0.25, which was even lower than that of Qdot lasers on GaAs . On the other hand, our group previously showed that the Ge-based Qdot laser exhibited 15-dB higher relative intensity noise (RIN) than the GaAs-based one with the same epitaxial layer structure , which was theoretically attributed to the high-density defects .
Integrated semiconductor lasers on the silicon platform inevitably suffer from the undesired optical feedback, which is produced by the light coupling waveguide and other integrated devices in the PICs. The optical feedback can increase the relative intensity noise (RIN) of the semiconductor lasers, and lead to coherence collapse (chaos) if the feedback strength exceeds the critical feedback level . Therefore, an optical isolator is usually required to avoid the back reflected light. However, it is difficult to integrate isolators on silicon, which increases the package size and the cost as well . Fortunately, Qdot lasers have been proved to be more resistant to the optical feedback than quantum well (Qwell) lasers, owing to the smaller linewidth broadening factor (LBF) and the higher damping factor . In , it was also theoretically shown that the Pauli blocking effect and the carrier capture dynamics significantly altered the damping factor and hence reduced the sensitivity to optical feedback. In 2017, A. Liu et al. compared the optical feedback sensitivity of a 1.3 µm InAs Qdot lasers monolithically integrated on Si (facet reflectivity is 55%) with a 1.5 µm Qwell lasers heterogeneously integrated on Si (facet reflectivity is 30%), and found that the former one had 20-dB reduced sensitivity . However, it is unknown whether the Ge/Si substrate and the epitaxial defects degrade the optical feedback resistance of Qdot lasers. In this work, we investigate the optical feedback sensitivity of Ge-based InAs Qdot lasers, associated with a GaAs-based Qdot laser of the same epilayer structure and of the same cavity structure. It is found that the Ge-based Qdot lasers exhibit higher tolerance to the optical feedback than the latter one, which is owing to the defect enhanced damping factor and reduced LBF. In addition, it is also demonstrated that a narrow ridge is favorable to reduce the sensitivity to the optical feedback.
2. Laser device and experimental setup
The Ge-based Qdot lasers were grown on a 4-inch Ge (100) wafer with 6° off-cut towards the  plane by the gas-source molecular beam epitaxy . As shown in Fig. 1, a 600-nm thick GaAs buffer layer was firstly grown on the Ge substrate in order to restrain the threading dislocation from reaching the active region. The threading dislocation density on the buffer layer surface was estimated to be around 106/cm2, by counting the number of rhombic pinholes in the atomic force microscopy (AFM) image. The active region contains 5 stacked layers of dot-in-well (DWELL) structures, and each layer is separated by a 40 nm GaAs spacer. The DWELL structure consists of 2.2 monolayer (ML) InAs Qdots, which are grown on a 2.0 nm In0.15 Ga0.85 As Qwell layer, and then capped by another 6.0 nm In0.15Ga0.85As Qwell layer. The Qdot density is about 2.0×1010/cm2 measured by the AFM, the average dot size is about 61 nm in diameter, and about 10 nm in height. The photoluminescence at room temperature exhibits a full-width at half-maximum linewidth of 33.7 meV. The laser material was fabricated into narrow-ridge waveguide lasers via standard photolithography and wet etching. The detailed growth and fabrication information can be found in . One Ge-based InAs/GaAs Qdot laser sample under study has a cavity length of 4.56 mm and a ridge width of 4 µm. Both laser facets are as-cleaved without any coating. For comparison, an InAs Qdot laser on the native GaAs substrate was grown with the same epilayer structure as in Fig. 1. In addition, the GaAs-based laser also has the same cavity structure as the Ge-based laser, which means both lasers have identical cavity length, ridge width, and cleaved facets. The threading dislocation defect density of the GaAs-based laser is less than 5.0×103/cm2 as usual InAs/GaAs Qdot lasers [18–20].
The optical feedback sensitivity of semiconductor lasers are usually characterized by measuring the optical spectrum or by measuring the intensity noise spectrum [21–23]. In this work, we employ the latter method, and the corresponding experimental setup is shown in Fig. 2. The tested laser is pumped by a low-noise DC current source (Newport 6100), and the temperature is kept constant at 20 °C using a thermo-electric cooler. The laser output is coupled into a lensed fiber (OZ Optics) and the power coupling ratio varies with the tested lasers, which is very carefully characterized. Then, the light is split into two paths by a 90:10 optical direction coupler, and 90% optical power couples into port 2 of an optical circulator. 60% of the output from port 3 is fed back to port 1 through a variable optical attenuator (VOA), which controls the optical feedback strength. The forward and backward power meters (PM) are used to measure the forward and backward light power, respectively. The optical feedback ratio is defined as the ratio of the backward power to the forward power, multiplied by the coupling ratio of the lensed fiber. In such way, the transmission loss in the fiber links is included in the calculation of the feedback ratio. A high-resolution (0.02 nm) optical spectrum analyzer (OSA, Yokogawa AQ6370D) is used to measure the optical spectrum, and a low-noise photodiode (Discovery DSC40S) with a bandwidth of 16 GHz is used to convert the optical signal into electrical signal. The AC part of the electrical signal is produced by the intensity noise of the laser. The weak noise signal is amplified by a broadband amplifier (SHF 810) with a gain of about 29 dB, and is recorded on an electrical spectrum analyzer (ESA, Keysight N9030B) with a resolution bandwidth set at 200 kHz.
3. Experimental results and discussion
The Qdot laser grown on Ge operates in the continuous-wave mode, and exhibits a lasing threshold current of Ith=75 mA (inset of Fig. 3(a)), corresponding to a threshold current density of 411 A/cm2. Figure 3 (a) shows that the Ge-based laser biased at 1.2×Ith emits around 1192 nm. In contrast, the Qdot laser grown on GaAs exhibits a lower lasing threshold current of Ith=60 mA, associated with a higher output power (inset of Fig. 3(b)). It is well known that the degraded lasing threshold and power performances are due to the high density of epitaxial defects, which leads to fast non-radiative recombination of carriers . In addition, the GaAs-based laser biased at 1.2×Ith emits at a longer wavelength around 1341 nm. The shorter lasing wavelength of the Ge-based laser can be attributed to the residual strain in the GaAs buffer layer arising from 0.1% lattice constant mismatch and 1.8% thermal expansion coefficient difference, which also leads to smaller size of Qdots [25–28]. The free spectral range of both lasers in Fig. 3 is about 9.0 GHz, while the different spectral shape can be due to the large dot size dispersion .
Figure 4 shows the optical feedback effect on the noise spectra of both Qdot lasers pumped at 2.8×Ith. For the laser on Ge in Fig. 4(a), the maximum achievable feedback ratio in the experimental setup is −15.7 dB. At this feedback ratio, the noise spectrum has little change with respect to the solitary laser. For the laser on GaAs in Fig. 4(b), however, the noise spectrum at low frequencies (<0.1 GHz) is raised by the optical feedback at a similar feedback ratio of −16.4 dB. In comparison with the solitary laser, the noise power at 0.01 GHz is increased by more than 10 dB. The maximum achievable feedback ratio for the GaAs-based laser reaches up to −11.8 dB, owing to its higher coupling ratio with the lensed fiber in comparison to the Ge-based laser. This can be attributed to the longer wavelength and better beam quality in the GaAs-based laser. The noise spectrum at −11.8 dB feedback shows clear periodic ripples with an interval of 6.0 MHz, due to the external cavity modes . It is worthwhile to mention that the noise spectra of both lasers with the DWELL active region do not exhibit any resonance peak owing to the high damping factor. This is beneficial to reduce the sensitivity to the optical feedback, because the critical feedback level increases with increasing damping factor . In contrast, lasers with the dot active region in our previous work showed undamped resonance peaks in the noise spectra . The overdamped resonance in the DWELL lasers is owing to the larger dot size, which shifts the lasing spectrum to longer wavelength as well .
Since the noise spectra in Fig. 4(b) only has apparent changes below 0.1 GHz, we take the mean noise power (MNP) in the range of 0.01–0.1 GHz to characterize the feedback sensitivity. The MNP ratio is defined as the MNP of the laser subject to the optical feedback divided by that of the solitary laser. Figure 5(a) shows that the optical feedback only slightly changes the MNP of the Qdot laser on Ge. The most sensitive pump current is at 2.4×Ith, where the MNP is merely increased by less than 4.0 dB at the feedback ratio of −15.1 dB. In Fig. 5(b), the Qdot laser on GaAs pumped at 1.2×Ith has low sensitivity to the optical feedback as well. However, the laser pumped at high pump currents (≥2.4×Ith) becomes sensitive to the optical feedback and the MNP ratio reaches more than 8.0 dB. Above 1.2×Ith, the MNP ratio has a sudden increase at a certain feedback ratio, which usually indicates the onset of the coherence collapse [23, 32]. However, we did not observe any obvious broadening in the optical spectrum. Besides, the noise spectrum above 0.1 GHz in Fig. 4(b) has little increase. Therefore, we believe the coherence collapse does not occur in the whole measurement range of the feedback ratio. Apparently, the Ge-based laser is more resistant to the optical feedback than the GaAs-based laser at high pump currents. The corresponding physical mechanism will be analyzed in the theoretical analysis section.
In addition, we investigate the ridge width influences on the optical feedback sensitivity of Ge-based Qdot lasers. Figure 6(a) shows the MNP ratio of the Ge-based laser with a ridge width of 6.0 µm and a cavity length of 5.0 mm. The MNP ratio at 1.2×Ith is not sensitive to the optical feedback, while those at higher pump currents increase with increasing feedback ratio. At a feedback ratio of −16.0 dB, the maximum MNP ratio reaches up to 13.7 dB, while that of the 4-µm ridge laser in Fig. 5(a) is only less than 4.0 dB. For the Ge-based laser with a ridge width of 8.0 µm and a cavity length of 4.49 mm in Fig. 6(b), the MNPs at all the measured pump current are raised by the optical feedback. The MNP ratio at a feedback ratio of −16.0 dB reaches as much as 17.1 dB, higher than that of the 6-µm ridge laser in Fig. 6(a). Both lasers do not exhibit any coherence collapse phenomenon as well. The poorer sensitivity in the wider ridge laser can be due to the stronger lateral mode competition [29, 33]. In addition, both lasers show that a higher pump current is more sensitive to the optical feedback. This behavior is in consistent with the observation in , where the high pump current enhances the LBF, due to the carrier populations in off-resonant states . In addition, the heavier thermal effect and the lateral mode excitation at the larger current also lead to the higher sensitivity .
4. Theoretical analysis of optical feedback sensitivity
The previous section has experimentally shown that the Ge-based laser has higher tolerance to optical feedback than the GaAs-based laser with the same epilayer and cavity structures. In order to explore the physical mechanism, we employ a set of coupled rate equations to investigate the critical feedback level of Qdot lasers, where the carrier dynamics in the carrier reservoir, the excited state, and the ground state are taken into account. The detailed rate equation model was described in . It is known that the epitaxial defect accelerates Shockley-Read-Hall (SRH) recombination lifetime, which is inversely proportional to the defect density . In GaAs-based Qdot lasers, the SRH lifetime is usually on the order of 10 ns, and hence is negligible because it is much longer than spontaneous emission lifetime (∼1 ns) . However, the high defect density in Ge-based lasers can accelerate the SRH lifetime to be below 0.1 ns, and thereby cannot be neglected. Therefore, the SRH recombination terms are coupled into the rate equations of all the three carrier states, and the SRH lifetimes are assumed to be the same 
Based on the rate equation model, Fig. 7(a) simulates the damping factor and the LBF variations as a function of the SRH lifetime. It is shown that a fast SRH lifetime significantly enhances the damping factor, which increases from 20.3 GHz at 10 ns up to 30.3 GHz at 0.1 ns. On one hand, it is because the SRH recombination shortens the carrier lifetimes of both the carrier reservoir and the excited states . On the other hand, the SRH recombination strongly increases the carrier accumulation in the carrier reservoir (not shown) . Figure 7(a) shows that the short SRH lifetime slightly reduces the LBF as well. This is again owing to the fast carrier lifetimes, while the carrier population in the carrier reservoir has little impact on the LBF . Based on Fig. 7(a) and Eq. (1), Fig. 7(b) derives the critical feedback level as a function of the SRH lifetime. It proves that a short SRH lifetime is helpful to increase critical feedback level and hence to reduce the feedback sensitivity. The critical feedback level increases from −13.8 dB at 10 ns to −9.4 dB at 0.1 ns. The simulation results are in good agreement with the experimental observation in Fig. 5. Another possible reason for the high optical feedback tolerance can be attributed to the smaller dot size in the Ge-based laser, which enlarges the energy interval between the excited state and the ground state , and thereby results in a smaller LBF . It is worthwhile to investigate the latter effect quantitatively in future work.
In summary, we investigated the optical feedback sensitivity of Qdot lasers epitaxially grown on Ge, which was compared with the Qdot laser grown on GaAs with the same epilayer structure and the same cavity structure. It is found that the tolerance of the Ge-based Qdot laser to the optical feedback is higher than the GaAs-based laser. This is because the high defect density accelerates the SRH lifetime, and hence enhances the damping factor and slightly reduces the LBF. In addition, it demonstrates that the Ge-based Qdot laser of a wider ridge is more sensitive to the optical feedback than the narrower one, due to the lateral mode competition. All the Qdot lasers do not show any coherence collapse within the tested optical feedback ratio up to −11.0 dB. The strong tolerance of the Qdot lasers epitaxially grown on Ge to the optical feedback suggests the high potential of isolator-free operation in PICs on Ge/Si platforms.
National Natural Science Foundation of China (NSFC) (61804095); Shanghai Pujiang Program (17PJ1406500).
The authors would like to thank Prof. Johann Peter Reithmaier at the University of Kassel, Germany for very helpful discussions.
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