High-speed optical communication and fast neuromorphic optical computation highly demand low-cost photonic integrated circuits (PIC) on the silicon platform^{[1, 2]}. A large variety of photonic devices on Si have been demonstrated, including optical waveguides, optical modulators, photodiodes, and laser sources^[3-6]. Among these devices, it is the most challenging to integrate III–V semiconductor lasers on Si. On one hand, Si is nonpolar material while III–V compound is polar material, and hence the monolithic integration results in antiphase boundaries^[7]. On the other hand, the lattice mismatch between Si and III–V compound leads to high density of threading dislocations^[8]. Both defects induce significant non-radiative recombination of carriers and thus hinder efficient radiative recombination for laser emission. Instead of monolithic integration, flip-chip bonding and wafer bonding provide alternative approaches for integration of semiconductor lasers on Si^[9-11]. These two methods are less challenging but the yield is low and the cost is high. Thanks to the individual nature of quantum dots (Qdot), Qdots are more tolerant to epitaxial defects than quantum well (Qwell) structures, and hence permit efficient stimulated emission in the presence of high-density defects^[12-14]. In addition, Qdot lasers have shown superior performances over conventional Qwell lasers, including low threshold current density, high temperature stability, strong resistance to residual optical feedback and so on^[15-17]. Consequently, III–V Qdot lasers become the primary choice for monolithic integrated laser sources on Si. The first epitaxial integration of InAs/GaAs Qdot lasers operated at room temperature was achieved on Ge substrate rather than Si substrate in 2011^[12], because the lattice constant of GaAs was closely matched to Ge (0.08% mismatch). Since then, tremendous works have been done to demonstrate the laser emission of InAs/GaAs Qdot lasers epitaxially grown on Ge-on-Si substrate, offcut Si substrate, and on-axis (001) Si substrate^[18-20]. A lot of efforts have been devoted to minimize the defect density through optimization of the buffer layer, and the defect density has been reduced down to the order of 10⁶ cm^–2, which is yet at least two orders of magnitude higher than that of Qdot laser on the native GaAs substrate^{[19, 21]}. Meanwhile, static performances of Qdot lasers on Ge or Si have shown considerable improvements, in aspects of the threshold current density, the quantum efficiency, the high temperature operation, as well as the aging lifetime^{[14, 20, 22]}. There are a bunch of papers discussing the steady-state characteristics of Ge- or Si-based Qdot lasers, and some review works can refer to references^[23-25].

Based on the improvement of static performances, dynamical characteristics of Ge- or Si-based Qdot lasers are drawing more and more attentions, which can directly determine the design of PIC systems. This article provides an overview of recent progresses on the laser dynamics of linewidth broadening factor (LBF), relative intensity noise (RIN), frequency noise (FN, or phase noise), sensitivity to optical feedback, intensity modulation, and mode locking operation, which are compared to those of Qdot lasers grown on native GaAs substrate. The paper is organized as follows: Section 2 introduces a rate equation model for Qdot lasers and analyzes all the dynamical characteristics theoretically. Section 3 discusses the LBF, and Section 4 discusses the RIN and its sensitivity to optical feedback. Section 5 investigates the direct intensity modulation including both the small-signal response and the large-signal response. Section 6 studies the mode locking characteristics of Si-based Qdot lasers. Section 7 discusses the future trends, and Section 8 summarizes this work.

The rate equation model for Qdot lasers takes into account the carrier dynamics in the carrier reservoir (RS, wetting layer), in the first excited state (ES), and in the ground state (GS). The Qdot laser is assumed to emit solely on a single mode at the GS, and the inhomogeneous broadening effect is not considered. The coupled rate equations for the carrier numbers (N_RS, N_ES, N_GS), the photon number (S), and the phase (φ) of the electric field are given by^[26]

$\frac{{{\rm{d}}{N_{\rm{RS}}}}}{{{\rm{d}}t}} = \eta \frac{I}{q} + \frac{{{N_{\rm{ES}}}}}{{\tau _{\rm{RS}}^{\rm{ES}}}} - \frac{{{N_{\rm{RS}}}}}{{\tau _{\rm{ES}}^{\rm{RS}}}}\left( {1 - {\rho _{\rm{ES}}}} \right) - \frac{{{N_{\rm{RS}}}}}{{\tau _{\rm{RS}}^{\rm{spon}}}} - \frac{{{N_{\rm{RS}}}}}{{{\tau _{nr}}}} + {F_{\rm{RS}}},$ (1)

$\begin{split} \frac{{{\rm{d}}{N_{\rm{ES}}}}}{{{\rm{d}}t}} = \, & \left( {\frac{{{N_{\rm{RS}}}}}{{\tau _{\rm{ES}}^{\rm{RS}}}} + \frac{{{N_{\rm{GS}}}}}{{\tau _{\rm{ES}}^{\rm{GS}}}}} \right)\left( {1 - {\rho _{\rm{ES}}}} \right) - \frac{{{N_{\rm{ES}}}}}{{\tau _{\rm{GS}}^{\rm{ES}}}}\left( {1 - {\rho _{\rm{GS}}}} \right) \\ & - \frac{{{N_{\rm{ES}}}}}{{\tau _{\rm{RS}}^{\rm{ES}}}} - \frac{{{N_{\rm{ES}}}}}{{\tau _{\rm{ES}}^{\rm{spon}}}} - \frac{{{N_{\rm{ES}}}}}{{{\tau _{\rm{nr}}}}} + {F_{\rm{ES}}}, \end{split} $ (2)

$\begin{split} \frac{{{\rm{d}}{N_{\rm{GS}}}}}{{{\rm{d}}t}} = & \frac{{{N_{\rm{ES}}}}}{{\tau _{\rm{GS}}^{\rm{ES}}}}\left( {1 - {\rho _{\rm{GS}}}} \right) - \frac{{{N_{\rm{GS}}}}}{{\tau _{\rm{ES}}^{\rm{GS}}}}\left( {1 - {\rho _{\rm{ES}}}} \right) \\ & - {\Gamma _{\rm P}}{v_{\rm g}}{g_{\rm{GS}}}S - \frac{{{N_{\rm{GS}}}}}{{\tau _{\rm{GS}}^{\rm{spon}}}} - \frac{{{N_{\rm{GS}}}}}{{{\tau _{\rm{nr}}}}} + {F_{\rm{GS}}}, \end{split} $ (3)

$\frac{{{\rm{d}}S}}{{{\rm{d}}t}} = \left({\Gamma _{\rm p}}{v_{\rm g}}{g_{\rm{GS}}} - \frac{1}{{{\tau _{\rm p}}}}\right)S + {\beta _{\rm{SP}}}\frac{{{N_{\rm{GS}}}}}{{\tau _{\rm{GS}}^{\rm{spon}}}} + {F_{\rm S}},$ (4)

$\frac{{{\rm{d}}{\varphi} }}{{{\rm{d}}t}} = \frac{1}{2}\Gamma _{\rm P}{v_{\rm g}}\left( {{g_{\rm{GS}}}{k_{\rm{GS}}} + {g_{\rm{ES}}}{k_{\rm{ES}}} + {g_{\rm{RS}}}{k_{\rm{RS}}}} \right) + {F_{\varphi} },$ (5)

where I is the pump current, and η is the current injection efficiency. is the carrier capture time from the RS to the ES, is the carrier relaxation time from the ES to the GS, and and are the corresponding carrier escape times due to thermal excitation. is the spontaneous emission lifetime, τ_p is the photon lifetime in the cavity, and τ_nr is the nonradiative recombination lifetime due to the defect, which is assumed to be the same for all the three carrier states. ρ_ES,GS is the carrier occupation probability, and g_RS,ES,GS is the material gain. Γ_p is the optical confinement factor, v_g is the group velocity of light, and β_sp is the spontaneous emission factor. k_RS,ES,GS is a coefficient weighting for the carrier contribution of each state to the LBF at the lasing mode. F_RS,ES,GS, F_S, and F_φ are Langevin noise sources for the carrier, the photon, and the phase, respectively. The laser dynamics are obtained through the small-signal analysis of the coupled rate equations, and the parameters used for the simulations are listed in Table 1^[26].

Epitaxial defect in semiconductors induces nonradiative recombination through the Shockley-Read-Hall process, and the nonradiative recombination lifetime τ_nr is inversely proportional to the defect density. The defect density in GaAs-based Qdot lasers is 10³–10⁴ cm^–2 or less, and the corresponding τ_nr is on the order of 10 ns, which is much longer than the spontaneous emission lifetime (~1.0 ns). Therefore, the nonradiative recombination term in the rate equations is negligible^[27]. On the other hand, the defect density in Ge- or Si-based Qdot lasers is at least two orders of magnitude higher (10⁶–10⁸ cm^–2) than that in GaAs-based lasers^{[12, 19]}. Therefore, the nonradiative lifetime of Ge- or Si-based lasers can be below 0.1 ns, which becomes shorter than the spontaneous emission lifetime and hence can not be neglected in rate equations. The simulations in this section focus on the impacts of the non-radiative recombination or the defect density on the laser dynamics. The emitted photon number is fixed at 2 × 10⁵ for all the simulations unless stated otherwise.

The simulations in Fig. 1 show that the fast nonradiative recombination process or the high defect density raises the threshold current, which is the same as widely observed in experiments^{[28, 29]}. In addition, carrier populations in the ES and in the RS are raised as well. On the other hand, the carrier population in the GS has no change because of the gain clamping effect^[30].

The LBF characterizes the coupling ratio of the carrier-induced refractive index variation to the gain variation in semiconductor lasers^[31]. It is a crucial parameter determining the spectral linewidth, the chirp under direct modulation, the nonlinear dynamics behavior like chaos, and so on^{[27, 32-35]}. Typical LBFs of Qwell lasers are in the range of 2.0–5.0, while the LBF of ideal Qdot lasers is expected to be near-zero owing to the delta-function like density of states^{[36, 37]}. However, the reported LBF values of Qdot lasers range from near-zero up to more than 10^[38-41], due to the inhomogeneous broadening effect and the influence of the ES^[42]. Fig. 2 shows that a fast nonradiative recombination rate slightly reduces the LBF. This is because a short carrier lifetime is helpful to reduce the LBF of semiconductor lasers^[26]. On the other hand, although the fast nonradiative recombination strongly increases the carrier accumulation in the RS, it has little impact on the LBF because the coefficient k_RS is small^[26].

The RIN characterizes the intensity noise of semiconductor lasers, and it is defined as the ratio of the power spectral density of intensity noise to the square of the averaged optical power^[27]. The RIN of semiconductor lasers originates from the intrinsic spontaneous emission noise, the intrinsic carrier noise^[44], as well as low-frequency technical noise sources including the current noise of the power source, the temperature fluctuation, and the mechanical vibrations^{[45, 46]}. The Langevin noise sources in rate Eqs. (1)–(5) characterize the intrinsic noise while the technical noise is not included in the model. Fig. 3(a) demonstrates that a short nonradiative recombination lifetime raises the RIN level at low frequencies. Fig. 3(c) shows that the low-frequency RIN increases from –144 dB/Hz at τ_nr = 10 ns up to –140 dB/Hz at τ_nr = 0.1 ns. The increase of the RIN is attributed to a shorten carrier lifetime induced by high density defects^{[27, 47]}.

The FN of semiconductor laser originates from the spontaneous emission as well. The high-frequency (> 20 GHz) FN inFig. 3(b) determines the Schawlow-Townes linewidth. However, the low-frequency (< 1.0 GHz) FN inFig. 3(b) is amplified by the LBF (α) by a factor of (1 + α²), which directly determines the total spectral linewidth of semiconductor lasers^[27]. Fig. 3(b) proves that the nonradiative recombination has little impact on either the Schawlow-Townes linewidth or the total spectral linewidth of Qdot lasers. However, the FN resonance peak is significantly suppressed for a short nonradiative recombination lifetime. The amplitude of the peak FN in Fig. 3(c) decreases from 1.40 × 10⁶ Hz²/Hz at τ_nr = 10 ns down to 0.98 × 10⁶ Hz²/Hz at τ_nr = 0.1 ns.

Fig. 4(a) shows that the fast nonradiative recombination suppresses the resonance peak. This is because the nonradiative recombination shortens the total carrier lifetime and hence significantly enhances the damping factor in Fig. 4(b). Consequently, the modulation bandwidth in Fig. 4(b) is reduced slightly from 5.9 GHz at τ_nr = 10 ns down to 5.5 GHz at τ_nr = 0.1 ns.

Semiconductor lasers in an optical system inevitably suffer from residual optical feedback due to optical connectors or other optical devices in the optical link. When the feedback strength reaches a certain level defined as the critical feedback level, the laser becomes oscillating in the chaos state, which is also known as coherence collapse^[48]. Both the RIN and the FN are significantly raised, and the coherence of the laser becomes extremely poor, which are destructive for optical communication or optical computing. Therefore, an optical isolator is usually packaged together with the semiconductor laser in commercial laser transmitters. In comparison with Qwell lasers, Qdot lasers have shown much stronger tolerance to optical feedback, and the critical feedback level is at least two orders of magnitude higher^{[15, 49]}. This makes Qdot lasers very promising for isolator-free operation in optical links.

There are several analytical models evaluating the critical feedback level of semiconductor lasers^[50-52]. One classical formula was proposed by Helms and Petermann^[51]:

${f_{\rm{ext,c}}} = \frac{{{\Gamma ^2}(1 + {\alpha ^2})}}{{{\alpha ^4}}}\frac{{\tau _{\rm{in}}^2R}}{{4{{(1 - R)}^2}}},$ (6)

where Г is the damping factor, R is the facet reflectivity, and τ_in is the light round-trip time in the laser cavity. According to Eq. (6), a large damping factor and/or a small LBF are desirable for increasing the critical feedback level. Surprisingly, fast nonradiative recombination in Fig. 5 raises the critical feedback level from –14.0 dB at τ_nr = 10 ns up to –10.4 dB at τ_nr = 0.1 ns. This is understandable because the nonradiative recombination substantially enhances the damping factor in Fig. 4(b), and slightly reduces the LBF in Fig. 2.

In experiments, the LBF of semiconductor lasers can be measured by a few techniques as reviewed in Ref. [32]. However, the most widely employed method is the Hakki-Paoli method^{[41, 42]}, which is based on the optical spectrum analysis of the amplified spontaneous emission when the laser is operated below the lasing threshold. Through measuring the wavelength shift (dλ) and the net modal gain variation (g_net) of longitudinal modes with the pump current change (dI), the LBF is determined by

$\alpha = - \frac{{2{\text{π}}}}{{L\Delta \lambda }}\times\frac{{{\rm{d}}\lambda /{\rm{d}}I}}{{{\rm{d}}{g_{\rm{net}}}/{\rm{d}}I}},$ (7)

with L being the cavity length, and Δλ being the adjacent mode spacing. However, the accuracy of this method is limited by the thermal effect, which induces red-shift of the longitudinal mode. Therefore, pulsed power source is usually used to pump the laser to reduce the thermal effect, which in turn weakens the optical signal. In 2016, Wang et al. proposed an improved Hakki-Paoli method taking advantage of the optical injection locking technique, which was thermally insensitive and hence improved the accuracy of LBF measurement^[53].

Fig. 6 investigates the sub-threshold LBFs of Qdot lasers epitaxially grown on a Ge(100) wafer with 6° off-cut towards [111] plane by the gas-source molecular beam epitaxy based on the Hakki-Paoli method. The active region of the two laser samples consists of five stack layers of dot-in-well structures. Both lasers are fabricated from the same wafer, and are operated on GS. The only difference between the two laser devices is the cavity length. Fig. 6(a) shows that the LBF of the Ge-based laser with a cavity length of 4.4 mm decreases from 3.0 at 1208 nm down to 2.0 at 1218 nm. The LBF at gain peak of 1213 nm is around 2.5. In contrast, Fig. 6(b) shows that the LBF of the Ge-based laser with a cavity length of 2.2 mm increases from 1.7 at 1184 nm up to 4.1 at 1194 nm. The LBF at the gain peak of 1190 nm is about 3.0. The different tendency of the LBF versus the lasing wavelength in both laser can be attributed to the large dot size dispersion^[43], which leads to a broad photoluminescence linewidth (full width at half maximum) of 48 meV^[54].

Fig. 7 studies sub-threshold LBFs of InAs/GaAs Qdot lasers epitaxially grown on an on-axis Si (001) wafer by the solid-source molecular beam epitaxy^[56]. The active region consists of 4 stack layers of dot-in-well structures. Fig. 7 shows that the undoped laser (closed circle) exhibits a low LBF of 0.31 at the gain peak, when the laser is operated at 293 K. The ultralow LBF is mainly attributed to the low Qdot size dispersion, which exhibits a rather narrow inhomogeneous broadening linewidth of 29 meV in the photoluminescence spectrum. Increasing the operation temperature slightly increases the LBF value of the undoped laser. In contrast, the p-doped laser (triangle) shows a reduced LBF of 0.13, owing to the lower transparency carrier density^[57]. Besides, the LBF of the p-doped laser is insensitive to the operation temperature.

It is remarked that although Fig. 2 shows that the nonradiative recombination slightly reduces the LBF, it is negligible in comparison with the inhomogeneous broadening effect^[43]. The different dot size dispersion from device to device leads to the wide spread of LBF values from near-zero up to more than 10^[39-42]. Therefore, as long as the dot size dispersion is similar, the LBFs of Ge- or Si-based Qdot lasers are expected to be comparable to those of GaAs- or InP-based ones.

Fig. 8 compares the measured RINs of a Ge-based Qdot laser and of a GaAs-based one. Both lasers have the same epilayer structure except the substrate^[58]. It is shown that the minimum RIN level of the Ge-based laser is about 15-dB higher than that of the GaAs-based one. This is in consistent with the simulation in Fig. 3(a), and hence the larger RIN in the Ge-based laser is attributed to the higher density of defect (~10⁶ cm^–2). It is worthwhile to mention that the broad peak around 9.0 GHz in Fig. 8(a) arises from the photon-photon resonance, which is owing to the quasi-phase locking of adjacent longitudinal modes^{[59, 60]}. The detailed analysis of the resonance will be reported elsewhere.

Fig. 9 compares the feedback sensitivity of a Ge-based Qdot laser and a GaAs-based one. Both lasers have the same epilayer structure and the same cavity structure^[43]. It is shown that the optical feedback with a feedback ratio of –15 dB raises the noise power of the Ge-based laser in Fig. 9(a) by about 4.0 dB. In contrast, the noise power of the GaAs-based laser in Fig. 9(b) is increased by 8.0 dB. This experimental result is in agreement with the simulation in Fig. 5, and the enhanced feedback tolerance of the Ge-based Qdot laser is mainly attributed to the higher damping factor as described in Fig. 4(b).

Fig. 10 compares the measured RINs of a 1.3 μm InAs/GaAs Qdot laser epitaxially grown on (001)Si and of a 1.5 μm AlGaInAs Qwell laser heterogeneously integrated on Si^[61]. It is shown that the RIN of the Qdot laser with very weak feedback (–60 dB) in Fig. 10(a) is about 15 dB higher than that of the Qwell laser in Fig. 10(b), which is again due to the high density defect. However, the RIN of the Qdot laser only slightly increases with increasing feedback level, and does not show any feature of coherence collapse. In contrast, the Qwell laser exhibits a critical feedback level around –30 dB, beyond which the feedback significantly raises the RIN level^[62].

The experimental observation in Fig. 10 is confirmed through measuring the optical spectrum and the electrical spectrum in Fig. 11^[63]. It is shown that the optical feedback has little effect on both the optical spectrum (Fig. 11(a)) and the electrical spectrum (Fig. 11(c)) of the Si-based Qdot laser up to a feedback ratio of –7.4 dB (100%). In contrast, the Qwell laser loses stability beyond a critical feedback level of –25 dB (1.7%). The optical spectrum (Fig. 11b) is significantly broadened, and the electrical spectrum (Fig. 11(d)) becomes very noisy within a broad bandwidth of 10 GHz. Finally, it is worthwhile to mention that Liao et al. reported a Si-based Qdot laser with a low RIN of less than –150 dB/Hz^[64]. The strong tolerance of Ge- or Si-based Qdot lasers to the optical feedback can enable the isolator-free operation in PICs on the silicon platform, which is very desirable for practical applications because fabrication of isolators on Si is technically challenging and costive^{[43, 61, 63, 65]}.

For short-reach optical links such as PICs and data centers, direct modulation scheme is more desirable than external modulation one, because the frequency chirp of the laser source does not affect a lot the signal quality in short distance. 1.3 μm InAs/GaAs Qdot lasers have shown record small-signal modulation bandwidth of 13 GHz^[66], and large-signal bit rate of 25 Gbps^[67]. Meanwhile, 1.5 μm InAs/InP Qdot laser have shown record small-signal bandwidth of 18 GHz^[68], and large-signal bit rate of 35 Gbps^[69].

Hantschmann et al. reported the small-signal modulation response of InAs/GaAs Qdot lasers epitaxially grown on (001) Si with 4° off-cut towards [001] plane^[70]. Two nominally identical lasers with a long cavity length of 2.5 mm were tested and the modulation responses are shown in Fig. 12. Both devices show a maximum 3-dB bandwidth of only 1.6 GHz, due to the limitation of long photon lifetime. The extracted K-factors for the two devices are 2.4 and 3.7 ns, respectively. Therefore, the resulting maximum intrinsic bandwidths are only 3.7 and 2.4 GHz. In addition, the inverse of the effective carrier lifetime are determined to be 4.0 and 2.0 ns^–1, respectively.

Inoue et al. reported the direct modulation characteristics of an InAs/GaAs Qdot laser epitaxially grown on on-axis (001)Si^[71]. The undoped Si-based laser in Fig. 13(a) exhibits a maximum bandwidth of 4.0 GHz, while the p-doped laser in Fig. 13(b) shows a higher bandwidth of 6.5 GHz. This is because the p-doping in the barriers suppresses the hole depletion, and assists the carrier transport to the dot active region. The K-factors for both lasers are 1.3 and 0.92 ns, respectively. This results in maximum intrinsic bandwidths of 6.8 and 9.5 GHz, respectively. Under direct modulation of non-return-to-zero pseudo random bit sequences, the p-doped laser in Fig. 13(c) exhibits extinction ratios of 3.9, 3.7, and 3.3 dB for modulation bit rates of 7.5, 10, and 12.5 Gbps, respectively. In addition, the laser shows no error-floor down to a bit error rate of 1.0 × 10^–13.

Mode-locking semiconductor lasers can generate a large number of coherent longitudinal modes. One mode-locking laser can be used as a multi-channel light source for wavelength division multiplexing communications^{[72, 73]}. In addition, the mode-locked tones can be used for the generation low-noise photonic microwaves through optical heterodyning, which is highly desirable for radio-over-fiber communications^{[74, 75]}. Besides, mode-locked lasers are also valuable for high-speed optical sampling and interchip clock distributions^{[76, 77]}. In comparison with Qwell lasers, Qdot lasers are more desirable for mode locking operation, because of the broad optical spectrum arising from the inhomogeneous broadening effect^{[72, 78]}. Passive mode-locked lasers usually consist of two sections – the gain section and the saturable absorber section, which are electrically isolated. The gain section is forward biased, while the absorber section is reversely biased. The mode locking output is achieved under proper conditions of forward bias current to the gain section associated with reverse bias voltage to the absorber section.

Fig. 14(a) illustrates the schematic structure of an InAs/GaAs Qdot laser epitaxially grown on on-axis (001)Si substrate^[71]. The total cavity length is 4.5 mm, and the absorber section length occupies 23%. The full-width of half maximum of the photoluminescence of the gain medium is around 30 meV. Fig. 14(b) presents the evolution of the signal-to-noise (SNR) ratio of the fundamental RF peak at 9.0 GHz, as functions of the forward bias current and the reverse bias voltage. The mode-locking operation is identified when the SNR is larger than 20 dB. It is demonstrated that the mode-locking regime enlarges at a high bias current. The SNR of the fundamental RF peak varies between 20 and 50 dB. On the other hand, the pulse width in Fig. 14(c) varies between 1.0 and 10 ps. A large reverse bias voltage is helpful to narrow the pulse width of the mode-locked laser, which is owing to the reduced absorption recovery time of the absorber section at a high bias voltage.

Fig. 15 shows the characteristics of another mode-locked Qdot laser epitaxially on on-axis (001) Si, which was fabricated in the same group as Fig. 14^[79]. The cavity length is 2.05 mm, and the absorption section length occupies 14%, leading to a pulse repetition rate of 20 GHz. The laser employs chirped Qdot design to broaden the width of photoluminescence up to 53 meV. Consequently, the 3-dB optical bandwidth of the mode-locked laser is as high as 6.1 nm, containing 58 longitudinal modes. The laser achieves a narrowest pulse width of 5.0 ps in Fig. 15(a), and the SNR of the fundamental RF peak reaches up to more than 60 dB in Fig. 15(b). In addition, the 3-dB RF linewidth is as narrow as 1.8 kHz in Fig. 15(c), which is comparable to the best mode-locked semiconductor lasers^{[80, 81]}. The timing jitter determined from the single-sideband phase noise (integrating from 4 to 80 MHz) in Fig. 15 (d) results in a record value of 82.7 fs.

In addition to the two-section mode locking scheme, Qdot lasers of one single gain section are widely found to exhibit mode locking as well^[82-84]. The physical mechanism for the single-section self-mode locking is still unclear. However, the strong gain compression effect and the large third-order susceptibility in Qdot lasers have been proved to play crucial roles in the self-mode locking behavior^[85-87]. Liu et al. reported a self-mode locked Qdot laser epitaxially grown on on-axis (001)Si, which exhibited a repetition rate of 31 GHz, associated with a pulse width of 490 fs^[84].

All the Ge- or Si-based Qdot lasers investigated in sections 3–6 are based on Fabry-Perot cavity, which emit on multimodes. However, practical applications in optical communication and in optical computing require single-mode laser sources, which are widely achieved through using the distributed feedback (DFB) gratings. Wang et al. have successfully demonstrated DFB Qdot laser arrays on off-cut (001) Si substrate, which showed a high side mode suppression ratio of 50 dB. Besides, the DFB laser arrays cover the full spectral span of the O band, with a channel spacing of 20 nm^[88]. However, there was no report on the spectral linewidth or the phase noise of the DFB lasers. The spectral linewidth of Qdot lasers on GaAs or InP is usually several hundred kilohertz, which is one order of magnitude smaller than typical Qwell lasers^[89-94]. The record linewidth of an InAs/InP Qdot DFB laser reaches as low as 50 kHz^[94]. Continuous-wave DFB laser is ready for external modulation, in combination with optical modulators. However, directly-modulated DFB Qdot lasers on Si are yet to develop in future work. For data transmission speed up to 10 Gbps, isolator-free Qdot laser with direct modulation may become the dominate solution for PICs on Si in the future. In contrast, external modulation scheme may be still required for speed more than 25 Gbps, due to the bandwidth limitation of Qdot lasers.

Most Qdot lasers epitaxially grown on Si are operated in the O band, while C band laser emission is required for long-haul communication. However, it is more challenging to directly grown 1.5 μm InAs/InP Qdot lasers on Si than 1.3 μm InAs/GaAs Qdot lasers, because the lattice mismatch between InP and Si is as large as about 8%, twice the mismatch between GaAs and Si. This problem is circumvented by using V-grooved Si substrate, which traps most twined stacking faults in Si^{[95, 96]}. However, the defect density at the interface of the InP buffer layer is still as high as 10⁹–10¹⁰ cm^–2[96]. In spite of these difficulties, Zhu et al. successfully demonstrated InAs/InP Qdot laser epitaxially grown on (001) Si, with pulsed current pumping^[97]. The dynamical characteristics of InAs/InP Qdot lasers on Si require investigation in future work, as those discussed in Sections 3–6.

Fabry-Perot or DFB lasers typically have a footprint in the millimeter range. In order to reduce the footprint of laser sources on Si down to the micrometer range, Si-based micro-disk lasers and micro-ring lasers have been developed^[98-103]. Particularly, Wan et al. demonstrated a Qdot micro-ring laser on (001) Si with an ultralow threshold of 0.6 mA^[101]. An alternative approach for reducing the footprint is to employ the nano-ridge structure^[104-107]. Using this structure, Han et al. successfully demonstrated InP/InGaAs nano-ridge lasers on (001) Si with optical pumping. Interestingly, the lasing wavelength is widely tunable ranging from O band up to the C band, through changing the excitation level and the nano-ridge length.

In summary, this work systematically discussed recent progresses on the dynamical characteristics of Qdot lasers epitaxially grown on Ge or Si, including the LBF, the RIN and the FN, the modulation response, the sensitivity to optical feedback, and mode-locked performances. Although there is high density of epitaxial defects, some dynamical performances of Ge- or Si-based Qdot lasers are becoming comparable to those of GaAs-based ones. Particularly, these lasers are highly tolerant to optical feedback, owing to the defect-enhanced damping factor. However, it is still highly desirable to further reduce the defect density for further improving both static and dynamic performances. Once Qdot lasers are properly integrated on the Si platform, the next challenging task in future work is to figure out approaches to efficiently couple the laser light into optical waveguides, which connect a large variety of photonic and optoelectronic devices in PICs.

This work is supported by National Natural Science Foundation of China (No. 61804095), and by Shanghai Pujiang Program (No. 17PJ1406500).