Abstract
1. Introduction
High-speed optical communication and fast neuromorphic optical computation highly demand low-cost photonic integrated circuits (PIC) on the silicon platform[
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.
2. Rate equation analysis
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 (NRS, NES, NGS), the photon number (S), and the phase (φ) of the electric field are given by[
where I is the pump current, and η is the current injection efficiency.
Epitaxial defect in semiconductors induces nonradiative recombination through the Shockley-Read-Hall process, and the nonradiative recombination lifetime τnr 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 τnr 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[
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[
Figure 1.(Color online) Nonradiative recombination effects on the threshold current and the carrier numbers in GS, ES, and RS at the threshold, respectively.
The LBF characterizes the coupling ratio of the carrier-induced refractive index variation to the gain variation in semiconductor lasers[
Figure 2.(Color online) Nonradiative recombination effects on the LBF. (Reproduced from Ref. [
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[
Figure 3.(Color online) Non-radiative recombination effects on (a) the RIN spectrum, (b) the FN spectrum, and (c) the low-frequency RIN and the peak FN.
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[
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 τnr = 10 ns down to 5.5 GHz at τnr = 0.1 ns.
Figure 4.(Color online) Non-radiative recombination effects on (a) the intensity modulation response, and (b) the 3-dB modulation bandwidth and the damping factor.
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[
There are several analytical models evaluating the critical feedback level of semiconductor lasers[
where Г is the damping factor, R is the facet reflectivity, and τin 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 τnr = 10 ns up to –10.4 dB at τnr = 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.
Figure 5.(Color online) Non-radiative recombination effects on the critical feedback level. (Reproduced from Ref. [
3. Linewidth broadening factor
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[
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[
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[
Figure 6.(Color online) Sub-threshold LBF of Ge-based Qdot lasers with a cavity length of (a) 4.4 mm and (b) 2.2 mm. Both lasers have a ridge width of 4.0
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[
Figure 7.(Color online) LBFs of Si-based undoped (closed circle) and p-doped (triangle) Qdot lasers. (Reproduced from Ref. [
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[
4. RIN and sensitivity to optical feedback
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[
Figure 8.(Color online) RINs of (a) Ge-based Qdot laser (
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[
Figure 9.(Color online) Optical feedback effects on the normalized intensity noise power of (a) Ge-based laser (
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[
Figure 10.(Color online) Effects of optical feedback on RINs of (a) a Qdot laser epitaxially grown on Si (
The experimental observation in Fig. 10 is confirmed through measuring the optical spectrum and the electrical spectrum in Fig. 11[
Figure 11.(Color online) Optical feedback effects on (a, b) the optical power distribution of two cavity modes, and (c, d) on the electrical power distribution. (a) and (c) are for a Si-based Qdot laser (
5. Direct modulation response
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[
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[
Figure 12.(Color online) Intensity modulation responses of two Si-based Qdot lasers. The threshold current of device 1 is 18.9 mA, and is 19.1 mA for device 2. The cavity length is 2.5 mm. (Reproduced from Ref. [
Inoue et al. reported the direct modulation characteristics of an InAs/GaAs Qdot laser epitaxially grown on on-axis (001)Si[
Figure 13.(Color online) Intensity modulation responses of (a) undoped and (b) p-doped Qdot lasers on Si. (c) Eye diagrams of the p-doped laser, under non-return-to-zero modulation. The cavity length is 0.58 mm. (Reproduced from Ref. [
6. Mode-locking operation
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[
Fig. 14(a) illustrates the schematic structure of an InAs/GaAs Qdot laser epitaxially grown on on-axis (001)Si substrate[
Figure 14.(Color online) (a) Schematic structure of a mode-locked Qdot laser on Si with a repetition rate of 9.0 GHz. (b) SNR of the fundamental RF peak. (c) Mode-locking pulse width as functions of forward bias current and reverse bias voltage. The threshold current is 90 mA without biasing the absorber section. (Reproduced from Ref. [
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[
Figure 15.(Color online) Si-based mode-locked Qdot laser with a repetition rate of 20 GHz. (a) Autocorrelation pulse shape. (b) RF spectrum. (c) RF lineshape. (d) Single-sideband phase noise. The threshold current is 42 mA without biasing the absorber section. (Reproduced from Ref. [
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[
7. Future trends
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[
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[
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[
8. Conclusion
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.
Acknowledgments
This work is supported by National Natural Science Foundation of China (No. 61804095), and by Shanghai Pujiang Program (No. 17PJ1406500).
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