All material growth was conducted on an IV/III-V hybrid Molecular Beam Epitaxy (MBE) system. Figure 1A shows the schematic diagram of the InAs/GaAs QD laser grown on the GaAs/Si (001) substrate. The GaAs/Si (001) platforms were achieved by growing III-V buffer layers on (111)-faceted silicon hollow substrates, which were obtained by homo-epitaxy of a silicon buffer layer on “U”-shaped patterned Si (001) substrates. The AlGaAs/GaAs superlattices (SLs) and InGa(Al)As/GaAs quantum-well structures as dislocation filters (DFLs) were grown to flatten the GaAs surface and reduce the threading dislocation density (TDDs). The growth details and characterizations of GaAs/Si (001) platforms can be found in our previous work (Wang et al., 2011; Wei et al., 2018; Wei et al., 2019; Zhang et al., 2019a). As shown in Figure 1A, a 4 μm-thick InAs/GaAs QD laser structure mainly consists of top- and bottom-AlGaAs cladding layers, GaAs contact layers, and a 7-layer InAs/GaAs dot-in-well (DWELL) active region. Each InAs/GaAs DWELL layer includes 8.1 Å InAs QDs sandwiched by a 1.5 nm InGaAs wetting layer and a 4 nm InGaAs capping layer, separated by a 49 nm GaAs spacer layer. Figure 1B shows the photoluminescence (PL) spectrum of the identical seven layers of InAs/GaAs DWELLs grown on the GaAs/Si (001) substrate. The PL spectrum presents a narrow emission peak of InAs/GaAs QDs on the Si (001) substrate, with a ground state peak wavelength of 1,276 nm, a full width at half maximum (FWHM) of 30.4 meV, and an excited state peak wavelength of 1,190 nm. The inset in Figure 1B displays the 1 × 1 μm² AFM image of the surface InAs/GaAs QDs on the GaAs/Si (001) substrate, which indicates the dot density of 5.12 × 10¹⁰ cm⁻².

Based on the materials prepared above, the narrow ridge FP lasers were fabricated with a ridge width of 4 μm and a cavity length of 2 mm. Figure 1C shows the color-enhanced cross-sectional scanning electron microscopy (SEM) image of a 4 μm-wide ridge laser on the Si (001) substrate with “top-top” contacts. The as-cleaved ridge laser shows a clean and mirror-like facet as shown in the SEM image in Figure 1C.

The experimental arrangement is shown as below in Figure 2, the sole excited-state laser is continuous-wave (CW) current injected, and mounted on a thermoelectric cooler (TEC) to ensure stable temperature operation. The laser output is then coupled into lensed fiber. A 10/90 fiber coupler and an optical fiber circulator are implemented to couple the desirable output strength to the variable optical attenuator (VOA), in order to control the feedback ratio (which is defined as the feedback power to the total output power from the laser). In the experimental set-up described above, the feedback ratio can only be tuned from 0 to 19.95%. In order to further measure the laser behavior at higher feedback levels, by connecting the 10/90 fiber coupler directly to a fiber back-reflector, the maximum measured feedback level can reach 50%. An optical isolator is introduced at the detection end to eliminate additional unwanted feedback noise from the characterization equipment. The optical spectrum is measured by the optical spectrum analyzer (OSA) (Yokogawa AQ6370D), while a photodetector (Optilab PD-40M) with responsivity of 0.575 A/W @ 1,200 nm typ. and 0.640 A/W @ 1,300 nm typ. is used to capture the optical output to generate RF signal for electrical spectral analysis. The RF signal is amplified by the RF amplifier (Optilab MD50) with an electrical spectrum analyzer (ESA) (Agilent E4440A) set behind for frequency characterization.

In this work, a sole excited-state InAs QD laser on Si is operated under EOF ranging from −27 to −3dB. An injection current of 130mA and operating temperature of 15°C are selected here to ensure stable laser operation. Both the QW FP laser and QW DFB laser are tested under EOF ranging from −37 to −7dB with an injection current of 14 and 22mA, respectively.

By implementing the experimental arrangement above, the evaluation of the optical spectral linewidth of a sole excited-state QD laser on Si is achieved as shown in Figure 3. In Figure 3A, significant laser linewidth broadening of the InAs QD laser on Si occurs at an EOF of −7.8 dB, which leads to a clear coherence collapse. Besides, the isolated linewidths under EOF both below and above the critical feedback level are investigated to further confirm the evolution of optical spectra. Figure 3D gives a clear demonstration of change of linewidth under different EOF. This broadening represents the start of chaotic state in the QD laser as shown in Figure 3A.

For comparison, both the commercial QW FP laser and DFB laser are characterized here for optical spectral analysis. The optical spectral mapping of the QW FP laser in Figure 3B shows continuous broadening under an EOF above −36 dB, which is confirmed by the evolution of the linewidth in Figure 3E. Simultaneously, we measured the optical spectral evolution of the QW DFB laser as shown in Figures 3C,F. In Figure 3C, the optical spectrum shows coherence collapse at an EOF of −14 dB, which is confirmed by the demonstration of linewidth evolution in Figure 3F. This result indicates that the QW DFB laser exhibits a stronger resistance against feedback with an increased critical feedback level of 22 dB over the FP structure with identical QW structures. The observed relatively high critical feedback level of the QW DBF laser benefits from the reduced feedback strength inside the laser cavity due to the DFB gratings. The overall optical spectral evolution analysis among all three types of lasers shows that the sole ES QD laser exhibits superior performance over the QW laser with an improved critical feedback level of 28.2 dB in the identical FP structure.

In order to verify the feedback resistance results extracted from optical spectral evolution, feedback-dependent measurements in the electrical frequency domain are also performed here. However, the critical feedback levels in ESA could be different from those in OSA due to the coupling variance during testing, therefore the values from optical spectra in Figure 3 will be adopted as the credible result for our experimental set-up.

The resonance frequency of FP modes can be calculated by Eq. 1. f = c 2 n eff L (1) where c is light speed in vacuum; n eff is the effective index of the material; and L is the distance from the laser to the external feedback facet.

The length of the total optical path is defined as the round trip between the front laser facet and the VOA, which is 8 m in our experimental set-up. As a result, the fundamental FP resonance frequency of the external circuit is 12.8 MHz while the frequency resolution of ESA in this experiment is 16.7 MHz. This explains the absence of fundamental FP resonance peaks in the following RF spectra and RIN.

Quasiperiodic peaks are observed between 0.5 and 3 GHz in Figure 4A when EOF reaches −15 dB, but they show little impact on the coherent lasing of the QD laser according to Figures 3A,D, so they should represent quasiperiodic relaxation oscillation (RO). Under an increased EOF of −7 dB, chaotic oscillation (CO) occurs over a range of 3–6.5 GHz, which represents the coherence collapse of the laser. The difference in critical levels acquired from OSA and ESA could come from the variance in coupling efficiency during tests.

In the case of the QW FP laser, the RF spectrum shows initial CO peaks ranging from 3 to 4 GHz under an EOF of −36 dB as shown in Figure 4B, followed by full chaotic operation, which is in line with the optical linewidth broadening previously observed. This result confirms that the coherence collapse in the QW FP laser happens at an EOF of −36 dB. The critical feedback level difference acquired from Figures 4A,B strongly supports the superior feedback insensitivity performance of QD materials.

Figure 4C shows the measured ESA spectral mapping of the QW DFB laser with increasing EOF. An abrupt increase in chaotic states occurs under an EOF of −15 dB. The comparison between Figures 4B,C suggests that the critical feedback level in the DFB QW laser is at least 21 dB higher than that of the QW FP laser, due to the grating structure.

We also performed relative intensity noise (RIN) measurements for three different laser structures. The RIN of an operating laser can be described by Eq. 2. (Zhou et al., 2017): R I N ( f ) = 10 l o g 10 [ N T − N t h R B W × G − N q P D C ] ( d B / H z ) (2) where N T is the total noise in the ESA spectrum; N t h is the thermal noise from the experimental set-up; RBW = VBW = 200 KHz; G, the gain of the RF amplifier is 30 dB; N q is the shot noise from the photodetector, defined as N q = 2 q I D C R L , where q is the elementary charge I D C is the DC current extracted from DC blocking, and R L is the resistance of ESA; and P D C is the DC power.

Usually, coherence collapse is defined as a collective phenomenon of the broadening of the laser spectrum with significant increases, such as an abrupt increase of RIN and frequency fluctuation (Cohen and Lenstra., 1991; Lenstra et al., 2019). Here in this work, we analyze the RIN spectra with different EOF below and above the critical feedback level to understand the dynamics of semiconductor lasers with feedback.

In Figure 5A, the QD laser shows relatively flat RIN spectra until −15 dB EOF, where the quasiperiodic RO frequency peaks arise, which however has no influence on the coherent operation of the laser as the optical linewidth remains the same as in Figure 3D. By further increasing the EOF level towards −7.5 dB, a broad electrical signal noise peak appears, which represents the coherence collapse of the QD laser. This behavior suggests that the electrical noise peaks over the frequency range above 3 GHz represents the dominant noise frequency that influences optical feedback sensitivity.

For the QW FP laser, even under a weak EOF of −37 dB, multiple frequency noise peaks already exist in the RIN diagram in Figure 5B. The periodic peaks could be the high-order harmonics of the fundamental RO frequency, which are caused by the intracavity resonance, and thus the coherence collapse follows in the RF spectrum and RIN diagram (Lin et al., 2018). With increasing EOF levels, the noise level continuously grows, which leads to significant optical spectral broadening in Figures 3B,E.

The initial peak of RIN shows up at an EOF of −13.7 dB, followed by broadening in the QW DFB laser, which is shown in Figure 5C. This agrees with the result from optical linewidth evolution in Figures 3C,F and the electrical spectrum in Figure 4C.

From electrical spectral analysis, including Figures 4A,B, 5A,B, the QD laser and QW laser clearly undergo different routes into chaotic states. The QD laser shows quasiperiodic oscillation of RO frequency before coherence collapse in the range of EOF from −15 dB to −7.5 dB. In comparison, the QW laser goes through a high-order harmonics RO process before moving into chaotic states. Different chaotic routes in QD lasers come from a unique quantum dots structure with higher confinement and thus reduces high-order harmonics behavior in the FP structure. The discrete energy state of QD lasers causes a lower enhancement factor and higher damping factor which are also well-accepted explanations for the higher feedback insensitivity of QD lasers over QW lasers (Duan et al., 2018). A lower enhancement factor suppresses the noise caused by EOF which otherwise can be amplified in the gain medium towards a chaotic operation (Lenstra et al., 2019).

The superior performance of the DFB structure lies in the distributed-feedback grating structure which can reduce the EOF strength entering the resonant cavity from the external circuits, while the FP laser will be strongly affected by the entered optical feedback. The suppression of high-order harmonics in DFB, which reduces the multimode competition in lasers, is also a main mechanism for higher feedback resistance.

The results in this paper analyzed the critical EOF level in different materials and structures. The high feedback insensitivity of the ES QD laser and the feedback noise suppression capability in the DFB structure are confirmed. We believe these results make it possible to fabricate better EOF insensitive QD DFB lasers, which can potentially achieve stable coherent operation with 100% EOF for future photonic integrations.