With the rapid growth of optical communication capacity, particularly in data centers and passive optical network systems, a rate of 100 Gbps per lane is imperative for the 400 Gbit Ethernet (400 GbE) standards. For the next-generation systems addressing the demand for 800 GbE and 1.6 TbE, research on the 200 Gbps per lane is underway while simultaneously reducing the number of lanes and footprint. In recent years, researchers have not only achieved 100 Gbps per lane by optimizing the design of the electro-absorption modulated laser (EML) [1,2], but have also further advanced to achieve 200 Gbps per lane through digital signal processing (DSP) technology [3,4]. Furthermore, by leveraging photonic integration with external modulators, a 16-channel transmission system operating at 53.125 Gbps and 106.25 Gbps per lane has been demonstrated to achieve transmission rates of 800 Gbps and 1.6 Tbps, respectively [5]. Compared to the aforementioned approaches, the directly modulated laser (DML) features high power efficiency, low-cost fabrication, and a small footprint, thus offering promising prospects for beyond-400 GbE applications. And how to improve the 3 dB bandwidth (BW) has always been the key issue in the optimization design of DMLs. Several types of distributed feedback (DFB) lasers with BW of 50 GHz and 65 GHz have been successfully showcased [6,7], and a 108 GHz DML based on membrane technology was also demonstrated and realized 256 Gbps transmission [8]. Furthermore, a 16-channel O-band membrane DML array on Si is demonstrated for 1.6 Tbps interconnects [9,10].

To enhance the modulation speed of DML, various technologies have been proven effective. These include enhancing carrier–photon resonance (CPR), utilizing photon–photon resonance (PPR) [6–8], the detuned-loading (DL) effect [11], and a high-pass response effect originating from frequency modulation to amplitude modulation conversion within the cavity [12]. In the design of DFB lasers utilizing the CPR effect, numerical simulation results suggest that a larger differential gain, shorter cavity length, and narrower waveguides are more conducive to enhancing bandwidth [13]. Through these optimizations, DFB lasers with BW of 37 GHz and 34 GHz have been achieved, respectively [14,15]. However, while a shorter laser cavity can reduce photon lifetime to enhance BW, it can also worsen the chip’s heat dissipation characteristics. Therefore, the impact of CPR on BW enhancement is limited, prompting the exploration of alternative approaches.

Optical feedback has been proved to be another effective strategy for enhancing BW of DML [16–18], especially introducing the PPR and DL effect. The PPR effect mainly takes advantage of the resonance effect between the main mode and the nearest side mode to resist the roll-off of CPR, while the DL effect can improve the effective differential gain of DML to enhance BW. Therefore, many DML schemes with various feedback structures have been proposed and analyzed, and DFB laser with integrated passive cavity (IPC-DFB) is the most typical. Examples include DFB with integrated passive waveguide (the DFB + R laser) [19], DFB with integrated short-cavity distributed reflector (the DR laser) [7], and the two-κ DBR laser [20]. By leveraging PPR and DL effects, BW of 55 GHz, 65 GHz, and 67 GHz has been achieved by utilizing these structures, respectively [7,19,20]. In general, choosing passive feedback waveguides and DR can reduce absorption losses and facilitate the adjustment of optical feedback phase. However, due to the butt-joint regrowth process, the fabrication of IPC-DFB becomes more complex, particularly for quantum well lasers containing aluminum. Furthermore, the complex epitaxial process also degrades the single-mode yield (SMY), thereby increasing the production cost of the chips.

To address the aforementioned complexity in the fabrication of IPC-DFBs, a DFB laser scheme with integrated active cavity (IAC-DFB), utilizing the identical active layer (IAL) technology, has been proposed. Several studies have been conducted to validate this scheme. For instance, DFB lasers with an integrated active feedback waveguide (AFDFB) with BW of 24 GHz [21] and 27 GHz [22] have been reported, respectively. Moreover, we have demonstrated that a partial corrugated grating DFB laser with integrated active optical feedback waveguide (PCG-AFDFB) exhibits a higher SMY than DFB lasers with uniform grating [13]. The reason is that the variation of power and carrier density distribution along the cavity of PCG laser has superior resistance to random facet phase. Therefore, while introducing IAC to simplify fabrication processes and enhance BW, we also incorporate PCGs in AFDFB design to improve the stability of lasing modes.

In this paper, we establish the lasing mode of the PCG-AFDFB, analyzing the influence of different structural parameters on performance parameters such as frequency spacing (FRS) between the lasing mode and the nearest side mode. Further, we fabricated four types of ridge waveguide AFDFBs based on the IAL technology. We discussed the influence of modulation section length (LM), feedback section length (LF), grating coupling coefficient (κ), as well as grating length and the injected current of the active feedback section (IF) on BW and mode stability. By leveraging the PPR and DL effect, we achieved a record-breaking bandwidth (>50GHz) in the IAL design. To validate its capabilities, a transmission experiment was conducted with 55 Gbps NRZ and 70 Gbps PAM4 signals.

Figure 1(a) illustrates a schematic of the proposed PCG-AFDFB consisting of a modulated section (MS) with length LM and an active feedback section (AFS) with length LF, which share the identical MQW. The injected currents are controlled by two separate electrodes. An air gap with a width and depth of 10 μm and 200 nm, respectively, is etched between the two sections to ensure adequate electrical isolation. The grating is partially etched near the side of the active feedback waveguide. Additionally, the facet reflectivity is essential for output power, feedback strength, and threshold current. There, based on numerical calculations, we apply a high-reflectivity (HR) coating to the rear facet and set the reflectivity of the front facet to 15% to maximize laser performance.

In theory, the laser’s threshold is usually determined by net round-trip gain (RTG), and the spectral characteristics are related to the round-trip phase (RTP). When implementing active optical feedback into DFB lasers, a portion of the optical power will be fed back into the MS, influencing the distribution of photons and carriers throughout the entire cavity and introducing additional phase shifts. These influences cause both net RTG and RTP within the cavity to vary over time, ultimately affecting the threshold and spectral characteristics of the laser. Considering the influence of AFS, the feedback strength C and phase shift Φ are given by C=r2e2×LF×(g−α),Φ=2πLF×nFλ,(1)where α represents the optical loss in AFS and MS, g is the gain coefficient, r2 is the reflectivity of the front facet, and nF is the effective refractive index. In practical design, the adjustment of g and nF in Eq. (1) can be achieved by changing the injection current IF. Therefore, we can control the feedback phase and feedback strength by adjusting IF and optimizing LF to meet the conditions for the PPR effect and DL effect, meanwhile maximizing the output optical power.

The BW enhancement of PPR effect is mainly achieved by resonant interaction between the main mode and its adjacent side modes. Therefore, we employ spectral analysis to investigate the influence of different structural parameters on the PPR effect. As shown in Fig. 1(b), to analyze the lasing mode of PCG-AFDFB, the cavity can be divided into multiple transmission matrix units. By introducing index and loss perturbation along a waveguide, the field along the cavity (z direction) can be expressed as the sum of two identical counterpropagating modes. These two modes can be described by the coupled wave equation: −dAdz+(g−α−iδ)A=iκB,(2)dBdz+(g−α−iδ)B=iκA,(3)where A and B represent the amplitude of the forward and backward waves. δ represents the phase detuning factor, and κ denotes the grating coupling coefficient. The general solutions of the above equations are A(z)=A1eγz+A2e−γz,(4)B(z)=B1eγz+B2e−γz.(5)

Substituting Eqs. (4) and (5) into Eqs. (2) and (3), and separately making the coefficients of eγz and e−γz equal (since the intermediate expressions must be true for all z), leads to relationships between A1 and B1, B2 and A2: A2=iκγ+(g−α−iδ)B2,(6)B1=iκγ+(g−α−iδ)A1,(7)γ2=(g−α−iδ)2+κ2.(8)

Substituting Eqs. (6) and (7) into Eqs. (4) and (5), the relations of the field of transmission matrix units A(z1), A(z2), B(z1), and B(z2) can be calculated by [A(z2)B(z2)]=[t11t12t21t22]⋅[A(z1)B(z1)],(9)t11=cosh(γ·Δz)+α−iδγsinh(γ·Δz),(10)t12=−iκγsinh(γ·Δz),(11)t21=iκγsinh(γ·Δz),(12)t22=cosh(γ·Δz)−α−iδγsinh(γ·Δz).(13)

By cascading each matrix unit together and incorporating the boundary conditions of A(z0)=0 and B(zL)=0 (since a laser usually does not need an external optical injection), we can establish the static lasing mode of the proposed PCG-AFDFB. Equation (14) provides the transmission expression for the entire resonant cavity, where the threshold condition corresponds to T22=0. Thus, based on numerical analysis methods, the gain threshold and FRS can be calculated. Meanwhile, by altering the reflectivity and phase of the front facet, further investigation into the influence of feedback strength C and phase shift Φ can be conducted: [A(zL)0]=[T11T12T21T22]⋅[0B(z0)].(14)

For the enhancement of bandwidth using the PPR effect, the FRS between the main mode and the nearest side mode determines whether resonant amplification occurs, as shown in Fig. 2(a). Therefore, based on the aforementioned static lasing mode, we calculated the influence of different structural parameters including facet reflectivity, phase, grating coupling coefficient, and section length on FRS (represented by Δf). For ease of analysis, considering the periodic variation of FRS itself, the phase is normalized to between 0 and π. As depicted in Fig. 2(b), with the increase of the front facet reflectivity r2 (which leads to the enhancement of the feedback strength C), the fluctuation range of Δf decreases, and the majority of solutions within the entire phase range of 0 to π concentrate in the 40–50 GHz range. Similarly, as shown in Fig. 2(c), a larger κ leads to an overall decrease in Δf. This is mainly because the increase in κ enhances the dispersion effect near the lasing mode. It should be noted that there are some singular points in Figs. 2(c)–2(f) primarily caused by mode hopping in the lasing model. Figure 2(d) illustrates that a longer LM generally leads to a smaller Δf at π/2 when the total cavity length is fixed (in the legend, the former and latter numbers represent the LM and LF, respectively). However, for the FRS range of 40–50 GHz, the number of solutions remains unchanged across the entire phase range. Figures 2(e) and 2(f) demonstrate that a longer LF and LM can reduce the Δf, because a longer length causes a smaller free spectral range of the FP cavity.

In AFDFB design, the active feedback waveguide essentially acts as an intra-cavity etalon. Therefore, if the lasing mode is situated on the falling edge of the reflection spectrum of this etalon, benefiting from the DL effect, the effective differential gain would be enhanced and consequently improve the BW. Here, through parameter iteration and optimization, we select LM=150μm, LF=300μm, and κ=11,000m−1 by varying the phase and calculating the RTP of the entire resonant cavity. As shown in Fig. 2(a), the main mode locates on the falling edge of the reflection spectrum; meanwhile a PPR mode is obtained with FRS=48.5GHz. In summary, compared with the IPC-DFB scheme, the integrated active waveguide not only enhances bandwidth but also amplifies output power.

Based on IAL technology, we fabricated and tested four types of PCG-AFDFB chips with different structural parameters, as shown in Table 1. In this paper we design both PCG-AFDFB and AFDFB with uniform corrugated grating (UCG-AFDFB) during fabrication. However, most UCG-AFDFBs exhibited multi-mode lasing due to strong optical feedback from the front face.Table 1.

Structural Parameters of Four PCG-AFDFBs

First, Laser-A with a cavity length of L=450μm is analyzed, with LM=150μm and LF=300μm. To improve mode stability, the grating length is set to 90 μm, with a κ of 7778m−1. Notably, to compare the performance of lasers with different κ within the same epitaxial wafer, we employed two different duty cycle grating designs in this wafer run. When the duty cycle is 0.5, κ is around of 11,000m−1, and when the duty cycle is 0.75, κ is around 7778m−1. To boost the output power, we designed the back facet with a reflectivity exceeding 95% and the front facet around 15%.

Figure 3(a) shows the output light versus IM (L-I curve) under various injected currents IF. The laser exhibits a threshold current of 1 mA, 5 mA, and 10 mA at IF=0mA, 5 mA, and 10 mA, respectively. Due to mode hopping, two “kink points” (40 mA, 69 mA for IF=0mA and 38 mA, 69 mA for IF=5mA, as well as 40 mA, 70 mA for IF=10mA) are observed within the bias current range of 0–80 mA. Moreover, around these points, the slope efficiency of the L-I curve increases with bias current increasing, indicating a decrease in mirror loss. This implies that the lasing wavelength locates at the falling edge of the intra-cavity etalon reflection profile. Consequently, due to the DL effect, the BW will be enhanced around these points. Figure 3(c) depicts the optical spectra at IM=55mA. As the IF increases from 0 mA to 10 mA, the side mode suppression ratio (SMSR) decreases but remains above 41 dB overall. In the zooming inset of Fig. 3(c), a side mode is detected at an FRS of around 48 GHz, coinciding with the PPR frequency. Meanwhile, its peak power exhibited a slight elevation with increasing IF. Furthermore, unlike the single-mode lasing observed in Laser-A with a grating duty cycle of 0.5, we fabricated another set of gratings with a duty cycle of 0.75 (corresponding to κ=11,000m−1) within the same epitaxial wafer and observed multimode lasing phenomena in the spectrum.

Figure 3(b) illustrates the measured small-signal responses of the Laser-A at several bias currents IM with a fixed IF of 10 mA. As IM increases from 50 mA to 75 mA, the 3 dB bandwidth curve experiences fluctuations of rising–dropping–rising again. This fluctuation can also be inferred from Eq. (1), where the feedback phase shift Φ undergoes continuous changes as the bias current increases, attributed to the wavelength redshift. The optimal value is measured at 55 mA, exceeding 50 GHz (limited by the bandwidth testing range of our vector network analyzer, 0–50 GHz), and the curve continues to rise at 50 GHz. It is worth noting that, to acquire the intrinsic response of the laser chip, the S21 of the probes, photodetectors, and high-frequency cables in the test setup are all measured and subtracted from the raw results. With the bias current set to 55 mA in the modulation section, Fig. 3(d) depicts the response curves under various IF in the feedback section. Thanks to the PPR and DL effects, as we increase IF from 0 mA to 10 mA, the 3 dB bandwidth also expands from 24.8 GHz to surpassing 50 GHz.

Since the BW of Laser-A is enhanced by the PPR effect at such a cavity length, we maintained the total cavity length 450 μm unchanged and designed Laser-B and Laser-C with same LM and LF of 200 μm and 250 μm, respectively. The differences are that Laser-B has a κ of 11,000m−1 with a grating length of 100 μm, while Laser-C has a κ of 7778m−1 with a grating length of 120 μm. The spectra and S21 of Laser-B and Laser-C are shown in Fig. 4. Laser-B achieves a maximum BW of 26.7 GHz at IM=70mA with IF=5mA, while Laser-C achieves a maximum BW of 24.2 GHz at IM=50mA with IF=5mA. Due to the limitations of multimode lasing, the IM for Laser-B and Laser-C can only be increased to 70 mA and 50 mA, respectively, and IF is limited to 5 mA. From the spectra shown in Fig. 4(a), it can be observed that the FRS of Laser-B decreases from 77 GHz to 47 GHz as the IM increases from 50 mA to 70 mA. However, due to the low peak power of the side mode at 70 mA, it does not result in a BW enhancement effect. From the spectra shown in Fig. 4(c), it can be observed that the FRS of Laser-C decreases from 65 GHz to 56 GHz as the IM increases from 40 mA to 50 mA. Therefore, due to the relatively larger FRS, it also does not result in a BW enhancement effect. Meanwhile, comparing the spectra of Laser-B and Laser-C reveals that Laser-C has a smaller FRS at 50 mA. This indicates that a larger κL can reduce the FRS. In summary, due to multimode lasing, the current IF of Laser-B and Laser-C could not be continually improved, which is one reason why they do not achieve the PPR effect.

To enhance BW through the PPR effect in the laser with LM=200μm, we fabricated Laser-D with LF=300μm. It has a κ of 11,000m−1 and a grating length of 80 μm. As shown in Fig. 5(b), its BW also increases with the increase of IM and IF, reaching 32 GHz and 39 GHz at IM=60mA with IF=5mA and IF=10mA, respectively. In Fig. 5(a), the FRS is observed around 35 GHz. However, bandwidth enhancement is only achieved when IM=60mA with IF=10mA, because the peak power of the side mode is relatively small at other currents. Additionally, because the FRS is close to the relaxation oscillation frequency (Fr), the bandwidth enhancement effect is not as significant as in Laser-A. As depicted in Figs. 5(c) and 5(d), the phenomenon becomes more pronounced at IM=70mA, where the FRS is 28 GHz, approaching Fr. Consequently, the relaxation oscillation peak is boosted to 11 dB and 13 dB, attributed to the resonant enhancement of the PPR effect. This leads to a bandwidth 34 GHz lower than at IM=60mA.

In summary, by adjusting the LM, LF, as well as κ and grating length, the FRS value can be modified to achieve the PPR effect. We have verified that structures with cavity lengths of 450 μm and 500 μm can achieve the PPR effect. Moreover, it can be observed that for the epitaxial structure we utilized, an FRS of 50 GHz is relatively suitable; meanwhile, it is also necessary to ensure that the peak power of the side mode is sufficiently high.

In the transmission system, PRBS13 NRZ and PAM4 signals are generated by a waveform generator (Keysight M9502A) and amplified by an amplifier (SHF S807C) at the transmitter. No pre-emphasis was applied. Laser-A operated at IM=55mA with IF=5mA. At the receiver side, only the sampling oscilloscope (Keysight N1092A) is used to analyze the optical eye diagrams. Figure 6(a) shows the back-to-back (BtB) eye diagram for 45 Gbps NRZ signal, and the extinction ratio (ER) is 4.7 dB. When increasing IF to 10 mA, ER remains at 4.7 dB. When the modulated speed increases to 55 Gbps, the ER still reaches 2.8 dB, as shown in Fig. 6(b). 60 Gbps and 70 Gbps PAM4 BtB eyes are depicted in Fig. 6(c) and Fig. 6(d), respectively, with the transmitter dispersion eye closure quaternary (TDECQ) measured at 3.2 dB and 3.4 dB using Keysight FlexDCA. Although the high-frequency losses introduced by packaging and two kink points in the L-I curve limit the improvement of ER, we can still observe a clear eye diagram.

We proposed a PCG-DFB with integrated active optical feedback waveguide. By designing based on IAL technology, the epitaxial process is simplified, and the BW is enhanced due to the PPR effect and DL effect. The fabricated laser achieved a bandwidth exceeding 50 GHz at multiple bias currents, which has a total cavity length of 450 μm, with LM=150μm and LF=300μm. We also fabricated another three types of lasers and discussed the influence of PCG-AFDFB’s parameters such as LM, LF, κ, and grating length on the BW enhancement effect. In the transmission experiments, the BtB eye diagrams for 55 Gbps NRZ signal with an ER of 2.8 dB and 70 Gbps PAM4 signal with a TDECQ of 3.4 dB are demonstrated, respectively. Consequently, we believe that such DMLs are a promising solution for low-power-consumption and high-capacity beyond-400 GbE applications.