# 47.5 GHz Membrane-III-V-on-Si Directly Modulated Laser for Sub-pJ/bit 100-Gbps Transmission
## 2 Materials and Methods
However, one should note that the DBR-1 in this case does not contribute to the generation of the DL and PPR effects. Additionally, in this design a second, longer DBR (\"DBR-2\") section was also integrated for enabling the DL and PPR effects. In order to use the longer wavelength side of the DBR-2 section for the DL effect, the Bragg wavelength detuning between the DBR-2 and DFB sections was designed to be nearly zero. On the other hand, the Bragg wavelength for the DBR-1 section was designed to be longer than that of the DFB sections in order to filter only the long-wavelength DFB mode, as shown in the schematic of Figure 1c. Moreover, for simplicity the designed grating coupling coefficient for the entire DR structure was kept the same value: 400 cm\({}^{-1}\). For low loss coupling to SSMF, we also integrated SiO\({}_{\mathrm{x}}\)-based spot-size converters on both facets based on 135 \(\upmu\)m-long InP tapers, as shown in Figure 1a [6]. In the design presented here, the laser was mainly emitting from the DBR-2-side facet. However, the rear spot-size converter was also integrated in order to evaluate the precise grating profile of DBR-1. Even though is not shown in Figure 1a, the SiO\({}_{\mathrm{x}}\) cores were covered by an SiO\({}_{2}\) overcladding. Such a structure was designed to have an output mode field diameter of around 4 \(\upmu\)m to match that of high-numerical aperture fibers (HNAFs). A schematic of the cross-section of the active DFB region is shown in Figure 1b. The structure and its fabrication procedure were based on our established membrane-III-V-on-Si described, e.g., in [5; 6]. For the active region, we used 6-period InGaAsAlAs multiple-quantum wells (MQWs) buried on InP, with a total III-V thickness of \(\sim\)300 nm. This membrane structure results in a high optical confinement factor, which enhances the \(f_{R}\), while ensuring a low bias current and power consumption. The DFB section was a buried waveguide while the DBR sections were based on InP channel waveguides. For all DFB and DBR sections, the grating was performed by surface etching on top of the  
Figure 1: Device schematic: (**a**) Bird’s eye view of the distributed reflector (DR) laser structure. The overcladding SiO\({}_{2}\) layer is omitted for visibility; (**b**) Cross-sectional view: \(x\)-\(y\) plane of distributed feedback (DFB) section (top) and \(y\)-\(z\) plane of entire laser (bottom). The grating was formed on the InP surface; (**c**) Lasing-mode selection (based on distributed Bragg reflector (DBR)-1) and detuned-loading (DL)+ photon–photon resonance (PPR) generation (based on DBR-2) mechanisms. InP layer. The grating periods were 219, 226, and 225 nm for the DFB, DBR-1, and DBR-2, respectively. All the gratings were formed on the InP with an etching depth of 20 nm. For the design and physical simulations of the longitudinal structure we developed an in-house travelling wave (TW) simulator based on the split-step method described in [20]. The main TW equation used is described in the Appendix A, together with the main simulation parameters used. The simulated spectra and the longitudinal mode analysis were based on the same TW model and the methods described in [21] and [22], respectively.