# 47.5 GHz Membrane-III-V-on-Si Directly Modulated Laser for Sub-pJ/bit 100-Gbps Transmission
## 3 Results  
### Laser Characterization  
The L-I-V and peak wavelength characteristics of a DML with \(L_{\text{DFB}}=\) 100 \(\upmu\)m, \(L_{\text{DBR-1}}=\) 80 \(\upmu\)m, and \(L_{\text{DBR-2}}=\) 200 \(\upmu\)m (\(L\) denotes section lengths here), are shown in Figure 2a,b, respectively. The measurements were performed by a butt-coupled HNAF and the use of an index-matching oil. The fiber-coupling loss was evaluated to be around 3.87 dB. The chip was measured at stage-controlled temperatures of 25 \({}^{\circ}\)C and 50 \({}^{\circ}\)C. The threshold current for this device was 1.35 mA at 25 \({}^{\circ}\)C and 2.0 mA at 50 \({}^{\circ}\)C, owing to the membrane structure. In the L-I curve, three distinct super-linear regions are visible, separated by mode-hoppings. This behavior is commonly observed in DBR-based DMLs exhibiting the DL and PPR effects [11]. This super-linear behavior is explained by an increase in mirror losses while the lasing mode follows the reflectivity slope of the DBR-2 due to the thermal wavelength shift caused by the bias current increase. As shown in Figure 2b, this thermal shift can be linearly fitted with a slope of about 0.127 nm/mA. In the same figure, the mode-hopping is more visible and it is attributed to different DRB-2 side-lobes. Moreover, within the mode-hopping regions, the lasing wavelength follows a nonlinear trend due to the phase change induced by the DBR-2 section in these spectral regions. The spectral characteristics of the device are summarized in Figure 3. As it can be observed from the contour spectrum plot of Figure 3a, the laser starts lasing in the first long-wavelength-side DBR side-lobe. The simulated longitudinal mode analysis presented in Figure 3b for a bias current of 9.1 mA is used to explain the PPR-generation mechanism. The \(y\)-axis of this plot denotes the mode damping [22], which is given by the imaginary part of the mode-eigenfunction solutions of the TW equation corresponding to the mode-gain margin. A negative or close-to-zero mode-damping value corresponds to dominant lasing modes. In this figure, the main lasing mode at the simulated bias current is marked as \"#0\", while the first four modes due to the compound-cavity attributed to the DBR-2 section are marked as \"#1\", \"#2\", \"#3\", and \"#4\", respectively. Lasing occurs between modes # 1 and # 2 up to the current value at which the first mode hopping occurs, and the lasing mode #0 observes a red-shift afterwards due to the thermal chirp. Therefore, the mode-hoppings observed in the L-I curve are due to the #0 mode coming close to #2, #3, and #4 modes. The optimum PPR conditions are in the spectral vicinity prior to these mode-hoppings. Figure 2: Static characteristics of the laser: (**a**) L-I-V curves at 25 \({}^{\circ}\)C and 50 \({}^{\circ}\)C based on fiber-coupled output powers; (**b**) Peak wavelength versus bias current at 25 \({}^{\circ}\)C. The dashed line presents a linear fitting of the thermal chirp coefficient (\(\partial\lambda/\partial l_{b}\)). Figure 3c,e present the simulated and experimentally-obtained static spectra for operations at 25 \({}^{\circ}\)C and 50 \({}^{\circ}\)C, respectively. The bias currents at these temperatures were 9.1 mA and 15.1 mA, respectively. Based on these spectra, mode separations corresponding to \(f_{PPR}=\) 30-40 GHz are obtained. In particular, for the 9.1 mA, 25 \({}^{\circ}\)C case of Figure 3c, \(\Delta\lambda\approx\) 0.22 nm and \(f_{PPR}\approx\) 39.5 GHz. At these bias currents and temperatures, the lasing wavelengths were 1292.41 nm and 1295.66 nm, respectively, as shown in Figure 3c,e. Moreover, the side-mode suppression ratio remained \(>\) 40 dB in both cases. The simulated and experimentally-obtained EO responses for this device are shown in Figures 4a and 4b, respectively. The linewidth was \(\sim\)5 GHz, which is comparable to previously fabricated devices without PPR.