## 3 Results and Discussion  
The lasing characteristics were tested at 10 \({}^{\circ}\)C under continuous-wave conditions. Figure 4a shows the typical fiber coupled output power as a function of injection currents for a four-channel LC-DFB laser array. The threshold currents are about 12 mA. Excellent slope efficiencies of above 0.26 W/A are achieved for all channels. The output power is about 20 mW at an injection current of 100 mA. Such excellent output power performance for LC-DFB lasers is attributed to the combination of a good epitaxy of AlGaInAs wafer and HR-AR facet coated. The four-channel wavelengths range from 1286 nm to 1303 nm with a channel spacing of about 1 THz, as shown in Figure 4b. An average SMSR exceeding 50 dB is obtained, which is comparable to that of conventional DFB lasers, indicating the good longitudinal mode selectivity of deep and planar lateral gratings.  
Figure 3: The comparison diagram of (**a**) BCB planarization process and (**b**) SiO\({}_{2}\) planarization process.  
Figure 2: (**a**) SEM image of the as-etched waveguide and lateral gratings. (**b**) Surface topography of the SiO\({}_{2}\) supporting layer. (**c**) SEM image of the waveguide and lateral gratings after removing SiO\({}_{2}\) on top of the current injection region.  
The DML array is p-side up soldered onto a copper block to improve the thermal characteristics. The p-type electrode is bonded to a AlN microstrip transmission line by gold wires through a matching resistor of 35 \(\Omega\). The 3-dBe bandwidths of the small-signal modulation response shown in Figure 5 exceed 14 GHz for all four channels. A bandwidth of about 18 GHz is obtained on lane 3 under an injection current of 100 mA. To our knowledge, this is the best small-signal modulation performance for LC-DFB lasers. The frequency response of the laser can be fitted as follows [15], in which the junction capacitance is taken into account:  
\[|H(f)|=\Bigg{|}\frac{f_{r}^{2}}{\sqrt{\left(f_{r}^{2}-f^{2}\right)^{2}+\left( \frac{\gamma}{2\pi f}\right)^{2}}}\Bigg{|}\Bigg{|}\frac{1}{\sqrt{1+ff/f_{PN}}} \Bigg{|}\Bigg{|}\frac{1}{\sqrt{1+(f/f_{RC})^{2}}}\Bigg{|} \tag{2}\]  
Here \(\gamma\) is the damping factor. The \(f_{PN}\) and \(f_{RC}\) are the cut-off frequencies caused by the junction capacitance, the contact capacitance and the series resistance. Figure 6a shows the relationships between \(f_{r}\) and the square root of the bias currents above the threshold for four channels. The \(D\) factors of the four-channel lasers are 1.56, 1.6, 1.49 and 1.23 GHz/mA\({}^{1/2}\), respectively. The values of the four-channel differential gain \(a\) are obtained from the \(D\) factors, as shown in Figure 6b. The differential gain tends to decrease with the increase of the lasing wavelength. Generally, a lasing wavelength shorter than the material peak gain provides a larger differential gain. The maximum appears at the 5 nm detuned grating wavelength to longer wavelengths with respect to the material peak gain, which is about 1285 nm.  
Figure 4: (**a**) Fiber coupled output power as a function of injection currents (L-I) of the LC-DFB laser array with the operating temperature at 10 \({}^{\circ}\)C. (**b**) The lasing spectra under injection currents of 100 mA at 10 \({}^{\circ}\)C.  
Figure 5: Small-signal frequency responses of the LC-DFB laser array with injection currents of 100 mA at 10 \({}^{\circ}\)C.