# High-Speed Directly Modulated Laser Integrated with SOA
Traveling wave semiconductor optical amplifiers (TW-SOAs) exhibit quasi-high-pass filter characteristics in gain-saturated states [15; 16], with a sharp decline in the low-frequency response and a relatively flat high-frequency response. It should be emphasized that the term \"frequency response of the SOA\" in this work does not refer to the intrinsic direct modulation capability of the SOA itself. Instead, it describes the dynamic gain response of the SOA--biased in the gain saturation regime--to intensity-modulated optical signals from the DFB section, with its gain varying differently for different modulation frequencies. This behavior is primarily driven by gain saturation and carrier lifetime effects. Low-frequency modulation signals deplete carriers significantly, leading to reduced gain, while high-frequency signals quickly replenish carriers, maintaining higher gain. The gain G of the SOA in a saturated state can be expressed as follows [17]:  
\[G=\frac{G_{0}}{1+\frac{P_{in}}{P_{inst}}}\cdot\frac{1+\mathrm{j}\mathrm{2}\pi f \tau_{0}\left(1+\frac{P_{in}}{P_{inst}}\right)}{1+\mathrm{j}\mathrm{2}\pi f \tau_{0}} \tag{2}\]  
where \(\tau_{0}\) represents the carrier lifetime, \(f\) is the modulation signal frequency, \(j\) is the imaginary unit, \(G_{0}\) denotes the saturated gain, and \(P_{in}\) and \(P_{inst}\) represent the input optical power and saturation optical power of the SOA, respectively. When the optical power injected from the laser into the SOA is sufficiently high, the carrier population in the SOA becomes significantly depleted at low modulation frequencies, leading to pronounced gain suppression. In contrast, at high frequencies, the modulation is too rapid for carriers to respond within each cycle, allowing the gain to be largely preserved. This asymmetric gain behavior--suppression at low frequencies and retention at high frequencies--results in a characteristic quasi-high-pass filtering effect. The magnitude of the frequency-dependent gain can be described by the following expression:  
\[|G(f)|=\frac{G_{0}}{1+\frac{P_{in}}{P_{inst}}}\cdot\frac{\sqrt{1+\left[(2\pi f \tau_{0})\left(1+\frac{P_{in}}{P_{inst}}\right)\right]^{2}}}{\sqrt{1+(2\pi f \tau_{0})^{2}}} \tag{3}\]  
It is worth emphasizing that although the modulation signal is applied solely to the DFB section, and the SOA is not directly electrically modulated, the optical signal incident on the SOA carries intensity modulation with multiple frequency components. As a carrier-injection-based optical amplifier dominated by stimulated emission, the SOA exhibits a frequency-dependent dynamic response due to the interplay between carrier depletion and replenishment. Specifically, under low-frequency modulation, the slowly varying optical power leads to sustained carrier depletion over a longer duration, while the fixed electrical injection rate cannot replenish the carriers in time, resulting in a noticeable drop in gain. In contrast, at higher frequencies, the input optical power fluctuates rapidly within shorter time intervals, during which the carriers are not fully depleted. The injection current is sufficient to maintain a quasi-steady-state carrier concentration, thereby sustaining the optical gain. This frequency-dependent nonlinear response enables the SOA, when operated in the gain saturation regime, to function as a passive quasi-high-pass filter, selectively enhancing the high-frequency components of the modulated signal and effectively reshaping the overall system modulation response. To address the challenge of achieving both increased bandwidth and high-power output while simplifying fabrication, we propose a DML design featuring a partially corrugated grating (PCG) integrated with a SOA. Simulation shows that the PCG design effectively mitigates random phase variations at the rear facet [18], enhancing mode stability. Experiments indicate a side-mode suppression ratio (SMSR) exceeding 44 dB, validating the grating's role in maintaining stability.