# Widely-Tunable Ring-Resonator Semiconductor Lasers
## 4 Advanced Designs for Linewidth Reduction
### Utilizing On-Chip High-Q Resonator  
High-\(Q\) resonators are another way of realizing narrow-linewidth lasers. We have explored the possibility of improving the linewidth of widely-tunable semiconductor lasers by utilizing an integrated high-\(Q\) ring cavity-on-chip [35]. Three potential strategies were analyzed: with the high-\(Q\) ring used as an external cavity with optical feedback in either all-pass or drop configuration, and with the high-\(Q\) ring being an integral part of the laser cavity. The laser performance can be influenced by coupling the laser to a distanced single mirror, or to a high-\(Q\) cavity. For a laser coupled to a single mirror, two modes of operation can be identified, depending on if the external cavity free-spectral range is larger, or smaller, than the relaxation oscillation frequency (\(\omega_{R}\)) of the standalone laser [26]. For short cavities (external cavity FSR > \(\omega_{R}\)), the linewidth reduction is modest, but the feedback system has a very broad effective bandwidth able to suppress noise to frequencies much larger than \(\omega_{R}\). In the case of a long cavity (external cavity FSR < \(\omega_{R}\)), the linewidth reduction can theoretically be much greater, but the effective bandwidth of the feedback system is narrower, resulting in strong external cavity modes. For stronger feedback, external cavity modes grow, and can cause the laser to become unstable. The optimal choice for narrow linewidth would therefore be an external cavity slightly shorter (FSR slightly larger) than \(\omega_{R}\), with relatively strong feedback. The limitation can be circumvented by coupling to a separate external cavity instead of a mirror. This has been typically done with Fabry-Perot cavities that were free-space coupled to semiconductor lasers [36; 37]. The use of a separate cavity for feedback breaks the limitation, as one can engineer the cavity to have the FSR larger than \(\omega_{R}\), keeping the laser stable with large effective bandwidth, and offering narrow linewidth due to increased photon lifetime inside the cavity. One of the benefits of integration is the reduced coupling loss between the laser and the external cavity. For an integrated design, one can use a ring resonator as an external cavity, utilizing the low propagation loss provided by a silicon (or silicon nitride) waveguide. We have studied the two configurations shown in Figure 12 using the frequency chirp reduction approach, as outlined in Section 2, and by calculating the negative optical feedback responsivity and bandwidth, following the procedure outlined in [38]. Both external cavity configurations allow for high frequency chirp reduction factors. The external cavity in all-pass configuration, theoretically provides for narrowest  
Figure 11: (**a**) The influence of feedback from external cavity when SOA is biased at 0 V. The \(x\)-axis is the squared current (I\({}^{2}\)–P) applied to external cavity phase tuner, the \(y\)-axis is the current collected by monitor photodetector (MPD) at the laser output and every curve corresponds to different laser bias between 30 and 80 mA in steps of 1 mA; (**b**) Measured linewidth across the full tuning range. The horizontal line shows the linewidth measured on similar laser structure with no external cavity. linewidth, due to higher \(Q\) of the external resonator, as it has lower loading and also provides larger negative optical feedback bandwidth, but is the most sensitive to laser operating frequency, and also suffers from potential multimode behavior at higher external feedback levels, as the all-pass ring does not help with filtering out other longitudinal modes. The external cavity in add-drop configuration should be easier to operate single mode, due to added filtering of the add-drop resonator, but has narrower optical feedback bandwidth, as well as lower responsivity. Both configurations require proper alignment of multiple cavities, which can complicate the laser operation.