# Widely-Tunable Ring-Resonator Semiconductor Lasers
## 4 Advanced Designs for Linewidth Reduction
### Utilizing Delayed On-Chip Optical Feedback  
A technique that has often been employed for improving the laser linewidth uses delayed optical feedback. Semiconductor lasers, as is well known, can significantly be affected by external optical feedback. For that reason, in the majority of applications, great care is taken to coat the laser facets with anti-reflection coating, and to place optical isolators as close to the cavity as possible; but as controlled feedback can improve certain laser parameters, it has been extensively studied. Depending on specific conditions, optical feedback has been shown to make the laser multi-stable, have hysteresis phenomena, enhance, prolong or suppress the relaxation oscillation in the transient output, improve the laser's performance through noise suppression, reduce nonlinear distortion and modulation bandwidth enhancement, and, what is most relevant for our application, improve the laser linewidth [26; 27; 28; 29; 30; 31]. The effects of feedback are typically divided into five distinct regimes with well-defined transitions [32]. The classic paper from 1980 has been revisited and expanded [33]. It is shown that the change of amplitude signal (\(\Delta E\)) always accompanies that of frequency change (\(\Delta v\)), due to feedback. The dependence is sinusoidal for weak feedback (\(\Delta E\approx E_{0}\cdot\cos(2 kL)\), \(2 kL\) being the optical phase associated with distance to external reflector), and becomes more complicated, leading to switching, hysteresis, and chaos, for higher levels of feedback. The full dynamics are complex and depend on many laser parameters, such as gain, loss, photon and carrier lifetime, and above all, the linewidth enhancement factor \(\alpha_{H}\). The feedback behavior can further be separated into four distinct regions: short vs. long cavities, and coherent vs. incoherent feedback. The latter condition relates the external cavity length \(L\) to the coherence length \(L_{coh}\) of the unperturbed source. The distinction between short and long cavities is made based on the relation between the relaxation resonance frequency (\(f_{R}\)), and the external cavity frequency. For short cavities, the length \(L<c/(2f_{R})\) and the oscillation regime is dependent upon the phase of the external path length. For long cavities \(L>c/(2f_{R})\), no dependence of the oscillation regime on phase should be observed. A schematic diagram of the integrated widely-tunable laser with on-chip external cavity is shown in Figure 10. The gain section is inside a 2 mm long cavity formed by loop-mirrors. The lasing wavelength is determined by the SWF formed from two ring resonators, and a cavity phase section, all of which are controlled by thermal phase tuners. The front loop mirror (at the output of the laser) has a 10% power reflection, and the output of the laser is terminated at the facet at an angle of 7\({}^{\circ}\), to minimize reflections. The back loop mirror, after the wavelength tuning section, has a power reflection of 60%, which couples part of the light to the external cavity. In order to allow for a long external cavity, a low-loss waveguide platform is needed. Here, we utilize optimized silicon waveguides with a loss of 0.67 dB/cm. The external cavity is \(\sim\)4 cm long and has its own phase adjustment section and gain section. The gain section in the external cavity is used to control the level of feedback. The external cavity is coupled on the side with the tuning section, so that the tuning rings filter out any spontaneously emitted light from the external semiconductor optical amplifier (SOA), improving the phase noise, and consequently, the linewidth performance. In the case of sufficient forward bias in the external SOA, the extended cavity can laste by itself. At the laser output, there is an on-chip monitor photodetector (MPD) that uses the same epitaxial material as the laser and the SOA. We have demonstrated 54+ nm of tuning range with high SMSR (>45 dB).