# Widely-Tunable Ring-Resonator Semiconductor Lasers
## 2 Basic Principle of Wide-Tunability Utilizing Ring Resonators  
Wide-tunability in chip-scale semiconductor lasers is commonly achieved by utilizing the Vernier effect. The effect has been utilized both with sampled Bragg grating reflectors and ring resonators. Ring resonators, provided that the utilized waveguide platform offers sufficiently low propagation losses, have an advantage, as the effective cavity length at ring resonance is significantly enhanced, directly reducing linewidth [16; 17]. A single ring resonator in add-drop configuration placed inside the laser Fabry-Perot cavity can be used for selecting an individual longitudinal mode. A typical transmission curve of a single ring resonator is shown in Figure 1a. An ideal ring with ideal broadband couplers (no wavelength dependence on the coupling strength) has a periodic response separated by ring free-spectral range (FSR), corresponding to the inverse round-trip time inside the ring. \[\text{FSR }[\text{Hz}]=c/(L\cdot n_{\text{g}}), \tag{1}\]  
where \(c\) is the speed of light in a vacuum, \(L\) is the circumference of the ring, and \(n_{\text{g}}\) is the group refractive index. To guarantee single longitudinal mode operation, the FSR of the ring should be larger than the gain bandwidth of the laser. With typical gain bandwidths in the 60 nm range, corresponding to \(\sim\)7.5 THz around 1550 nm, ring circumferences, assuming \(n_{\text{g}}=3\), are limited to very small values, around 10 \(\upmu\)m. Such small circumferences might be impractical for at least two reasons, despite SOI technology providing very sharp bend radii with low loss. Tight bends, with losses lower than 0.09 dB per bend for bending radiuses of only 1 \(\upmu\)m, were demonstrated more than ten years ago [18]. The first problem is designing such short couplers (two are needed for add-drop ring configuration), and the second problem is providing wide wavelength tuning. In Si photonics, two tuning mechanisms are typically used: carrier based (either injection or depletion), or thermal based. Carrier injection results in increased losses due to free carrier absorption, while carrier depletion generally has much lower efficiency, but allows for higher speed, and is the method of choice for high-speed modulators. Thermal tuning is often used for slower adjustments (10s of kHz, limited by thermal constants of the whole structure), especially as with proper design, there is no change in optical losses with tuning. This is the main reason we use thermal heaters for all of our devices, as low losses allow for narrower linewidth. In this work, the heaters are deposited above Si waveguides, with \(\sim\)1 \(\upmu\)m of SiO\({}_{2}\) deposited in-between, to prevent the interaction between the metal and the optical mode, which would result in increased propagation loss. Devices based on silicon are readily thermally tunable due to the large thermo-optic coefficient (\(\text{d}n/\text{d}T\)) of silicon. A value of \(\text{d}n/\text{d}T\) of 1.87 \(\times\) 10\({}^{-4}\)/K at room temperature and 1.5 \(\upmu\)m is generally reported, and the coefficient increases at shorter wavelength, to 1.94 \(\times\) 10\({}^{-4}\)/K at 1.3 \(\upmu\)m [19]. This translates to tuning of \(\sim\)0.08 nm/\({}^{\circ}\)C at 1550 nm, so a temperature change for 60 nm of tuning can be as high as 700 \({}^{\circ}\)C. In practice, for passive devices, tuning ranges of up to 20 nm have been demonstrated [20], but still, such high temperatures close to the gain section would have negative influence on the laser performance. Much more efficient tuning is possible by using two or more rings with slightly different circumferences. Typical circumferences of the two rings are designed so that the FSR is between 200 GHz and 400 GHz, corresponding to \(\sim\)1.6 nm or \(\sim\)3.2 nm in wavelength. This allows for tuning the ring in full FSR by changing the temperature by only 20-40 \({}^{\circ}\)C, which is straightforward to achieve.