## 3 Device Structure and Simulation Results
### Integrated ODL Simulation Results  
The Lumerical INTERCONNECT [39] is used to model the integrated ODL of which the functional blocks are shown in Figure 5. It is constructed with three MODE waveguides, two thermal modulators, two 3 dB couplers, two DC source components, and an optical network analyzer. In each component block, we import the exact file that comes from the previous MODE simulation. The waveguide and modulator properties are imported from data saved from MODE simulations. Data of the upper modulator modeling the index perturbation due to Heater 1 can be loaded into \"Optical Modulator 1,\" and data of the lower modulator modeling index perturbation due to Heater 2 can be loaded into \"Optical Modulator 2.\" The response of the devices was measured by means of the Optical Network Analyzer that allows the power transmission spectrum and group delay spectrum to be characterized. Figure 6a depicts the group delay, power transmission, and wavelength at the resonant condition as a function of the input power of Heater 2 when the input power of Heater 1 is fixed at 0 mW. It corresponds to the case where only the coupling coefficient of the ODL is tuned. By tuning the input power of Heater 2 from 0 to 8 mW, the group delay, measured at the resonant peak, varies from 17.81 to 150.07 ps, while the corresponding power transmission efficiency, measured at the transmission dip in the spectrum, can be kept above 80% (<1 dB loss) over the tuning range. However, the peak  
Figure 5: Lumerical INTERCONNECT schematic for the optical delay line (ODL) based on racetrack resonator and MZI. wavelength varies from 1550.74 to 1550.86 nm during tuning. That is, the wavelength drifts at a rate of 0.015 nm/mW with respect to the power of Heater 2. This wavelength drift will result in a change in the group delay for a fixed wavelength and alter the tuning curve. Similarly, Figure 6b shows the results for tuning the racetrack loop phase with Heater 1 by fixing the input power of Heater 2 at 0 mW. The peak group delay and power transmission are almost constant during Heater 1 tuning, but the wavelength varies linearly with a slope of 0.03 nm/mW. Thus, Heater 1 can be used to correct the resonant wavelength without affecting the group delay and power transmission. Figure 7 shows contour plots of the wavelength and maximum (peak) group delay of the proposed ODL as a function of the input power of the two heaters. The contour plots will be used to illustrate how to tune the group delay and keep the peak wavelength intact. Figure 7a shows the tuning of the peak wavelength versus the power to Heater 1 and 2, as indicated by the red arrow in Figure 7a. This figure shows only one of the peaks among the multiple peaks caused by the ring resonance. Figure 7b shows that the peak group delay can be continuously tuned by simply changing the input power to Heater 2 while it remains unchanged in tuning Heater 1. From Figure 6, the wavelength drift rate is different for tuning Heater 2 and Heater 1. Moreover, the wavelength shifts to the same direction (longer wavelength) for tuning both heaters. To stabilize the wavelength in tuning the group delay, the two heaters need to be operated at the push-pull mode. That is, the heater power to Heater 1 must be decreased when the power to heater 2 increases. As indicated by the orange arrows in Figure 7a, b as an example, the input power of Heater 2 is increased to increase the group delay; then, the input power to Heater 1 needs to be decreased to maintain the same peak wavelength. The dashed blue line in Figure 7a indicates the data points with the same resonant wavelength during the push-pull mode, i.e., 1550.89 nm. Figure 8a shows the tuning spectrum for the push-pull operation. As the wavelength drift rate for tuning Heater 1 is about double that for tuning Heater 2, the input power for Heater 2 and Heater 1 is of a step of 2 and 1 mW, respectively, for the spectra shown in Figure 8a. The resonant wavelength remains fixed during group delay tuning.