# Scalable Photonic Digital-to-Analog Converters
## 3 Alignment of the Resonances and the Dynamic Range  
The MRMs are designed identically to have the same properties, but their resonances usually occur at different wavelengths due to fabrication imperfections. By tuning the ring heaters, i.e., applying a bias voltage as needed, all the MRM resonances can be aligned to the center wavelength (marked as \"C\" in Figure 4a), and the PDAC extinction ratio becomes maximal, as shown in Figure 4a. In all device operational temperatures, ring heaters draw a relatively low amount of power, ranging from 0 to 9 mW, to have all resonances aligned. This power could be avoided by post-fabrication trimming techniques [26]. The center wavelength C is chosen such that the operating wavelength (marked as \"O\" in Figure 4a) is located on either of the slopes of the resonance dip in the transmission spectrum. Before combining the modulated optical signals from each branch, their phases need to match for constructive coherent MMI coupling, leading to a correct representation of the analog output intensities. Thus, the phase shifters are tuned for constructive interference among the coupling signals, manifested by the maximum CW light transmission at the operating wavelength. For correct phase shifter tuning, the ring modulators need to be aligned beforehand. Illustrated for a 2-bit PDAC, Figure 4b shows the change in the CW signal transmission as the bias to the phase shifter connected to the MSB branch is varied between 0 V to 6 V, while the wavelength is set to the operating wavelength O. The maximum transmission is obtained at 4.4 V drawing 2.88 mA current by the PS thermal heater. Having this bias applied, Figure 4c shows the PS voltage sweep of the LSB branch. The optimum transmission is obtained for a 0 V bias, while the previous PS is set to 4.4 V. The MRMs can be operated in two modes based on the plasma dispersion effect--carrier injection and carrier depletion. By biasing the modulator pn-junction in forward bias, carriers are injected to change the medium index, causing a resonance blue-shift. Since the pn-junction current increases exponentially with the applied forward bias voltage, the change in the medium index is accordingly high, resulting in a large resonance blue-shift. Biasing the deployed MRMs in the carrier injection mode, an approximately 0.8 nm/V wavelength shift is observed, corresponding to a relatively low V\({}_{\pi}\) of 370 mV. In carrier injection mode, we experimentally achieved a maximum of 4 Gbps data rate with the 4-bit PDAC. However, because of the relatively long lifetime of the minority carriers, the carrier injection mode  
Figure 3: Experimentally measured spectral transmission (solid line, left vertical axis) with the corresponding phase response (dashed line, right vertical axis) of the same microring modulator in (**a**) its under-coupled state (1.3 V reverse bias, \(\lambda_{\text{res}}\) = 1543.75 nm) and (**b**) its over-coupled state (1.2 V reverse bias, \(\lambda_{\text{res}}\) = 1543.90 nm). In the under-coupled state, an MRM exhibits a small phase difference between the on- and off-operation points with a linear negative slope overlapping the ring resonating wavelength, leading to mainly intensity modulation. In the over-coupled state, an MRM can operate as a pure phase-shifter when the two operation points are symmetrically chosen with respect to the resonance point. We select the operation points to have a \(\pi\)-phase difference and identical amplitudes. is not suitable for high-speed operation [26; 27]. Therefore, in this work, we adopted the carrier depletion mode for PDAC operation. Under the reverse bias condition, the carriers near the pn-junction are swept away by the applied electric field, widening the depletion region. This induces a resonance redshift through the plasma dispersion effect. The alteration of the effective refractive index is smaller than the carrier injection scenario although much faster. Our experimental study in the carrier depletion mode demonstrates a resonance wavelength shift of 14.3 pm/V.