## 2 Notations and Methodology  
### Presentation of a Typical High Speed Short Reach Interconnect  
The structure of a high speed short reach interconnect is presented schematically in Figure 1. It is made of a laser source hybridized to a Silicon Photonic circuit with a fiber coupled to the output port. In a Space Division Multiplexing (SDM) configuration, usually, a single laser source is split onto parallel MZM based transmit circuits, each is coupled to an individual output single polarization grating coupler (SPGC). On the receiver side, individual input Polarization Splitting Grating Coupler (PSGC) are directly connected to parallel receiver circuits. In a dual fiber configuration using Wavelength Division Multiplexing (WDM), the transmitter silicon photonic circuit consists of a number of MZM connected to individual laser sources on one side and, on the other side, to a wavelength multiplexer followed by a SPGC. The corresponding receiver consists of an input PSGC followed by a wavelength de-multiplexer and parallel receiver circuits.  
We consider as variables only the input optical power feeding the MZM, \(P_{\text{LAS}}\) and the parameters defining the MZM that we aim to optimize. These are the insertion loss of the doped electrodes \(\text{IL}_{\text{MZM}}\), the modulation efficiency measured as the half wave voltage \(V_{\pi}\), and the electro-optic bandwidth \(\text{BW}_{\text{MZM}}\). As we aim at maximizing the tolerable path loss, the laser relative intensity noise contribution to the link performance is assumed to be negligible and thus the laser source is considered perfect.  
At the MZM output, these parameters leads to a given average optical output power \(P_{\text{TX}}\) and extinction ratio ER or Optical Modulation Amplitude (OMA). Based on these output parameters and on the link configuration (\(\text{IL}_{\text{PATH}}\), which is a sum of the multiplexing, fiber coupling and fiber losses),  
Figure 1: Simplified schematic of a high speed short reach link with the parameters used in the simulation. MZM: Mach-Zehnder Modulator; PD: Photo-Detector.  
the average power reaching the photodetectors is denoted \(P_{\text{RX}}\). Note that the chromatic dispersion of the link, which is assumed to be operated around 1.3 \(\upmu\)m, is considered negligible. Different photodetector parameters will lead to a given sensitivity i.e., the minimum power required, when the input optical signal is \"perfect\", to reach a Bit Error Rate (BER) better than \(10^{-9}\). This parameter is denoted \(P_{\text{SEN}}\). In our case, as the signal reaching the photo-receiver will not be ideal (for instance, it may exhibit a low ER), the input power required to reach a BER < \(10^{-9}\) will be larger than \(P_{\text{SEN}}\). Let us denote this value \(P_{\text{REQ}}\).  
We aim to identify the best choice of the MZM parameters \(\left[\begin{array}{cc}\Pi_{\text{LMZM}}&V_{\pi}&\text{BW}_{\text{MZM}}\\ \end{array}\right]\) that maximizes the optical budget \(\Pi_{\text{PATH}}\) that the system can accommodate i.e., the difference between \(P_{\text{TX}}\) and \(P_{\text{REQ}}\). In order to be more realistic, this optimization will be made under the constraint that the RF driving amplitude of the MZM is equal to \(V_{\text{data}}=2.4\) V and that the MZM is driven either in single drive or in dual drive configuration (with \(1/2\times V_{\text{data}}\) on each arm). With our simplified model, the single ended and push-pull operation of the MZM are equivalent to one another.