# Optical Transmitters without Driver Amplifiers--Optimal Operation Conditions
## 2 Influence of Pulse Shape on the Electrical Eye-Opening  
The swing of the electrical eye-opening depends on the maximum available DAC output voltage and the chosen pulse shape. Generally, the maximum of the signal waveform is normalized to the maximum of the DAC output swing \(d_{\mathrm{DAC}}\). The eye-opening \(d_{\mathrm{Eye}}\) is then a fraction thereof, as shown Figure 1. This fraction depends on the pulse shape. In the past, pulse shaping was mostly done by pulse carving. Here, a second optical modulator was used to shape the form of the optical pulses in a desired manner [46; 47; 48; 49]. Pulse carving with different duty cycles showed advantages in transmission distance [50] and also enabled high-capacity links [51]. Carving of sinc-shaped pulses with very high quality was also shown [52]. However, due to the simplified set-up and versatility, we restricted the analysis of this article to digital pulse shaping and the use of only one optical modulator. Digital pulse shaping is extremely versatile and allows for arbitrary pulse shapes. Due to the advantageous characteristics in transmission, raised-cosine pulse shapes emerged. They are an efficient trade-off between the rectangular and the sinc-like pulse. In transceivers, the raised-cosine (RC) frequency response can be split into a square-root-raised-cosine (SRRC) filter at the transmitter and an SRRC filter at the receiver. This allows matched filtering and leads to inter-symbol interference (ISI)-free waveforms [53]. The excess bandwidth \(B\) of these filters depends on the roll-off factor (ROF) and the symbol rate \(R\), and is calculated by \(B=~{}0.5(1+ROF)R\)We analyzed the amplitude of the eye-opening for RC and SRRC and found different dependencies for the ROF. Figure 1 shows the results of this analysis, where we used a pulse-amplitude modulation (PAM) signal with two levels and determined the amplitude of the waveform. In Figure 1a, the amplitude over ROF is plotted for signals with RC pulse shape in blue and for signals with SRRC pulse shape in red. Here, we show the amplitude at the eye-opening as a solid line and the amplitude between the eye-openings as a dashed line. For the simulations, we always determined the maximum value at these positions, as this defines the scaling for the DAC. In Figure 1a, we also show experimentally determined results for the RMS amplitude plotted with square markers. The experimental results were linearly scaled to fit to the simulation. For RC signals, the amplitude of the eye-opening increases with the ROF. This value is marked as \(d_{\text{Eye}}\) in Figure 1. The increase can be seen in simulations and measurements in blue in Figure 1a, as well as in the eye-diagrams for RC signals in Figure 1b. The reason for this is the decreasing swing in between the eye-openings. Since the waveform is normalized to this maximum value, this leads to an effective increase of the eye-opening. The dependence of the overshoot between two symbols for Nyquist filtering and the resulting restrictions were also discussed in Reference [31]. For SRRC signals, the behavior is different. When increasing the ROF, the amplitude of the eye-opening increases until 0.4, but does not further increase above that amplitude [54] (red square markers). After an ROF of slightly above 0.4, the maximum value between the eye-openings becomes smaller than the value at the eye-opening (intersection of red dashed and red solid line). For simplicity, we used 0.4 as the ROF for the intersection. Figure 1: Investigation of transmitter electrical amplitude and its dependence on pulse shape. (**a**) Normalized amplitude against roll-off factor (ROF) for raised-cosine (RC; blue) and square-root-raised-cosine (SRRC; red) signals. Simulations for maximum amplitude at eye-opening (solid lines), maximum amplitude between eye-openings (dashed line), and electrical measurements of the root-mean-square (RMS) amplitude (square markers). (**b**) Simulated eye-diagrams of RC and SRRC signal with roll-off factors of 0.1, 0.4, and 0.9.