## 6 Measurement Results and Discussion  
In this section, the measurement results are shown and discussed. Figure 10 shows the resulting eye diagram for different forms of pre-emphasis. In Figure (a)a, a linear FFE was used. Figure (b)b,c illustrate the results for the proposed digitally tuned non-linear FFE with a set of 4 as well as 12 coefficients. All measurements were performed at a baud rate of 40 Gbaud. The average measured optical power was 1.4 mW for all three experiments. The adaptive structures are able to correct any skewing of the eyes. This was achieved by compensating the asymmetric rise-and-fall times through data-dependent pre-emphasis. To understand this effect, one can think of the VCSEL as an RC low-pass filter with a changing time constant. When a step function is applied, increasing the time constant of the filter can be counteracted by increasing the amplitude of the step, resulting in the same slew rate at the output. Although both adaptive structures are able to correct skewing, only the 12 sets of coefficient filter significantly increases the eye openings and achieves BER reduction. The BER reduces by a factor of 15, as shown in Table 2. When using four additional taps of Receiver (RX) equalization (added in the oscilloscope software), the effectiveness of the adaptive filter grows even bigger: The 12 coefficient filter achieves an over 30-fold decrease in BER in respect to the linear variant. Comparing the vertical bathtubs in Figure (c)c, it is obvious that the skewing is mainly limiting the eye performance of the linear filter because the BER is dominated by the top  
Figure 10: 80 Gbit/s eye diagrams using different pre-emphasis: 6 TX taps of, (**a**) linear FFE, (**b**) adaptive FFE with four sets of coefficients and (**c**) adaptive FFE with 12 sets of coefficients. Figure 9: Experimental measurement setup. and bottom eye. Choosing a sub-par sampling point or large values of jitter would even amplify this effect since moving the sampling point to the right, the top eye's BER would significantly increase, moving it to the left, the bottom eye would act accordingly. The four-coefficient filter (Figure 11b) is mostly limited by mid-and bottom eye performance. This could simply be due to the fact that the slicing time where optimum BER performance is reached is a little off center, or that the topmost eye is most open. Interestingly, the Ratio of Level Mismatch (RLM) performance shown in Table 2, varies a lot between the filters, even though DC levels were identical for all transmission experiments. The vertical bathtub using the 12 coefficient adaptive FFE shown in Figure 11c, shows that all three eyes share roughly the same BER at the optimal sampling point, making it less susceptible to jitter. Since the adaptive FFE with 12 sets of coefficients proved to be most effective, it was also tested at a baud rate of 56\(\,\)Gbaud. The measurement setup was changed by replacing the packaged and bonded VCSEL with a chip exhibiting a higher bandwidth of 28\(\,\)GHz. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **TX EQ** & **no RX eq** & **4 Tap RX** \\ \hline BER & 6 Tap with 1 Coeff. & \(9.9\cdot 10^{-8}\) & \(8.1\cdot 10^{-8}\) \\  & 6 Tap with 4 Coeff. & \(6.9\cdot 10^{-8}\) & \(3.7\cdot 10^{-8}\) \\  & 6 Tap with 12 Coeff. & \(6.7\cdot 10^{-9}\) & \(2.6\cdot 10^{-9}\) \\ \hline RLM & 6 Tap with 1 Coeff. & 96.1\% & 95.9\% \\  & 6 Tap with 4 Coeff. & 93.7\% & 93.6\% \\  & 6 Tap with 12 Coeff. & 97.7\% & 98.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Bit-Error Rates and RLM for different equalization settings at 40\(\,\)Gbaud. Figure 11: 80\(\,\)Gbit/s eye diagrams with additional four taps linear FFE in the receiver using six TX taps of (**a**) linear FFE, (**b**) adaptive FFE with four sets of coefficients and (**c**) adaptive FFE with 12 sets of coefficients. The optical device was mounted on a chuck, probed via a GS-probe and coupled into a fiber pigtail. Overall, the physical measurement setup was identical as in [24].