## 4 Signal Modulation  
The 25 Gbps signal modulation was investigated over the wide wavelength range, using the non-return-to-zero (NRZ) pseudo-random-bit sequence (PRBS). Although the voltages from PPG (Anritsu MP1800A, Atsugi, Japan) were set as \(V_{\mathrm{b}}\approx-1\) V and \(V_{\mathrm{PP}}=2.0\) V, actual applied voltages should be modified by the open-ended electrodes, as mentioned above. The operation was first measured at \(\lambda=1561\) nm. Since the device and measurement setup had losses as outlined above, the output light from the device was amplified using EDFA and BPF, and then received and analyzed by an optical sampling oscilloscope (Keysight 86100C, 86109A, Santa Rosa, CA, USA). Figure 5a shows the eye pattern when the initial phase of the MZ arms was adjusted so that \(ER\approx 3\) dB was obtained. The open eye was observed with \(ML=0.5\) dB, which is comparable to that in a previous study [15]. Figure 5b shows a clearer open eye with \(ER=3.9\) dB when the \(ML\) was slightly increased to 1 dB.  
Figure 4: Fluctuations in frequency response over the wide wavelength range: (**a**) \(n_{\mathrm{g}}\) spectrum; (**b**)\(f_{\mathrm{3 dB}}\) spectrum calculated from Equations (2) and (3) with the measured \(n_{\mathrm{g}}\) and EE \(S_{\mathrm{21}}\) estimated with \(R=96\)\(\Omega\) and \(C=50\) fF; (**c**) Frequency response spectrum \(R\)(_f_, \(\lambda\)) obtained from the averaged response at each \(\lambda\), such as those represented by the black line in Figure 3b. The \(f_{\mathrm{3 dB}}\) is shown by the boundary between red and yellow regions. The fluctuation in the measurement setup was smaller than 1 GHz.  
Figure 5: The 25 Gbps eye patterns of modulated light: (**a**) \(ML=0.5\) dB and (**b**) 1.0 dB with PRBS lengths of \(2^{31}-1\) and \(2^{7}-1\), respectively.  
Next, \(ER\) was repeatedly measured, changing the wavelength in steps of 0.5 nm between the range \(\lambda\) = 1549.5-1565.5 nm. The initial phase was adjusted such that the output intensity with no \(V_{\mathrm{pp}}\) was decreased to 2 dB lower than the maximum, thus giving \(ML\) = 2 \(-\)\(ER\)/2. This is almost the same condition as that in Figure 5. Figure 6 shows the spectra of \(ER\) and \(n_{\mathrm{g}}\). Although they do not agree completely, they exhibit similar patterns. \(ER\) ranges between 2 and 3 dB and fluctuates by \(\sim\)1 dB. Furthermore, \(ER\) and \(BER\) were measured, within the range \(\lambda\) = 1558-1560 nm in steps of 0.2 nm. For the \(BER\) measurement, amplified light was detected by an OE converter (Agilent 11982A) after passing through a variable optical attenuator, where the electrical signal was incident on an error detector module (Anritsu MU183040B) after removing the DC components. Voltages from the PPG and initial phase were set similarly to those presented in Figure 6. Figure 7a shows \(BER\) measured as a function of the received powers \(P_{\mathrm{r}}\) at the OE converter. The error-free operation of \(BER\) < 10\({}^{-11}\) was confirmed. Figure 7 compares the \(BER\) and \(ER\) spectra measured in steps of 0.2 nm in the range of \(\lambda\) = 1558-1560 nm. \(ER\) fluctuated by 1 dB, similarly to that in Figure 6. In other words, the \(BER\) finally reflects the fluctuations in \(n_{\mathrm{g}}\) through those in the \(ER\). This indicates that a margin larger than 1 dB is necessary in \(ER\) for a stable, error-free operation. For optical interconnects, \(ER\) is required to be larger than 3 dB, although it depends on the specifications of the transmitter and receiver. However, for the modulator described in this study, \(ER\) should be greater than 4 dB, including the margin. This is achieved by increasing the \(ML\) by 0.5 dB and the loss is compensated by increasing the output power from the light source or reducing the passive losses.