## 5 Slow-Light Enhancement  
Thus far, the modulation characteristics have been presented with a fixed \(n_{\mathrm{g}}\)\(\approx\) 20. In this section, the characteristics for a varied \(n_{\mathrm{g}}\) are presented. For a SiO\({}_{2}\)-cladded PCW, without a lattice shift, \(n_{\mathrm{g}}\) increases as \(\lambda\) increases towards the photonic band edge. Since this increase is smaller than that in air-bridge structures which have been extensively studied in the past, this allows for a wide scan  
Figure 6: Spectra of \(n_{\mathrm{g}}\) and \(ER\) measured at 25 Gbps. Operating condition was similar to that for Figure 5.  
Figure 7: \(BER\) characteristics at 25 Gbps for \(2^{7}-1\) bit NRZ-PRBS signals: **(a)**\(BER\) at \(\lambda\) = 1559.6 nm; **(b)**\(BER\) and \(ER\) at \(\lambda\) = 1558–1560 nm. of \(n_{\rm g}\) and the comprehensive investigation of the slow-light enhancement, by only changing \(\lambda\). Here, the PCW was designed with specifications of \(a=400\) nm, \(2r=200\) nm, and \(s=0\) nm. Due to different fabrication lots, doping concentrations were lower than those given above, _i.e._, \(N_{\rm A}=4.8\times 10^{17}\) cm\({}^{-3}\) and \(N_{\rm D}=4.8\times 10^{17}\) cm\({}^{-3}\), and the p-n junction profile was linear. Therefore, the modulation efficiency should be lower than that in the device described in the previous sections. The absolute value of the efficiency was neglected, while focusing on the relative change of the modulation characteristics with \(n_{\rm g}\). Figure 8 presents the measured \(n_{\rm g}\) spectrum, with the \(f_{\rm 3 dB}\) spectrum calculated in the same way as that for Figure 4b, and measured \(R(f,\lambda)\) at \(\lambda=1534\)-\(1540\) nm. It is shown that \(n_{\rm g}\) changes widely from 20 to 60 within this range. The calculated \(f_{\rm 3 dB}\) decreases with the increasing \(n_{\rm g}\), showing the influence of the phase mismatch. The \(f_{\rm 3 dB}\) estimated from the measured \(R(f,\lambda)\) was 10-20 GHz at \(n_{\rm g}\approx 20\), but then fell to less than 10 GHz for higher \(n_{\rm g}\), which almost agrees with the calculated one. Thus, some solution to suppress the phase mismatch is necessary when \(n_{\rm g}\) is increased to enhance \(\Delta\phi\). Solutions need to slow down the RF signals and/or to shift back the phase of the RF signals inside the electrode. For the former, a slow-wave electrode consisting of a loaded transmission line has previously been studied [6; 19; 20; 21; 22]. However, their slow-down factors are too small to compensate the phase mismatch. For the latter, it is possible to add a delay line, such as a meander line; however, this will increase the device footprint as its length will be in the order of millimeters. Furthermore, the fluctuations in \(f_{\rm 3 dB}\) in Figure 8 become particularly large at \(n_{\rm g}>40\), possibly caused by the oscillation of \(n_{\rm g}\). As previously mentioned, a large \(n_{\rm g}\) generates strong back-scattering and, in particular, enlarges the spectral oscillation. A more advanced CMOS process is necessary to completely improve this situation, which may be costly. Alternatively, \(n_{\rm g}\) can be set to no higher than 40 if the current CMOS process is used, with the application of the slow light to the modulator. Figure 9 shows the result of the signal modulations. Although the voltages are the same as for Figure 5, the initial phase was set such that the transmission with no \(V_{\rm PP}\) was reduced to 9 dB lower than the maximum, resulting in a large \(ML\), and, hence, compensating for the low modulation  
Figure 8: Characteristics of PCW device without lattice shifts in the wide wavelength range: (**a**) \(n_{\rm g}\) spectrum; (**b**) \(f_{\rm 3 dB}\) spectrum calculated from Equations (2) and (3) with the measured \(n_{\rm g}\) and EE \(S_{\rm 21}\) estimated with \(R=96\)\(\Omega\) and \(C=50\) fF; (**c**) Frequency response spectrum \(R(f,\lambda)\). efficiency. The \(ER\) was 2.5 dB at \(n_{\mathrm{g}}=25\), but increased to 8.1 dB at \(n_{\mathrm{g}}=64\).