## 4 Discussion  
Our results demonstrate that, even in a system with strong technological and cost-related constraints, it is possible to reduce filter insertion losses, by carefully optimizing the waveguide \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Units** & **Racetracks** & **Rings** \\ \hline Bus waveguide (width \(\times\) height) & nm \(\times\) nm & 500 \(\times\) 220 & 500 \(\times\) 100 \\ Resonator waveguide (width \(\times\) height) & nm \(\times\) nm & 500 \(\times\) 220 & 800 \(\times\) 100 \\ Straight-leg & nm & 8160 & N.A. \\ Curve radius (@ waveguide center) & nm & 3600 & 8400 \\ Bus-to-Resonator gap & nm & 250 & 515 \\ Inter-Resonator gap & nm & 460 & 355 \\ \hline \end{tabular}
\end{table} 
Table 4: Parameters used for the second fabrication of the filters. Figure 5: OSA-acquired spectra from the drop and through output channel of the best performing ring filter, showing an insertion loss of 0.8 dB. The insertion loss due to grating-coupling is about 7 dB/grating, and the ripple present on the green line is due to a grating-to-grating parasitic cavity. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Units** & **Racetracks** & **Rings** \\ \hline Insertion Loss & dB & 1.9–2.9 & 0.8–1.5 \\ \(-\)3 dB Bandwidth & GHz & 37–40 & 35–39 \\ \(-\)20 dB Bandwidth & GHz & 115–131 & 95–109 \\ Suppression @ 100 GHz & dB & 26–35 & 30–35 \\ Thermo-optical tuning efficiency & mW/nm & 2.5–2.6 & 4.8–5.5 \\ \hline \end{tabular}
\end{table} 
Table 5: Minimum and maximum values measured on filters based on the second design. cross-section and filter geometry. It is also interesting to note that the choice of a filter design with a relaxed fabrication tolerance, did not reduce filter performances. Comparing our results and designs with those already reported in the literature, this approach seems to be the first time that integrated filters fabricated in Silicon, with insertion losses as low as 0.8 dB, have been obtained (with strip waveguides). With regards to using these filter designs as building blocks for NG-PONs and related fibre-network applications, a comparison of Tables 1 and 5 shows that the only technical specification which is not satisfied, is the case of the double-ring filter, which has a \(-\)3 dB bandwidth in the range 35-39 GHz, instead of being >40 GHz. In any case, due to the high suppression of adjacent channels, this filter is expected to satisfy all requirements, by slightly reducing its bus-to-ring gap. As nonlinear effects can play a significant role in determining the losses of optical filters, especially for those based on Silicon-resonant cavities, a nonlinear characterization of the integrated filters has been carried out. The target was to estimate the \"threshold\" input power, which should not be exceeded, in order to avoid a non-linear degradation of the filter performance. For the nonlinear characterization, an external cavity laser (linewidth < 100 kHz), and tunable from 1490 nm to 1590 nm, was used as the optical source, instead of the ASE radiation. The light output from the laser was amplified by an EDFA, and then sent to a fiber polarization controller, in order to maximize the optical power, coupled by the 1D input grating coupler. The rest of the experimental setup is the same as the one presented in Figure 3.  
Initially, the laser beam was set at a very low power (<\(-\)15 dBm) and its wavelength was tuned to match the filter resonance. The beam power was then progressively increased, while the power output from the drop port of the filter was recorded. The results obtained for the two filter configurations showed a linear relationship between input- and output-power levels (i.e., a constant IL) up to a certain threshold, which depends on the considered filter structure. When the input power is increased above this threshold level, the drop-port output power begins to saturate, due to a number of nonlinear effects, such as two-photon absorption, free-carrier dispersion, and free-carrier absorption.