*4.1. Simulations for the SWR-Caused Optical Scattering Loss*

In the CLSM system shown in Figure 2, the measurements shown in Figure 3 presented that an SOI waveguide generally had much lower SWR value than silicon dioxide (SiO2) waveguides, even when they were fabricated under the same etching technique, ICP. Thus, it could be forecasted that the waveguide dimensions of both core and cladding layers of a waveguide system probably have significant effects on the optical scattering loss apart from the sidewall roughness itself.

Based on the optical performance of the real SOI waveguide functional device, we selected an SOI waveguide sample having the rib width and height of 4.0 and 0.5 μm, respectively; at 1550 nm wavelength, the refractive index silicon film was 3.4777 [18], and the refractive index of both the BOX layer and upper cladding layer was 1.4394 and 1.4449 for TE and TM modes, respectively; then, the effective indices of 3.3254 and 3.3168, respectively, were obtained with the simulation of beam propagation method (BPM) software. Further, by selecting the 2-D SWR construction defined by Equation (9a) and with the improved model Equation (7), we obtained the simulation results of the SWR dependences of the OPL coefficient, as shown in Figure 4a. Note from Figure 4a that the SWR-induced OPL of TM-mode was higher than that of TE mode for the SOI waveguide, which was not consistent with the results published in the literature [11,12]. Thus, it turned out that both the core and cladding layers of the waveguide system probably had significant effects on the optical scattering loss apart from the sidewall roughness itself. In contrast, by selecting the 3-D SWR construction defined by Equation (9b) and with the improved model Equation (7) of the SWR-caused OPL, we obtained the simulation results of the roughness dependences of the OPL coefficient for the same waveguide sample, as shown in Figure 4b. Note from Figure 4b that with the consideration of the 3-D construction of the roughness, there were two different points of the OPL coefficient between TE and TM modes. One was that the absolute TE-TM difference of the 3-D roughness was relatively larger than that of the 2-D roughness, and the other was that the OPL of TE mode was higher than that of TM mode, which was inverse to the 2-D roughness, but it was really in accord with the measured values published in the literature [11,12]. However, for the measured SWR value in Figure 3, ~20 nm, the OPL values for both the 2-D and 3-D SWR constructions were in the range of 3–3.5 dB/cm.

**Figure 4.** Simulations for the optical loss coefficient of SOI waveguide vs. SWR for two SWR constructions: (**a**) the 2D SWR, (**b**) the 3D-SWR.

As mentioned above, the measurements showed that the SOI-waveguides sample fabricated in the ICP technique only had an average roughness of 20 nm, namely, the 2-D statistic values at both the horizontal and vertical directions were the same. Then, with the 3-D roughness construction and the same values of the SOI waveguide parameters as used for the simulations in Figure 4b, we simulated the synchronous dependences of the roughness-induced optical propagation loss coefficient on both the correlation length *Lc* and the rib width *Wr*(2*d*) of the waveguide, as shown in Figure 5.

The most impressive finding from Figure 5 was that once the SWR values were given, the correlation length *Lc* had the most dominant impact, and the waveguide width 2*d* had the nonignorable impact upon the roughness-induced OPL in addition to the SWR itself. Accordingly, based on the optimal states of both the SWR and geometrical configuration of a waveguide, to significantly increase the correlation length *Lc* of the waveguide was the most effective metrology to completely solving the OPL of SOI waveguides. However, the *Lc* is a function pertaining to the SWR and the dimension of the waveguide [8].

**Figure 5.** Simulations for the dependences of optical loss of SOI waveguide on both the correlation length and the waveguide width apart from SWR itself of the TE-mode of the waveguide.
