To begin our design, we start simulating an optical waveguide with a 500nm width and 220nm height. As it is possibile to see from Fig.1 and Fig.2, it is a quasi-TE waveguide. From the simulation we also obtain the effective index and group index versus wavelengths (Fig. 3 and Fig. 4) and, from this data we can observe the effective index decreasing with the wavelengths while the group index is increasing with it.
After this simulation, we can use this data to achieve the compact model of the waveguide with MatLab and we obtain:
\(n_{eff}\left(\lambda\right)=2.445-1.130\cdot\left(\lambda-\lambda_0\right)-0.042\cdot\left(\lambda-\lambda_0\right)\)