Extraction of group refractive index of silicon waveguide using two racetrack resonators

We present the extraction of group refractive index of a silicon waveguide of $450 \mathrm{~nm} \times 220 \mathrm{~nm}$ with a slab of 70 nm using the spectral responses of two racetrack resonators with perimeters of $405.66 \mu \mathrm{m}$ and $505.66 \mu \mathrm{m}$, respectively. We assume a cubic polynomial relation between the effective refractive index and the wavelength. An analytic expression for the group refractive indexes of both straight and bend waveguides can be obtained using the two measured spectra. The calculated $n_{\mathrm{g}}$ at 1550 nm is 3.922. This method offers a simple calibration tool in the optical delay line design.