Fig. 1. (a) Dispersion curves of silicon-on-insulator (SOI) waveguides with different dimensions, including the one (gray line) from Ref. 14. Inset: Cross-section of a silicon ring resonator used for Kerr frequency comb modeling. (b), (d) The wavevector mismatch and associated spectra of frequency combs, with the working points indicated in (a). The near-bottom spectra are the corresponding primary comb lines. (c) The wavelength-dependent Kerr coefficient and its interpretation in the time domain in the single-soliton comb state, indicated by smooth and modulated curves in black. The pattern of the temporal soliton is also given in blue, corresponding to the upper (τ) and right (power) axis.

Fig. 2. (a) Schematics of a step-index waveguide. (b) The chromatic dispersion parameter (D) of a silicon waveguide with a width and a height of 750 and 300 nm, respectively [n=3.48 for the waveguide core, with an air upper cladding and silica (n=1.44) for the bottom cladding]. (c) Schematics of a graded-index waveguide ensuring a self-adapting (SAB) condition (as defined in the text) and operating in a single-mode regime in the explored wavelength range. (d) Chromatic dispersion parameter D of the waveguide mode. The width and height of the waveguide are 750 and 340 nm, respectively.

Fig. 3. (a) Schematic of a graded-index waveguide ensuring a self-adapting (SAB) condition. Inset: Possible a configuration comprising doped regions for free-carrier extraction. (b) Chromatic dispersion parameter D of the four possible configurations of the proposed bilevel geometry. The silicon height is t=340nm. (c) The calculated wavevector mismatch and (d) the single-soliton comb spectrum for our proposed SAB waveguide, at the working point in (b), compared with the reference rib microring described in Fig. 1 (red color). The two predicted Cherenkov radiation points are marked by the dashed circles in (c).

Fig. 4. (a) Chromatic dispersion parameter D of four bilevel configurations with different parameters and based on the subwavelength silicon waveguides shown in Fig. 3(a). The silicon height is t=340nm. (b) and (c) The calculated wavevector mismatch and single-soliton comb spectra corresponding to the working point in (a) and that from Fig. 1 (red color/reference Si rib waveguide). The near-bottom spectra are the corresponding primary comb lines. (d) and (e) The corresponding comb generation process of the comb in deep blue. The two predicted Cherenkov radiation points are marked by the dashed circles or the white labels. The frequency detuning for achieving the final single-soliton comb is 1.272 GHz from the initialization.