Previous experimental results showed that Silicon waveguides cladded by a silicon nitride layer exhibit a second order nonlinear susceptibility. From these preliminary results, the of the susceptibility tensor can be assumed different from zero and between 0.7 and 1.2 pm/V.

A study of Si microring resonators on silica layer (thickness: 3 µm), cladded by a Si₃N₄ layer (thickness: 140 nm) surrounded by air has been conducted to determine the conditions allowing an efficient second harmonic generation (SHG). From the assumption , the fundamental was considered TE polarized (Hz) and the SH TM (Ez). Besides, to take advantage of the modal phase matching, the SH is chosen with a radial number p = 3.

Fig. 1(a) shows some geometries that can be used when the pump wavelength is between 2.2 µm (TPA limit) and 2.4 µm (larger available wavelength on our setup). For instance, considering the first orange point (m=70, where m is the fundamental azimuthal number), we can see that a microring of thickness e = 275 nm, width = 900 nm and internal radius R = 10.10 µm can be used with a pump wavelength λ = 2.32 µm.

Fig.1: (a) Overview of the dimensions and pump wavelengths allowing an efficient SHG. e is the thickness and w the width of the microring. (b) Dispersion parameter in the fundamental wavelength range for different geometries. The values in the grey bar are the ratio of the width w over the thickness e.

For the comb generation, dispersion engineering is of prime importance. The evaluation of the effective indexes of different modes surrounding the modes of interest for SHG allowed to estimate the dispersion parameter. Fig. 1(b) shows that when the profile of the waveguide tends to a square (ratio w/e tends to one) the dispersion parameter increases. The geometries based on a thickness of 275 nm and width = 900 nm (orange line) exhibit a slight anomalous dispersion and were chosen for the first experimental realization.

For these geometries, the conversion efficiency η = P_SH/P_in, with P_SH and P_in the powers of the SH and fundamental in the bus waveguide, was evaluated around 0.1%, for an input power of 1 mW and pm/V , which is very promising in respect to recent experimental results in other Si-based systems. Nevertheless, the experimental precision on the realization of the microrings can lead to an important loss of efficiency as shown on Fig. 2. Keeping the pump resonant (red curve), 4 to 5 orders of magnitude can be lost (excluding the narrow peak were the situation is even worse) when the radius is different from the nominal one.