Nowadays, electro-optical modulators are widely used devices in several applications, which range from optical communications to quantum optics. For this reason, it is necessary to make these devices faster and more performing as well as integrated. Compared to other methods, such as the thermo-optical or plasma dispersion effects, second order optical non-linearities can provide a higher modulation speed. A non-linear process widely used to make electro-optical modulators is the Pockels effect but, being a second order non-linear effect, it is possible only if the second order susceptibility is different from zero. Silicon is a centrosymmetric material, and therefore it has . Thus, to use this material, its centrosymmetric must be broken. This can be done by stressing silicon: a chi(2)xxy=-1.8 pm/V has been recently measured [1]. Another way to make an electro-optical modulator is to use the direct-current Kerr effect, which is a third order non-linear effect. To apply a strong electric field inside the silicon waveguide, lateral p-n junctions can be used [2, 3, 4]. We studied the direct-current Kerr and plasma-dispersion effects in resonators with lateral p-n junctions [3]. The study is performed both from an experimental and a simulation point of view. First, we measured the IV characteristics of the p-n junctions. Then, we measured the field-induced refractive index variation in silicon micro-rings where p-n junctions have been realized, see Fig. 1.

Figure 1 Variation of resonant wavelength and effective mode index as a function of reverse bias voltage.

Using simulations, we modelled the refractive index variation due to the applied reverse bias voltage. In addition, we estimate an equivalent chi(2)=16 pm/V in our devices. Compared to the strained-silicon platform, this method yields higher nonlinearities and offers interesting perspectives for the realization of high-speed integrated electro-optic modulators in silicon.

References

[1] M. Berciano, et al., “Fast linear electro-optic effect in a centrosymmetric semiconductor”, Communications Physics 1, 64 (2018).

[2] E. Timurdogan, et al., “Electric field-induced second-order nonlinear optical effects in silicon waveguides”, Nature Photonics 11.3, 200 (2017).

[3] C. Castellan, R. Franchi, S. Biasi, M. Bernard, M. Ghulinyan and L. Pavesi, “Field-Induced Nonlinearities in Silicon Waveguides Embedded in Lateral p-n Junctions”, Front. Phys. 7:104 (2019). doi: 10.3389/fphy.2019.00104

[4] R. Franchi, C. Castellan, M. Ghulinyan and L. Pavesi, “Second harmonic generation in periodically poled silicon waveguides by lateral p-n junctions”, preprint (2020)