Second-harmonic generation in germanium-on-insulator from visible to telecom wavelengths

The second-order $\chi^{2}$ process underpins many important nonlinear optical applications in the field of classical and quantum optics. Generally, the $\chi^{2}$ process manifests itself only in a non-centrosymmetric dielectric medium via an anharmonic electron oscillation when driven by an intense optical field. Due to inversion symmetry, group-IV semiconductors like silicon (Si) and germanium (Ge) are traditionally not considered as ideal candidates for second-order nonlinear optics applications. Here, we report the experimental observation of the second-harmonic generation (SHG) in a Ge-on-insulator (GOI) sample under femtosecond optical pumping. Specially, we report the first-time measurement of the SHG signal from a GOI sample in the telecom S-band by pumping at $\sim$$3000$ nm.