Introduction . Second-harmonic generation (SHG)1plays a fundamental role in the realm of nonlinear optics, as it enables linking octave-spaced regions of the spectrum while preserving the coherence of the optical field. Applications range from laser physics and technology2 , 3to imaging4, material science5, and self-referencing of frequency combs6, to name a few. Since its inception in 19611, SHG has widely been applied in bulk optics, whereas the no...