  Recent experiments in the topological Weyl semimetal TaAs have observed
record-breaking second-harmonic generation, a non-linear optical response at
$2\omega$ generated by an incoming light source at $\omega$. However, whether
second-harmonic generation is enhanced in topological semimetals in general is
a challenging open question because their band structure entangles the
contributions arising from trivial bands and topological band crossings. In
this work, we circumvent this problem by studying RhSi, a chiral topological
semimetal with a simple band structure with topological multifold fermions
close to the Fermi energy. We measure second-harmonic generation (SHG) in a
wide frequency window, $\omega\in [0.27,1.5]$eV and, using first principle
calculations, we establish that, due to their linear dispersion, the
contribution of multifold fermions to SHG is subdominant as compared with other
regions in the Brillouin zone. Our calculations suggest that parts of the bands
where the dispersion is relatively flat contribute significantly to SHG. As a
whole, our results suggest avenues to enhance SHG responses.
