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Observation of excitonic resonances in the second harmonic spectrum of MoS$_2$

We measure the second-harmonic (SH) response of MoS$_2$ in a broad fundamental photon energy range between 0.85 and 1.7 eV, and present a continuous SH spectrum capturing signatures of both the fundamental A and B excitons in addition to the intense C resonance. Moreover, we interpret our results in terms of the first exciton simulation of the SH properties of multi-layered MoS$_2$ samples, represented by a study of trilayer MoS$_2$. The good agreement between theory and experiments allows us to establish a connection between the measured spectrum and the underlying electronic structure, in the process elucidating the non-linear excitation of electron-hole pairs.