  We introduce a nanomechanical platform for fast and sensitive measurements of
the spectrally-resolved optical dielectric function of 2D materials. At the
heart of our approach is a suspended 2D material integrated into a
nanomechanical resonator illuminated by a wavelength-tunable laser source. From
the heating-related frequency shift of the resonator as well as its optical
reflection measured as a function of photon energy, we obtain the real and
imaginary parts of the dielectric function. Our measurements are unaffected by
substrate-related screening and do not require any assumptions on the underling
optical constants. This fast ($\tau_{rise}$ $\sim$ 135 ns), sensitive
(noise-equivalent power = 90 $\frac{pW}{\sqrt{Hz}}$ ), and broadband (1.2 $-$
3.1 eV, extendable to UV-THz) method provides an attractive alternative to
spectroscopic or ellipsometric characterisation techniques.
