Sub-ppm Nanomechanical Absorption Spectroscopy of Silicon Nitride

Material absorption is a key limitation in nanophotonic systems; however, its characterization is often obscured by diffraction and scattering loss. Here we show that nanomechanical frequency spectroscopy can be used to characterize the absorption of a dielectric thin film at the parts-per-million level, and use it to characterize the absorption of stoichiometric silicon nitride (Si3N4), a ubiquitous low-loss optomechanical material. Specifically, we track the frequency shift of a high-Q Si3N4 trampoline resonator in response to photothermal heating by a ~10 mW laser beam, and infer the absorption of the thin film from a model including thermal stress relaxation and both radiative and conductive heat transfer. A key insight is the presence of two thermalization timescales, a short (~100 msec) black-body thermalization of the thin film resonator, and a long (~100 sec) thermalization of the silicon substrate due to conductive heating. We infer the extinction coefficient of Si3N4 to be between 0.1 and 1 ppm in the 633 - 950 nm range, lower than previous upper bounds set by waveguide resonators and membrane-in-the-middle cavity optomechanics. Our approach is applicable to a broad variety of photonic materials and may offer new insights into their potential.