Self-referencing photothermal common-path interferometry to measure absorption of Si3N4 membranes for laser-light sails

Laser-light sails are a spacecraft concept wherein lightweight "sails" are propelled to high speeds by lasers with high intensities. The sails must comprise materials with low optical loss, to minimize the risk of laser damage. Stoichiometric silicon nitride (Si$_3$N$_4$) is a candidate material with low loss in the near infrared, but the precise absorption coefficient has not been characterized in the membrane form-factor needed for sails. We use photothermal common-path interferometry (PCI), a sensitive pump-probe technique, to measure the absorption coefficient of stoichiometric and nonstoichiometric silicon nitride. To calibrate PCI measurements of membranes, we developed a self-referencing technique where a measurement is performed twice: once on a bare membrane, and a second time with a monolayer of graphene deposited on the membrane. The absorption of the sample with graphene can be measured by both PCI and more-conventional spectroscopic techniques, enabling the calibration of the PCI measurement. We find that with an absorption coefficient of (2.09 $\pm$ 0.76) $\times$ 10$^{-2}$ cm$^{-1}$ at 1064 nm, Si$_3$N$_4$ is a suitable laser-sail material for laser intensities as high as ~10 GW/m$^{2}$, which have been proposed for some laser-sail missions, while silicon-rich SiN$_x$ (x~1), with an absorption coefficient of 7.94 $\pm$ 0.50 cm$^{-1}$, is unlikely to survive such high laser intensities.